anderson transition in a three dimensional kicked rotor we investigate anderson localization in a three dimensional 3d kicked rotor by a finite size scaling analysis we identify a mobility edge for a certain value of the kicking strength k k c for k k c dynamical localization does not occur all eigenstates are delocalized and the spectral correlations are well described by wigner dyson statistics this can be understood by mapping the kicked rotor problem onto a 3d anderson model am where a band of metallic states exists for sufficiently weak disorder around the critical region k approximately k c we carry out a detailed study of the level statistics and quantum diffusion in agreement with the predictions of the one parameter scaling theory opt and with previous numerical simulations the number variance is linear level repulsion is still observed and quantum diffusion is anomalous with proportional t 2 3 we note that in the 3d kicked rotor the dynamics is not random but deterministic in order to estimate the differences between these two situations we have studied a 3d kicked rotor in which the kinetic term of the associated evolution matrix is random a detailed numerical comparison shows that the differences between the two cases are relatively small however in the deterministic case only a small set of irrational periods was used a qualitative analysis of a much larger set suggests that deviations between the random and the deterministic kicked rotor can be important for certain choices of periods heuristically it is expected that localization effects will be weaker in a nonrandom potential since destructive interference will be less effective to arrest quantum diffusion however we have found that certain choices of irrational periods enhance anderson localization effects

critical statistics for non hermitian matrices we introduce a generalized ensemble of non hermitian matrices interpolating between the gaussian unitary ensemble the ginibre ensemble and the poisson ensemble the joint eigenvalue distribution of this model is obtained by means of an extension of the itzykson zuber formula to general complex matrices its correlation functions are studied both in the case of weak non hermiticity and in the case of strong non hermiticity in the weak non hermiticity limit we show that the spectral correlations in the bulk of the spectrum display critical statistics the asymptotic linear behavior of the number variance is already approached for energy differences of the order of the eigenvalue spacing to lowest order its slope does not depend on the degree of non hermiticity close the edge the spectral correlations are similar to the hermitian case in the strong non hermiticity limit the crossover behavior from the ginibre ensemble to the poisson ensemble first appears close to the surface of the spectrum our model may be relevant for the description of the spectral correlations of an open disordered system close to an anderson transition

transition from localized to extended eigenstates in the ensemble of power law random banded matrices we study statistical properties of the ensemble of large n times n random matrices whose entries h ij decrease in a power law fashion h ij sim i j alpha mapping the problem onto a nonlinear sigma model with non local interaction we find a transition from localized to extended states at alpha 1 at this critical value of alpha the system exhibits multifractality and spectral statistics intermediate between the wigner dyson and poisson one these features are reminiscent of those typical for the mobility edge of disordered conductors we find a continuous set of critical theories at alpha 1 parametrized by the value of the coupling constant of the sigma model at alpha 1 all states are expected to be localized with integrable power law tails at the same time for 1 alpha 3 2 the wave packet spreading at short time scale is superdiffusive langle r rangle sim t frac 1 2 alpha 1 which leads to a modification of the altshuler shklovskii behavior of the spectral correlation function at 1 2 alpha 1 the statistical properties of eigenstates are similar to those in a metallic sample in d alpha 1 2 1 dimensions finally the region alpha 1 2 is equivalent to the corresponding gaussian ensemble of random matrices alpha 0 the theoretical predictions are compared with results of numerical simulations

practical criterion for delay estimation using random perturbations many systems contain an internal time delay which significantly influences their dynamical properties methods to estimate this delay from times series in the presence of dynamical noise are not systematically studied addressing this problem we demonstrate that it is sufficient to analyze the system s response to short correlated external disturbances or internal noise following this idea it is shown for linear and nonlinear systems as well as for periodic dynamics that the delay can be estimated by analyzing the correlation function this method covers the case of strong noise and multiple delays

adaptive approximation method for joint parameter estimation and identical synchronization of chaotic systems we introduce a numerical approximation method for estimating an unknown parameter of a primary chaotic system which is partially observed through a scalar time series specifically we show that the recursive minimization of a suitably designed cost function that involves the dynamic state of a fully observed secondary system and the observed time series can lead to the identical synchronization of the two systems and the accurate estimation of the unknown parameter the salient feature of the proposed technique is that the only external input to the secondary system is the unknown parameter which needs to be adjusted we present numerical examples for the lorenz system which show how our algorithm can be considerably faster than some previously proposed methods

