quantum superimposing multiple cloning cum complementing machine we prove that the nonorthogonal states randomly selected from a set can evolve into a linear superposition of multiple original and orthogonal complementing states with failure branch if and only if the input states are linearly independent the results for a single input state are also generalized into the case of several copies of an input state

resonant response in nonequilibrium steady states the time dependent probability density function of the order parameter of a system evolving toward a stationary state exhibits an oscillatory behavior if the eigenvalues of the corresponding evolution operator are complex the frequencies n with which the system reaches its stationary state correspond to the imaginary part of such eigenvalues if the system at the stationary state is further driven by a small and oscillating perturbation with a given frequency we formally prove that the linear response to the probability density function is enhanced when n for n n we prove that the occurrence of this phenomenon is characteristic of systems that are in a nonequilibrium stationary state in particular we obtain an explicit formula for the frequency dependent mobility in terms of the relaxation to the stationary state of the unperturbed probability current we test all these predictions by means of numerical simulations considering an ensemble of noninteracting overdamped particles on a tilted periodic potential

the trading time risks of stock investment in stock price drop abstract this article investigates the trading time risk ttr of stock investment in the case of stock price drop of dow jones industrial average dji and hushen300 data csi300 respectively the escape time of stock price from the maximum to minimum in a data window length dwl is employed to measure the absolute ttr the ratio of the escape time to data window length is defined as the relative ttr empirical probability density functions of the absolute and relative ttrs for the dji and csi300 data evidence that i whenever the dwl increases the absolute ttr increases the relative ttr decreases otherwise ii there is the monotonicity or non monotonicity for the stability of the absolute or relative ttr iii there is a peak distribution for shorter trading days and a two peak distribution for longer trading days for the pdf of ratio iv the trading days play an opposite role on the absolute or relative ttr and its stability between dji and csi300 data

spatio temporal patterns in population dynamics abstract the transient dynamics of interacting biological species extracted from two ecosystems is investigated we model the environment interaction by a multiplicative noise and the temperature oscillations by a periodic forcing we find noise induced effects such as enhanced temporal oscillations spatial patterns and noise delayed extinction for the model of two competing species we extend our analysis to an ecosystem of three interacting species namely one predator and two preys we find spatial patterns induced by the noise

integral criteria for a classification of solutions of linear differential equations are positive continuous function on the interval 0 co by solution we always mean a continuously differentiable function such that r t x t has a continuous derivative satisfying e when the func tion r is continuous but does not have a continuous derivative e can be interpreted as the first order system for the vector x y x rx 381

signatures of noise enhanced stability in metastable states the lifetime of a metastable state in the transient dynamics of an overdamped brownian particle is analyzed both in terms of the mean first passage time and by means of the mean growth rate coefficient both quantities feature nonmonotonic behaviors as a function of the noise intensity and are independent signatures of the noise enhanced stability effect they can therefore be alternatively used to evaluate and estimate the presence of this phenomenon which characterizes metastability in nonlinear physical systems

different delays induced regime shifts in a stochastic insect outbreak dynamics abstract considering time delays in the deterministic and stochastic forces we construct stochastic delayed differential equations to investigate the regime shifts in an insect ecosystem the stationary probability distribution spd and mean first passage time mfpt are obtained respectively our main results show i the multiplicative noise positive cross correlation noise between two noises and time delays can induce the regime shifts from the boom outbreak state to the bust one but the additive noise and negative cross correlation can induce the regime shifts from the bust outbreak state to the boom one ii for the negative cross correlation the mfpt as a function of noise strengths exhibits one maximum which shows the characteristic of the noise delayed switching for the boom outbreak state but for the no cross correlation or positive cross correlation the mfpt decreases with the noise strengths iii two different types of time delays play same roles on the maximal mfpt with additive noise and play opposite roles on the maximal mfpt with multiplicative noise the mechanisms for noises and delays induced regime shifts between two states can be explained physically through the effective potential of ecological model

asymptotic integration of nonlinear differential equations abstract for a wide class of higher order nonlinear differential equations global existence of solutions which behave at infinity like polynomials is established by combining two fixed point results

small delay approximation of stochastic delay differential equations delay differential equations evolve in an infinite dimensional phase space in this paper we consider the effect of external fluctuations noise on delay differential equations involving one variable thus leading to univariate stochastic delay differential equations sdde s for small delays a univariate nondelayed stochastic differential equation approximating such a sdde is presented another approximation complementary to the first is also obtained using an average of the sdde s drift term over the delayed dynamical variable which defines a conditional average drift this second approximation is characterized by the fact that the diffusion term is identical to that of the original sdde for small delays our approach yields a steady state probability density and a conditional average drift which are in close agreement with numerical simulations of the original sdde we illustrate this scheme with the delayed linear langevin equation and a stochastic version of the delayed logistic equation the technique can be used with any type of noise and is easily generalized to multiple delays s1063 651x 99 08304 x