estimation of parameters in nonlinear systems using balanced synchronization using synchronization between observations and a model with undetermined parameters is a natural way to complete the specification of the model the quality of the synchronization a cost function to be minimized typically is evaluated by a least squares difference between the data time series and the model time series if the coupling between the data and the model is too strong this cost function is small for any data and any model and the variation of the cost function with respect to the parameters of interest is too small to permit selection of an optimal value of the parameters we introduce two methods for balancing the competing desires of a small cost function for the quality of the synchronization and the numerical ability to determine parameters accurately one method of balanced synchronization adds to the synchronization cost function a requirement that the conditional lyapunov exponent of the model system conditioned on being driven by the data remain negative but small in magnitude the other method allows the coupling between the data and the model to vary in time according to the error in synchronization this method succeeds because the data and the model exhibit generalized synchronization in the region where the parameters of the model are well determined examples are explored which have deterministic chaos with and without noise in the data signal

commutative ideal theory without finiteness conditions completely irreducible ideals an ideal of a ring is completely irreducible if it is not the intersection of any set of proper overideals we investigate the structure of completely irrreducible ideals in a commutative ring without finiteness conditions it is known that every ideal of a ring is an intersection of completely irreducible ideals we characterize in several ways those ideals that admit a representation as an irredundant intersection of completely irreducible ideals and we study the question of uniqueness of such representations we characterize those commutative rings in which every ideal is an irredundant intersection of completely irreducible ideals

multifractality of one electron eigen states in 1d disordered long range models abstract one investigates the spatial structure of one electron eigenstates for the one dimensional anderson model with long range off diagonal disorder h n m 1 1 n m where a b means a uniform random distribution between a and b two cases are considered according to the choices for the on site energy e n namely e n 0 and e n 0 1 for 1 all states are critical and the multifractal spectra f is computed for the states near the center of the band the level spacing distribution function is also obtained and its behavior for both small and large separations are studied

family of solvable generalized random matrix ensembles with unitary symmetry we construct a very general family of characteristic functions describing random matrix ensembles rme having a global unitary invariance and containing an arbitrary one variable probability measure which we characterize by a spread function various choices of the spread function lead to a variety of possible generalized rmes which show deviations from the well known gaussian rme originally proposed by wigner we obtain the correlation functions of such generalized ensembles exactly and show examples of how particular choices of the spread function can describe ensembles with arbitrary eigenvalue densities as well as critical ensembles with multifractality

statistics of resonances and delay times in random media beyond random matrix theory we review recent developments in quantum scattering from mesoscopic systems various spatial geometries whose closed analogues show diffusive localized or critical behaviour are considered these are the features that cannot be described by the universal random matrix theory results instead one has to go beyond this approximation and incorporate them in a non perturbative way here we pay particular attention to the traces of these non universal characteristics in the distribution of the wigner delay times and resonance widths the former quantity captures time dependent aspects of quantum scattering while the latter is associated with the poles of the scattering matrix

estimating model parameters by chaos synchronization using chaos synchronization and a proposed iterative method of parameter adaptation we precisely estimate the model parameters of chaotic systems and synchronize two chaotic systems with originally mismatching model parameters this parameter adaptation method can be applied to a spatiotemporal chaotic system with a one way coupled map lattice as a biomedical application this method is capable of estimating the asymmetric tension parameter of a vocal fold model

energy level statistics of a critical random matrix ensemble we study energy level statistics of a critical random matrix ensemble of power law banded complex hermitian matrices we compute the level compressibility via the level number variance and compare it with the analytical formula for the exactly solvable model of moshe neuberger and shapiro

superbosonization formula and its application to random matrix theory starting from gaussian random matrix models we derive a new supermatrix field theory model in contrast to the conventional non linear sigma models the new model is applicable for any range of correlations of the elements of the random matrices we clarify the domain of integration for the supermatrices and give a demonstration of how the model works by calculating the density of states for an ensemble of almost diagonal matrices it is also shown how one can reduce the supermatrix model to the conventional sigma model