a class of separable quantum states we present a sufficient condition for a bipartite state to be separable via the strong positive partial transposition structure introduced in chru ci ski et al 2008 phys rev a 77 022113 from which we obtain a class of separable states in particular we prove that any classical quantum state is a state of our class but not vice versa both finite and infinite dimensional systems are considered

role of the initial conditions on the enhancement of the escape time in static and fluctuating potentials we present a study of the noise driven escape of an overdamped brownian particle moving in a cubic potential profile with a metastable state we analyze the role of the initial conditions of the particle on the enhancement of the average escape time as a function of the noise intensity for fixed and fluctuating potentials we observe the noise enhanced stability effect for all the initial unstable states investigated for a fixed potential we find a peculiar initial condition xc which separates the set of the initial unstable states in two regions those which give rise to divergences from those which show nonmonotonic behavior of the average escape time for fluctuating potential at this particular initial condition and for low noise intensity we find large fluctuations of the average escape time

spike train statistics for consonant and dissonant musical accords in a simple auditory sensory model the phenomena of dissonance and consonance in a simple auditory sensory model composed of three neurons are considered two of them here so called sensory neurons are driven by noise and subthreshold periodic signals with different ratio of frequencies and its outputs plus noise are applied synaptically to a third neuron so called interneuron we present a theoretical analysis with a probabilistic approach to investigate the interspike intervals statistics of the spike train generated by the interneuron we find that tones with frequency ratios that are considered consonant by musicians produce at the third neuron inter firing intervals statistics densities that are very distinctive from densities obtained using tones with ratios that are known to be dissonant in other words at the output of the interneuron inharmonious signals give rise to blurry spike trains while the harmonious signals produce more regular less noisy spike trains theoretical results are compared with numerical simulations

noise enhanced stability in fluctuating metastable states we derive general equations for the nonlinear relaxation time of brownian diffusion in randomly switching potential with a sink for piece wise linear dichotomously fluctuating potential with metastable state we obtain the exact average lifetime as a function of the potential parameters and the noise intensity our result is valid for arbitrary white noise intensity and for arbitrary fluctuation rate of the potential we find noise enhanced stability phenomenon in the system investigated the average lifetime of the metastable state is greater than the time obtained in the absence of additive white noise we obtain the parameter region of the fluctuating potential where the effect can be observed the system investigated also exhibits a maximum of the lifetime as a function of the fluctuation rate of the potential

hitting time distributions in financial markets we analyze the hitting time distributions of stock price returns in different time windows characterized by different levels of noise present in the market the study has been performed on two sets of data from us markets the first one is composed by daily price of 1071 stocks trade for the 12 year period 1987 1998 the second one is composed by high frequency data for 100 stocks for the 4 year period 1995 1998 we compare the probability distribution obtained by our empirical analysis with those obtained from different models for stock market evolution specifically by focusing on the statistical properties of the hitting times to reach a barrier or a given threshold we compare the probability density function pdf of three models namely the geometric brownian motion the garch model and the heston model with that obtained from real market data we will present also some results of a generalized heston model r 2007 elsevier b v all rights reserved

effect of time delay on pattern dynamics in a spatial epidemic model time delay accounting for constant incubation period or sojourn times in an infective state widely exists in most biological systems like epidemiological models however the effect of time delay on spatial epidemic models is not well understood in this paper spatial pattern of an epidemic model with both nonlinear incidence rate and time delay is investigated in particular we mainly focus on the effect of time delay on the formation of spatial pattern through mathematical analysis we gain the conditions for hopf bifurcation and turing bifurcation and find exact turing space in parameter space furthermore numerical results show that time delay has a significant effect on pattern formation the simulation results may enrich the finding of patterns and may well capture some key features in the epidemic models

the geometric approach to quantum correlations computability versus reliability we propose a modified metric based on the hilbert schmidt norm and adopt it to define a rescaled version of the geometric measure of quantum discord such a measure is found not to suffer from pathological dependence on state purity although the employed metric is still non contractive under quantum operations we show that the resulting indicator of quantum correlations is in agreement with other bona fide discord measures in a number of physical examples we present a critical assessment of the requirements of reliability versus computability when approaching the task of quantifying or measuring general quantum correlations in a bipartite state

mean escape time in a system with stochastic volatility we study the mean escape time in a market model with stochastic volatility the process followed by the volatility is the cox ingersoll and ross process which is widely used to model stock price fluctuations the market model can be considered as a generalization of the heston model where the geometric brownian motion is replaced by a random walk in the presence of a cubic nonlinearity we investigate the statistical properties of the escape time of the returns from a given interval as a function of the three parameters of the model we find that the noise can have a stabilizing effect on the system as long as the global noise is not too high with respect to the effective potential barrier experienced by a fictitious brownian particle we compare the probability density function of the return escape times of the model with those obtained from real market data we find that they fit very well

role of the noise on the transient dynamics of an ecosystem of interacting species abstract we analyze the transient dynamics of an ecosystem described by generalized lotka volterra equations in the presence of a multiplicative noise and a random interaction parameter between the species we consider specifically three cases i two competing species ii three interacting species one predator two preys iii n interacting species the interaction parameter in case i is a stochastic process which obeys a stochastic differential equation we find noise delayed extinction of one of two species which is akin to the noise enhanced stability phenomenon other two noise induced effects found are temporal oscillations and spatial patterns of the two competing species in case ii the noise induces correlated spatial patterns of the predator and of the two preys concentrations finally in case iii we find the asymptotic behavior of the time average of the ith population when the ecosystem is composed of a great number of interacting species

novel cloning machine with supplementary information probabilistic cloning was first proposed by duan and guo then pati established a novel cloning machine ncm for copying superposition of multiple clones simultaneously in this paper we deal with the novel cloning machine with supplementary information ncmsi for the case of cloning two states we demonstrate that the optimal efficiency of the ncmsi in which the original party and the supplementary party can perform quantum communication equals that achieved by a two step cloning protocol wherein classical communication is only allowed between the original and the supplementary parties from this equivalence it follows that ncmsi may increase the success probabilities for copying also an upper bound on the unambiguous discrimination of two nonorthogonal pure product states is derived our investigation generalizes and completes the results in the literature

cross correlated bounded noises induced the population extinction and enhancement of stability in a population growth model abstract the bounded noises as a new typed non gaussian noise have important practical significance in this paper the steady state and transient dynamical properties of the population growth model subjected to the cross correlated sine wiener bounded noise are investigated based on the approximate fokker planck equation the analytical expressions of stationary probability distribution function and extinction time of the population growth model are obtained the results show that the bounded noise intensity and the cross correlated bounded noise intensity can cause the population extinction in particular the population density are sensitive to the environmental fluctuation multiplicative noise and the self correlated time on the other hand the effects of noise intensities on the extinction time are discussed the results indicate that the extinction time can be decreased with the intrinsic stochasticity additive noise and the self correlated time increasing for the positive correlated case the result is similar to the additive noise and the self correlated time however for the negative correlated case the extinction time can be increased with the intensity increasing in particular the environmental fluctuation multiplicative noise causes noise enhanced stability for the negative correlated case and the extinction time firstly decreases for the small environmental fluctuation and then increases for the large environmental fluctuation for the positive correlated case the numerical results are in basic agreement with the theoretical predictions

dynamic behaviors and measurements of financial market crash rate abstract this paper proposes the conditional crash rate ccr to study the degree of financial market crisis and evaluate the risk of financial market crash based on maximum drawdown and escape rate it is found that the ccr of stock price in financial market is equivalent to the escape rate of the drawdown time series corresponding to price series based on the mean escape rate the analytical solution of ccr of financial market of stock price described by black scholes model is obtained for the ccr empirical researches show that the theoretical results of the heston model are in good agreement with the results of the real financial data of the sp ii we can find critical phenomena resonance and inverse resonance behaviors in the function of ccr vs mean reversion of volatility ii the parameter variation induces the appearance of noise enhancement stability in the function of ccr vs amplitude of volatility fluctuation

bounds on entanglement distillation and secret key agreement for quantum broadcast channels the squashed entanglement of a quantum channel is an additive function of quantum channels which finds application as an upper bound on the rate at which secret key and entanglement can be generated when using a quantum channel a large number of times in addition to unlimited classical communication this quantity has led to an upper bound of log 1 eta 1 eta on the capacity of a pure loss bosonic channel for such a task where eta is the average fraction of photons that make it from the input to the output of the channel the purpose of this paper is to extend these results beyond the single sender single receiver setting to the more general case of a single sender and multiple receivers a quantum broadcast channel we employ multipartite generalizations of the squashed entanglement to constrain the rates at which secret key and entanglement can be generated between any subset of the users of such a channel along the way developing several new properties of these measures we apply our results to the case of a pure loss broadcast channel with one sender and two receivers

asymptotic behavior of nonoscillatory solutions to n th order nonlinear neutral differential equations abstract for a class of n th order nonlinear neutral differential equations sufficient conditions for all nonoscillatory solutions to satisfy lim t t 1 n x t a are established for another class of equations necessary and sufficient conditions for nonoscillatory solutions to satisfy the above condition are obtained our theorems complement and extend recent results reported in the literature

a simple analytics framework for evaluating mean escape time in different term structures with stochastic volatility abstract the aim of this paper is to propose a simple framework for analyzing the mean escape time of interest rate product in different term structures with stochastic volatility in the modeling perspective we utilize the one factor hull white model to design the dynamics of interest rate returns whose stochastic volatility term is assumed to follow the cox ingersoll ross process furthermore we apply the nelson siegel function to simulate various scenarios of term structure based on the us treasury bill and european bond then we analyze the mean escape time surfaces of different term structures for theoretical flat yield curves and two empirical s shaped yield curves whose term structures of short mid and long term maturities are shifted by the modified parameters of the nelson siegel function we observe that the survival probability begins with one and reduces to zero with different rate of decay for different interest rates and volatilities furthermore the results of empirical term structures imply that the adjustment in the yield of long term maturity changes the structure of met surface more significantly than that of short and long term maturities lastly we detect the noise enhanced stability phenomenon from the mean escape time for all cases of flat yield treasury bill and european bond