ideal theory in prufer domains an unconventional approach abstract in prufer domains of finite character ideals are represented as finite intersections of special ideals which are proper generalizations of the classical primary ideals we show that representations of ideals as shortest intersections of primal or quasi primary ideals exist and are unique moreover every non zero ideal is the product of uniquely determined pairwise comaximal quasi primary ideals semigroups of primal and quasi primary ideals with fixed associated primes are also investigated in arbitrary prufer domains their structures can be described in terms of the value groups of localizations

dynamic algorithm for parameter estimation and its applications we consider a dynamic method based on synchronization and adaptive control to estimate unknown parameters of a nonlinear dynamical system from a given scalar chaotic time series we present an important extension of the method when the time series of a scalar function of the variables of the underlying dynamical system is given we find that it is possible to obtain synchronization as well as parameter estimation using such a time series we then consider a general quadratic flow in three dimensions and discuss the applicability of our method of parameter estimation in this case in practical situations one expects only a finite time series of a system variable to be known we show that the finite time series can be repeatedly used to estimate unknown parameters with an accuracy that improves and then saturates to a constant value with repeated use of the time series finally we suggest an important application of the parameter estimation method we propose that the method can be used to confirm the correctness of a trial function modeling an external unknown perturbation to a known system we show that our method produces exact synchronization with the given time series only when the trial function has a form identical to that of the perturbation

return probability and scaling exponents in the critical random matrix ensemble we study an asymptotic behavior of the return probability for the critical random matrix ensemble in the regime of strong multifractality the return probability is expected to show critical scaling in the limit of large time or large system size using the supersymmetric virial expansion we confirm the scaling law and find analytical expressions for the fractal dimension of the wavefunctions d2 and the dynamical scaling exponent by comparing them we verify the validity of chalker s ansatz for dynamical scaling

synchronization based estimation of all parameters of chaotic systems from time series by a simple combination of adaptive scheme and linear feedback with the updated feedback strength for a large class of chaotic systems it is proved rigorously by using the invariance principle of differential equations that all unknown model parameters can be estimated dynamically this approach supplies a systematic and analytical procedure for estimating parameters from time series and it is simple to implement in practice in addition this method is quite robust against the effect of noise and able to respond rapidly to changes in operating parameters of the experimental system lorenz and r ossler hyperchaos systems are used to illustrate the validity of this technique

spectral fluctuations of billiards with mixed dynamics from time series to superstatistics a statistical analysis of the eigenfrequencies of two sets of superconducting microwave billiards one with mushroomlike shape and the other from the family of the limacon billiards is presented these billiards have mixed regular chaotic dynamics but different structures in their classical phase spaces the spectrum of each billiard is represented as a time series where the level order plays the role of time two most important findings follow from the time series analysis first the spectra can be characterized by two distinct relaxation lengths this is a prerequisite for the validity of the superstatistical approach which is based on the folding of two distribution functions second the shape of the resulting probability density function of the so called superstatistical parameter is reasonably approximated by an inverse chi2 distribution this distribution is used to compute nearest neighbor spacing distributions and compare them with those of the resonance frequencies of billiards with mixed dynamics within the framework of superstatistics the obtained spacing distribution is found to present a good description of the experimental ones and is of the same or even better quality as a number of other spacing distributions including the one from berry and robnik however in contrast to other approaches toward a theoretical description of spectral properties of systems with mixed dynamics superstatistics also provides a description of properties of the eigenfunctions in terms of a superstatistical generalization of the porter thomas distribution indeed the inverse chi2 parameter distribution is found suitable for the analysis of experimental resonance strengths in the limacon billiards within the framework of superstatistics

density of states for almost diagonal random matrices we study the density of states dos for disordered systems whose spectral statistics can be described by a gaussian ensemble of almost diagonal hermitian random matrices the matrices have independent random entries h i or j with small off diagonal elements approximately 1 using the recently suggested method of a virial expansion in the number of interacting energy levels j phys a 36 8265 2003 we calculate the leading correction to the poissonian dos in the cases of the gaussian orthogonal and unitary ensembles we apply the general formula to the critical power law banded random matrices and the unitary moshe neuberger shapiro model and compare the dos s of these models