when noise decreases deterministic diffusion dynamical noise acting homogeneously in each time step can enhance the stability of an unstable fixed point however if dynamical noise is added locally in state space additional clear enhancement can be achieved if this restriction is chosen properly a systematic analysis of the influence of local and global dynamical noise on the residence time of an unstable state is presented and optimal parameters for the stabilizing mechanisms are discussed as a consequence it is demonstrated that local dynamical noise can yield increased localization in deterministic diffusion models

escape times in fluctuating metastable potential and acceleration of diffusion in periodic fluctuating potentials abstract the problems of escape from metastable state in randomly flipping potential and of diffusion in fast fluctuating periodic potentials are considered for the overdamped brownian particle moving in a piecewise linear dichotomously fluctuating metastable potential we obtain the mean first passage time as a function of the potential parameters the noise intensity and the mean rate of switchings of the dichotomous noise we find noise enhanced stability phenomenon in the system investigated and the parameter region of the fluctuating potential where the effect can be observed for the diffusion of the overdamped brownian particle in a fast fluctuating symmetric periodic potential we obtain that the effective diffusion coefficient depends on the mean first passage time as discovered for fixed periodic potential the effective diffusion coefficients for sawtooth sinusoidal and piecewise parabolic potentials are calculated in closed analytical form

nonlocal coupling can prevent the collapse of spatiotemporal chaos spatiotemporal chaos on a regular ring network of excitable gray scott dynamical elements is transient we find that the addition of very few nonlocal network connections drastically changes the average lifetime of spatiotemporal chaos in the presence of a single shortcut local interface formation delays the collapse of spatiotemporal chaos this competes with a reduced average characteristic path length that advances the collapse process two added shortcuts can prevent the collapse of spatiotemporal chaos by causing an asymptotic local collapse

delay fokker planck equations perturbation theory and data analysis for nonlinear stochastic systems with time delays we study nonlinear stochastic systems with time delayed feedback using the concept of delay fokker planck equations introduced by guillouzic l heureux and longtin we derive an analytical expression for stationary distributions using first order perturbation theory we demonstrate how to determine drift functions and noise amplitudes of this kind of systems from experimental data in addition we show that the fokker planck perspective for stochastic systems with time delays is consistent with the so called extended phase space approach to time delayed systems

the influences of delay time on the stability of a market model with stochastic volatility abstract the effects of the delay time on the stability of a market model are investigated by using a modified heston model with a cubic nonlinearity and cross correlated noise sources these results indicate that i there is an optimal delay time o which maximally enhances the stability of the stock price under strong demand elasticity of stock price and maximally reduces the stability of the stock price under weak demand elasticity of stock price ii the cross correlation coefficient of noises and the delay time play an opposite role on the stability for the case of the delay time o and the same role for the case of the delay time o moreover the probability density function of the escape time of stock price returns the probability density function of the returns and the correlation function of the returns are compared with other literatures

noise intensity fluctuation in langevin model and its higher order fokker planck equation abstract in this paper we investigate a langevin model subjected to stochastic intensity noise sin which incorporates temporal fluctuations in noise intensity we derive a higher order fokker planck equation hfpe of the system taking into account the effect of sin by the adiabatic elimination technique stationary distributions of the hfpe are calculated by using the perturbation expansion we investigate the effect of sin in three cases a parabolic and quartic bistable potentials with additive noise b a quartic potential with multiplicative noise and c a stochastic gene expression model we find that the existence of noise intensity fluctuations induces an intriguing phenomenon of a bimodal to trimodal transition in probability distributions these results are validated with monte carlo simulations

trace distance from the viewpoint of quantum operation techniques in the present paper the trace distance is exposed within the quantum operations formalism the definition of the trace distance in terms of a maximum over all quantum operations is given it is shown that for any pair of different states there are an uncountably infinite number of maximizing quantum operations conversely for any operation of the described type there are an uncountably infinite number of those pairs of states that the maximum is reached by the operation the behaviour of the trace distance under considered operations is studied relations and distinctions between the trace distance and the sine distance are discussed

probabilistic cloning and orthogonal complementing of an unknown epr state abstract in this paper a novel scheme is proposed where with the help of victor a state preparer an unknown epr pair is copied in a certain probability so that three parties of communication can obtain the epr state respectively the first stage of this scheme is to teleport an unknown epr state to carla one receiver the second stage of this scheme alice a sender and bob the other receiver get the same epr pair or an orthogonal complement copy of the epr pair with the help of victor