scaling and eigenfunction correlations near a mobility edge abstract the scaling form of the frequency and wavevector dependent diffusion constant is discussed near a mobility edge the consequences are stressed of fractal eigenfunction fluctuations for behaviour in the low frequency large wavevector regime

recovery of systems with a linear filter and nonlinear delay feedback in periodic regimes we propose a set of methods for the estimation of the parameters of time delay systems with a linear filter and nonlinear delay feedback performing periodic oscillations the methods are based on an analysis of the system response to regular external perturbations and are valid only for systems whose dynamics can be perturbed the efficiency of the methods is illustrated using both numerical and experimental data

structure identification based on steady state control experimental results and applications we report experimental results on structure identification of nonlinear systems by a steady state control method the idea underlying the method is to drive the nonlinear system to steady state by applying a suitable feedback control input it turns out experimentally that this control based structure identification method can be used for some applications such as estimation of initial conditions and state variables of nonlinear systems and structure identification of some special elements two attractors of the chua oscillator are presented to illustrate the reliability of the suggested techniques under the hypotheses of measurable state variables and physical access to the system for implementing the proportional feedback

commutative ideal theory without finiteness conditions primal ideals our goal is to establish an efficient decomposition of an ideal a of a commutative ring r as an intersection of primal ideals we prove the existence of a canonical primal decomposition a p xa a p where the a p are isolated components of a that are primal ideals having distinct and incomparable adjoint primes p for this purpose we define the set ass a of associated primes of the ideal a to be those defined and studied by krull we determine conditions for the canonical primal decomposition to be irredundant or residually maximal or the unique representation of a as an irredundant intersection of isolated components of a using our canonical primal decomposition we obtain an affirmative answer to a question raised by fuchs and also prove for p spec r that an ideal a c p is an intersection of p primal ideals if and only if the elements of r p are prime to a we prove that the following conditions are equivalent i the ring r is arithmetical ii every primal ideal of r is irreducible iii each proper ideal of r is an intersection of its irreducible isolated components we classify the rings for which the canonical primal decomposition of each proper ideal is an irredundant decomposition of irreducible ideals as precisely the arithmetical rings with noetherian maximal spectrum in particular the integral domains having these equivalent properties are the prufer domains possessing a certain property

critical statistics in quantum chaos and calogero sutherland model at finite temperature we investigate the spectral properties of a generalized gaussian orthogonal ensemble capable of describing critical statistics the joint distribution of eigenvalues of this model is expressed as the diagonal element of the density matrix of a gas of particles governed by the calogero sutherland cs hamiltonian taking advantage of the correspondence between cs particles and eigenvalues and utilizing a recently conjectured expression by kravtsov and tsvelik for the finite temperature density density correlations of the cs model we show that the number variance of our random matrix model is asymptotically linear with a slope depending on the parameters of the model such linear behavior is a signature of critical statistics this random matrix model may be relevant for the description of spectral correlations of complex quantum systems with a self similar or fractal poincare section of its classical counterpart this is shown in detail for two examples the anisotropic kepler problem and a kicked particle in a well potential in both cases the number variance and the delta 3 statistic are accurately described by our analytical results

partial synchronization of chaotic systems with uncertainty we suggest an approach to partial synchronization of chaotic systems with uncertainty this method contains two steps i transforming the synchronization system into the canonical form by the well known feedback linearization theory and ii finding a control signal to ensure the asymptotic stability of the canonical system this partial synchronization approach requires very little system information by applying a finite time convergence technique to estimate uncertainties caused by unknown states parameters or structure we also argue in detail that this partial synchronization method can be extended to parameter identification sub structure estimation and even phase detection several examples are presented to illustrate the partial synchronization approach suggested