colored noise induced discontinuous transitions in symbiotic ecosystems a symbiotic ecosystem is studied by means of the lotka volterra stochastic model using the generalized verhulst self regulation the effect of fluctuating environment on the carrying capacity of a population is taken into account as dichotomous noise the study is a follow up of our investigation of symbiotic ecosystems subjected to three level trichotomous noise r mankin a ainsaar a haljas and e reiter phys rev e 65 051108 2002 relying on the mean field theory an exact self consistency equation for stationary states is derived in some cases the mean field exhibits hysteresis as a function of noise parameters it is established that random interactions with the environment can cause discontinuous transitions the dependence of the critical coupling strengths on the noise parameters is found and illustrated by phase diagrams predictions from the mean field theory are compared with the results of numerical simulations our results provide a possible scenario for catastrophic shifts of population sizes observed in nature

effect of time delay in fitzhugh nagumo neural model with correlations between multiplicative and additive noises abstract we study the effect of time delay in the fitzhugh nagumo neural model with correlations between multiplicative and additive noise terms based on the corresponding fokker planck equation the explicit expressions of the stationary probability distribution function spdf the mean first passage time mfpt and the signal to noise ratio snr are obtained respectively research results show that i the system undergoes a succession of two phase transitions i e the reentrance phenomenon as the noise correlation parameter is increased and a single phase transition as the time delay is increased ii the mfpt as a function of the multiplicative noise intensity exhibits a maximum this maximum for mfpt identifies the noise enhanced stability nes effect the noise correlation parameter intensifies the nes effect while the time delay and the additive noise intensity weakens it iii the existence of a maximum in the snr as a function of the multiplicative noise intensity is the identifying characteristic of the stochastic resonance sr phenomenon the noise correlation parameter enhances the sr while the time delay and the additive noise intensity weaken it

stability measures in metastable states with gaussian colored noise we present a study of the escape time from a metastable state of an overdamped brownian particle in the presence of colored noise generated by ornstein uhlenbeck process we analyze the role of the correlation time on the enhancement of the mean first passage time through a potential barrier and on the behavior of the mean growth rate coefficient as a function of the noise intensity we observe the noise enhanced stability effect for all the initial unstable states used and for all values of the correlation time tau c investigated we can distinguish two dynamical regimes characterized by weak and strong correlated noises depending on the value of tau c with respect to the relaxation time of the system

decay of unstable equilibrium and nonequilibrium states with inverse probability current taken into account we study the causes of noise delayed decay of unstable states in nonlinear dynamic systems within the framework of the overdamped brownian motion model for the analysis we use the exact expressions for the decay times of unstable states which take into account the inverse probability current in contrast to the well known mean first passage time method these expressions are valid for any intensity of fluctuations and for arbitrary potential profiles the effect of delay is shown to arise under the decay of unstable nonequilibrium states due to the action of two different mechanisms these mechanisms are caused by the inverse probability current and by the nonlinearity of potential describing an unstable state

the roles of mean residence time on herd behavior in a financial market abstract we investigate the herd behavior of stock prices in a finance system with the heston model based on parameter estimation of the heston model obtained by minimizing the mean square deviation between the theoretical and empirical return distributions we simulate mean residence time of positive return mrtpr plots of mrtpr against the amplitude or mean reversion of volatility demonstrate a phenomenon of herd behavior for a positive cross correlation between noise sources of the heston model also for a negative cross correlation a phenomenon of herd behavior is observed in plots of mrtpr against the long run variance by increasing amplitude or mean reversion of volatility

multipartite quantum correlations and local recoverability characterizing genuine multipartite quantum correlations in quantum physical systems has historically been a challenging problem in quantum information theory more recently however the total correlation or multipartite information measure has been helpful in accomplishing this goal especially with the multipartite symmetric quantum msq discord piani et al 2008 phys rev lett 100 090502 doi 10 1103 physrevlett 100 090502 1 and the conditional entanglement of multipartite information cemi yang et al 2008 phys rev lett 101 140501 doi 10 1103 physrevlett 101 140501 2 here we apply a recent and significant improvement of strong subadditivity of quantum entropy fawzi renner 2014 in order to develop these quantities further in particular we prove that the msq discord is nearly equal to zero if and only if the multipartite state for which it is evaluated is approximately locally recoverable after performing measurements on each of its systems furthermore we prove that the cemi is a faithful entanglement measure i e it vanishes if and only if the multipartite state for which it is evaluated is a fully separable state along the way we provide an operational interpretation of the msq discord in terms of the partial state distribution protocol which in turn as a special case gives an interpretation for the original discord quantity finally we prove an inequality that could potentially improve upon the fawzi renner inequality in the multipartite context but it remains an open question to determine whether this is so 1 http dx doi org 10 1103 physrevlett 100 090502 2 http dx doi org 10 1103 physrevlett 101 140501

hellinger distance as a measure of gaussian discord especially investigated in recent years the gaussian discord can tentatively be quantified by a distance between a given two mode gaussian state gs and the set of all the zero discord two mode gss however as this set consists only of product states such a distance captures all the correlations quantum and classical between modes therefore it is merely an upper bound for the geometric discord no matter which is the employed distance in this work we choose for this purpose the hellinger metric that is known to have many beneficial properties recommending it as a good measure of quantum behaviour in general this metric is determined by affinity a relative of the uhlmann fidelity with which it shares many important features as a first step of our work the affinity of a pair of n mode gss is written then in the two mode case we succeeded in determining exactly the closest gaussian product state and computed the gaussian discord accordingly the obtained general formula is remarkably simple and becomes still friendlier in the significant case of symmetric two mode gss we then analyse in detail two special classes of two mode gss of theoretical and experimental interest as well the squeezed thermal states and the mode mixed thermal ones the former are separable under a well known threshold of squeezing while the latter are always separable it is worth stressing that for symmetric states belonging to either of these classes we find consistency between their geometric hellinger discord and the originally defined discord in the gaussian approach at the same time the gaussian hellinger discord of such a state turns out to be a reliable measure of the total amount of its cross correlations

resonant activation in a bistable system the analog simulation of an overdamped brownian particle in a quartic double well potential driven by an external either gaussian or dichotomic multiplicative noise is performed with special focus on the phenomenon of resonant activation such an effect is shown to occur on increasing the correlation time of the multiplicative noise while keeping the noise variance constant the asymptotic behavior of the relevant escape times for large noise correlation time and large variance is also investigated simple qualitative arguments are produced to justify the results thus obtained furthermore the traversal barrier that is the effective barrier at the time the system switches state is shown to have a minimum for a certain value of the noise correlation time though not always in coincidence with the relevant resonant activation value textcopyright 1996 the american physical society

theoretical analysis of destabilization resonances in time delayed stochastic second order dynamical systems and some implications for human motor control a linear stochastic delay differential equation of second order is studied that can be regarded as a kramers model with time delay an analytical expression for the stationary probability density is derived in terms of a gaussian distribution in particular the variance as a function of the time delay is computed analytically for several parameter regimes strikingly in the parameter regime close to the parameter regime in which the deterministic system exhibits hopf bifurcations we find that the variance as a function of the time delay exhibits a sequence of pronounced peaks these peaks are interpreted as delay induced destabilization resonances arising from oscillatory ghost instabilities on the basis of the obtained theoretical findings reinterpretations of previous human motor control studies and predictions for future human motor control studies are provided 2006 the american physical society

no local broadcasting theorem for multipartite quantum correlations we prove that the correlations present in a multipartite quantum state have an operational quantum character even if the state is unentangled as long as it does not simply encode a multipartite classical probability distribution said quantumness is revealed by the new task of local broadcasting i e of locally sharing preestablished correlations which is feasible if and only if correlations are stricly classical our operational approach leads to natural definitions of measures for quantumness of correlations it also reproduces the standard no broadcasting theorem as a special case

stochastic time delayed systems driven by correlated noises steady state analysis abstract in the present paper a class of stochastic time delayed systems driven by correlated gaussian white noises are considered novikov s theorem is used to derive delay fokker planck equations in the case of small time delays approximate stationary solutions are obtained as a special case the delay fokker planck equation and the approximate stationary probability density function is obtained for a bistable system numerical simulations show that the small delay approximation is a good approximation in the case of small delay furthermore the effects of the correlated noises and the feedback are investigated the critical curve separating the unimodal and bimodal regions of the stationary probability distribution is shown to be affected by the degree of the correlation of the noises and e the strength of the feedback both and e can change the curve of the stationary probability density function from a bimodal to a unimodal structure

functional characterization of linear delay langevin equations we present an exact functional characterization of linear delay langevin equations driven by any noise structure defined through its characteristic functional this method relies on the possibility of finding an explicitly analytical expression for each realization of the delayed stochastic process in terms of those of the driving noise general properties of the transient dissipative dynamics are analyzed the corresponding interplay with a color gaussian noise is presented as a full application of our functional method we study a model for population growth with non gaussian fluctuations the gompertz model driven by multiplicative white shot noise

effects of time delay on transient behavior of a time delayed metastable system subjected to cross correlated noises abstract the effects of time delay on the transient properties of a time delayed metastable system subjected to cross correlated noises are studied by means of a stochastic simulation method it is found that i both additive noise and multiplicative noise can produce the noise enhanced stability nes effect ii the time delay induces critical behavior on the nes i e there is a critical value of the delay time c 1 2 2 above which the time delay increases the stability of the system enhanced by the additive noise and below which the nes effect induced by the additive noise disappears iii there exists another critical value of the delay time c 2 3 0 above which the time delay increases the stability of the system enhanced by the multiplicative noise and below which the time delay decreases it