the multiplicative ideal theory of leavitt path algebras abstract it is shown that every leavitt path algebra l of an arbitrary directed graph e over a field k is an arithmetical ring that is the distributive law a b c a b a c holds for any three two sided ideals of l it is also shown that l is a multiplication ring that is given any two ideals a b in l with a b there is always an ideal c such that a b c an indication of a possible rich multiplicative ideal theory for l existence and uniqueness of factorization of the ideals of l as products of special types of ideals such as prime irreducible or primary ideals is investigated the irreducible ideals of l turn out to be precisely the primary ideals of l it is shown that an ideal i of l is a product of finitely many prime ideals if and only the graded part g r i of i is a product of prime ideals and that i g r i is finitely generated with a generating set of cardinality no more than the number of distinct prime ideals in the prime factorization of g r i as an application it is shown that if e is a finite graph then every ideal of l is a product of prime ideals the same conclusion holds if l is two sided artinian or two sided noetherian examples are constructed verifying whether some of the well known theorems in the ideal theory of commutative rings such as the cohen s theorem on prime ideals and the characterizing theorem on zpi rings hold for leavitt path algebras

commutative rings in which every ideal is a product of primary ideals abstract a q ring is a commutative ring in which every ideal is a product of primary ideals we show that r is a q ring if and only if r is a laskerian ring every ideal has a primary decomposition and every nonmaximal prime ideal of r is finitely generated and locally principal we also show that r x or r x is a q ring if and only if r is a finite direct product of dedekind domains and special principal ideal rings

synchronization based approach for estimating all model parameters of chaotic systems the problem of dynamic estimation of all parameters of a model representing chaotic and hyperchaotic systems using information from a scalar measured output is solved the variational calculus based method is robust in the presence of noise enables online estimation of the parameters and is also able to rapidly track changes in operating parameters of the experimental system the method is demonstrated using the lorenz rossler chaos and hyperchaos models its possible application in decoding communications using chaos is discussed

class semigroups of prufer domains abstract the class semigroup of a commutative integral domainris the semigroup s r of the isomorphism classes of the nonzero ideals ofrwith the operation induced by multiplication the aim of this paper is to characterize the prufer domainsrsuch that the semigroup s r is a clifford semigroup namely a disjoint union of groups each one associated to an idempotent of the semigroup we find a connection between this problem and the following local invertibility property an idealiofris invertible if and only if every localization ofiat a maximal ideal ofris invertible we consider the property introduced in 1967 for prufer domainsr stating that if 1and 2are two distinct sets of maximal ideals ofr then rm m 1 rm m 2 let c be the class of prufer domains satisfying the separation property or with the property that each localization at a maximal ideal if finite dimensional we prove that ifrbelongs to c then the local invertibility property holds onrif and only if every nonzero element ofris contained only in a finite number of maximal ideals ofr moreover ifrbelongs to c then s r is a clifford semigroup if and only if every nonzero element ofris contained only in a finite number of maximal ideals ofr

a supersymmetry approach to almost diagonal random matrices we develop a supersymmetric field theoretical description of the gaussian ensemble of the almost diagonal hermitian random matrices the matrices have independent random entries hi j with parametrically small off diagonal elements we derive a regular virial expansion of correlation functions in the number of interacting supermatrices associated with different sites in the real space and demonstrate that the perturbation theory constructed in this way is controlled by a small parameter the general form of the integral expression for the mth virial coefficient governed by the interaction of m supermatrices is presented and calculated explicitly in the cases of 2 and 3 matrix interaction the suggested technique allows us to calculate both the spectral correlations and the correlations of the eigenfunctions taken at different energies and in different space points

level compressibility in a critical random matrix ensemble the second virial coefficient we study spectral statistics of a gaussian unitary critical ensemble of almost diagonal hermitian random matrices with off diagonal entries hij 2 b2 i j 2 small compared to diagonal ones hii 2 1 using the recently suggested method of virial expansion in the number of interacting energy levels yevtushenko and kravtsov 2003 j phys a math gen 36 8265 we calculate a coefficient b2 1 in the level compressibility b we demonstrate that only the leading terms in b coincide for this model and for an exactly solvable model suggested by moshe et al 1994 phys rev lett 73 1497 the sub leading terms b2 being different numerical data confirm our analytical calculation

on asymptotic expansions and scales of spectral universality in band random matrix ensembles we consider real random symmetric n n matrices h of the band type form with characteristic length b the matrix entries are independent gaussian random variables and have the variance proportional to where u t vanishes at infinity we study the resolvent in the limit and obtain the explicit expression for the leading term of the first correlation function of the normalized trace