linear and nonlinear experimental regimes of stochastic resonance we investigate the stochastic resonance phenomenon in a physical system based on a tunnel diode the experimental control parameters are set to allow the control of the frequency and amplitude of the deterministic modulating signal over an interval of values spanning several orders of magnitude we observe both a regime described by the linear response theory and the nonlinear deviation from it in the nonlinear regime we detect saturation of the power spectral density of the output signal detected at the frequency of the modulating signal and a dip in the noise level of the same spectral density when these effects are observed we detect a phase and frequency synchronization between the stochastic output and the deterministic input

noise enhanced stability of periodically driven metastable states we study the effect of noise enhanced stability of periodically driven metastable states in a system described by piecewise linear potential we find that the growing of the average escape time with the intensity of the noise is depending on the initial condition of the system we analytically obtain the condition for the noise enhanced stability effect and verify it by numerical simulations

roles of capital flow on the stability of a market system abstract the roles of capital flow in an ensemble composed of sub markets are investigated a modified heston model and recycled noises are employed to describe the dynamics of stock price and capital flow in the ensemble respectively the mean escape times of two sub markets with a cubic nonlinearity are calculated by using numerical simulation the results evidence that i there is a worst delay time or rate of capital inflow concerning the minimal stability of stock price and an optimal delay time or rate of capital outflow concerning the maximal stability of stock price when 0 denotes strength of correlation between two wiener processes of the stock price and the volatility ii when 0 the stability of stock price is maximally enhanced by an optimal delay time or rate of capital inflow and reduced by a worst rate of capital outflow but monotonously strengthened by delay time of capital outflow

quantum state separation unambiguous discrimination and exact cloning unambiguous discrimination and exact cloning reduce the square overlap between quantum states exemplifying the more general type of procedure we term state separation we obtain the maximum probability with which two equiprobable quantum states can be separated by an arbitrary degree and find that the established bounds on the success probabilities for discrimination and cloning are special cases of this general bound the latter also gives the maximum probability of successfully producing n exact copies of a quantum system whose state is chosen secretly from a known pair given m initial realizations of the state where n m we also discuss the relationship between this bound and that on unambiguous state discrimination

effects of cross correlation on the relaxation time of a bistable system driven by cross correlated noise we study the effects of correlations between additive and multiplicative noise on relaxation time in a bistable system driven by cross correlated noise using the projection operator method we derived an analytic expression for the relaxation time t c of the system which is the function of additive ensuremath alpha and multiplicative d noise intensities correlation intensity ensuremath lambda of noise and correlation time ensuremath tau of noise after introducing a noise intensity ratio and a dimensionless parameter r d ensuremath alpha and then performing numerical computations we find the following i for the case of rl1 the relaxation time t c increases as r increases ii for the cases of rg 1 there is a one peak structure on the t c ensuremath r plot and the effects of cross correlated noise on the relaxation time are very notable iii for the case of rl1 t c almost does not change with both ensuremath lambda and ensuremath tau and for the cases of rg 1 t c decreases as ensuremath lambda increases however t c increases as ensuremath tau increases ensuremath lambda and ensuremath tau play opposite roles in t c i e ensuremath lambda enhances the fluctuation decay of dynamical variable and ensuremath tau slows down the fluctuation decay of dynamical variable

translocation time of periodically forced polymer chains in this work we study the presence of both a minimum and clear oscillations in the frequency dependence of the translocation time of a polymer described as a unidimensional rouse chain driven by a spatially localized oscillating linear potential the observed oscillations of the mean translocation time arise from the synchronization between the very mean translocation time and the period of the external force we have checked the robustness of the frequency value for the minimum translocation time by changing the damping parameter finding a very simple relationship between this frequency and the correspondent translocation time the translocation time as a function of the polymer length has been also evaluated finding a precise l 2 scaling furthermore the role played by the thermal fluctuations described as a gaussian uncorrelated noise has been also investigated and the analogies with the resonant activation phenomenon are commented

the state variable correlation function of the bistable system subject to the cross correlated noises abstract the effects of correlations between additive and multiplicative noises on the state variable correlation function of a bistable system driven by cross correlated noises were studied applying an approximate fokker planck equation to the system the analytic expression for the state variable correlation function of the system is derived by projection operator method from numerical computations we find that the normalized correlation function c s decreases exponentially as the decay time s increases and decreases with increasing cross correlated strength however c s increases with increasing cross correlated time and play opposing roles in the c i e enhances the rate of fluctuation decay of dynamical variable and the slows down the rate of fluctuation decay of dynamical variable

phase diagram of the random frequency oscillator the case of ornstein uhlenbeck noise abstract we study the stability of a stochastic oscillator whose frequency is a random process with finite time memory represented by an ornstein uhlenbeck noise this system undergoes a noise induced bifurcation when the amplitude of the noise grows the critical curve that separates the absorbing phase from an extended non equilibrium steady state corresponds to the vanishing of the lyapunov exponent that measures the asymptotic logarithmic growth rate of the energy we derive various expressions for this lyapunov exponent by using different approximation schemes this allows us to study quantitatively the phase diagram of the random parametric oscillator

separability problem for multipartite states of rank at most 4 one of the most important problems in quantum information is the separability problem which asks whether a given quantum state is separable we investigate multipartite states of rank at most 4 which are ppt i e all their partial transposes are positive semidefinite we show that any ppt state of rank 2 or 3 is separable and has length at most 4 for separable states of rank 4 we show that they have length at most 6 it is six only for some qubit qutrit or multiqubit states it turns out that any ppt entangled state of rank 4 is necessarily supported on a 3 3 or a 2 2 2 subsystem we obtain a very simple criterion for the separability problem of the ppt states of rank at most 4 such a state is entangled if and only if its range contains no product vectors this criterion can be easily applied since a four dimensional subspace in the 3 3 or 2 2 2 system contains a product vector if and only if its plucker coordinates satisfy a homogeneous polynomial equation the chow form of the corresponding segre variety we have computed an explicit determinantal expression for the chow form in the former case while such an expression was already known in the latter case

robustness of quantum correlations against linear noise relative robustness of quantum correlations rroqc of a bipartite state is firstly introduced relative to a classically correlated state robustness of quantum correlations roqc of a bipartite state is then defined as the minimum of rroqc of the state relative to all classically correlated ones it is proved that as a function on quantum states roqc is nonnegative lower semi continuous and neither convex nor concave especially it is zero if and only if the state is classically correlated thus roqc not only quantifies the endurance of quantum correlations of a state against linear noise but also can be used to distinguish between quantum and classically correlated states furthermore the effects of local quantum channels on the robustness are explored and characterized

an approach for measuring corporation financial stability by econophysics and bayesian method abstract corporation financial stability was investigated by the method of econophysics and bayesian approach in this paper a stochastic predator prey model was built to describe the corporation financial condition the mean limiting extinction time was proposed to measure the corporation financial stability the model parameters were estimated by using bayesian approach with real corporation financial data experimental results show that i an increase of system risk corresponds to a decrease of the corporation stability ii the optimal initial financial condition enhances the corporation stability to its maximum extent iii under the optimal initial financial condition the optimal system parameters and system risk strength can be observed

stability properties of nonhyperbolic chaotic attractors with respect to noise we study local and global stability of nonhyperbolic chaotic attractors contaminated by noise the former is given by the maximum distance of a noisy trajectory from the noisefree attractor while the latter is provided by the minimal escape energy necessary to leave the basin of attraction calculated with the hamiltonian theory of large fluctuations we establish the important and counterintuitive result that both concepts may be opposed to each other even when one attractor is globally more stable than another one it can be locally less stable our results are exemplified with the holmes map for two different sets of parameter and with a juxtaposition of the holmes and the ikeda maps finally the experimental relevance of these findings is pointed out

statistics of residence time for levy flights in unstable parabolic potentials we analyze the residence time problem for an arbitrary markovian process describing nonlinear systems without a steady state we obtain exact analytical results for the statistical characteristics of the residence time for diffusion in a fully unstable potential profile in the presence of levy noise we get the conditional probability density of the particle position and the average residence time the noise enhanced stability phenomenon is observed in the system investigated results from numerical simulations are in very good agreement with analytical ones

multiple cross correlation noise induced transition in a stochastic bistable system abstract based on the stochastic equivalent rules the fokker planck equation for a general one dimensional nonlinear system subjected to n component noises and cross correlation noises is derived and the greatest advantage of the method lies in its simplicity applying this method the effects of multiple sources of noise and the correlation forms of noises among them i e two multiplicative noises an additive noise and the correlation between the three noises on the steady state properties and the mean first passage time mfpt of a stochastic bistable system are discussed in details the results show rich transition phenomena such as the reentrance like noise induced phenomenon and the switch between the bimodal and the unimodal structure for different noise intensities moreover the effects of the cross correlation among the three noise sources on the mfpt are also discussed and the noise enhanced stability phenomenon and the resonant activation phenomenon are observed the numerical results are in basic agreement with the theoretical predictions

probabilistic broadcasting of mixed states it is well known that the non broadcasting theorem proved by barnum et al is a fundamental principle of quantum communication as we are aware optimal broadcasting ob is the only method to broadcast noncommuting mixed states approximately in this paper motivated by the probabilistic cloning of quantum states proposed by duan and guo we propose a new way for broadcasting noncommuting mixed states probabilistic broadcasting pb and we present a sufficient condition for pb of mixed states to a certain extent we generalize the probabilistic cloning theorem from pure states to mixed states and in particular we generalize the non broadcasting theorem since the case that commuting mixed states can be exactly broadcast can be thought of as a special instance of pb where the success ratio is 1 moreover we discuss probabilistic local broadcasting plb of separable bipartite states

statistics of equally weighted random paths on a class of self similar structures we study the statistics of equally weighted random walk paths on a family of sierpinski gasket lattices whose members are labelled by an integer b 2 b 2 mean path end to end distance grows more slowly than any power of its length n we provide arguments for the emergence of usual power law critical behaviour in the limit b when fractal lattices become almost compact