lieb robinson bounds for the toda lattice we establish locality estimates known as lieb robinson bounds for the toda lattice in contrast to harmonic models the lieb robinson velocity for these systems do depend on the initial condition our results also apply to the entire toda as well as the kac van moerbeke hierarchy under suitable assumptions our methods also yield a finite velocity for certain perturbations of these systems

pair approximation for the noisy threshold q voter model in the standard q voter model a given agent can change its opinion only if there is a full consensus of the opposite opinion within a group of influence of size q a more realistic extension is the threshold q voter where a minimal agreement at least 0 q 0 q opposite opinions is sufficient to flip the central agent s opinion including also the possibility of independent nonconformist choices variants of this model including nonconformist behavior have been previously studied in fully connected networks mean field limit here we investigate its dynamics in random networks particularly while in the mean field case it is irrelevant whether repetitions in the influence group are allowed we show that this is not the case in networks and we study the impact of both cases with or without repetition furthermore the results of computer simulations are compared with the predictions of the pair approximation derived for uncorrelated networks of arbitrary degree distributions

on the exponential decay of the n point correlation functions and the analyticity of the pressure the goal of this paper is to provide estimates leading to a direct proof of the exponential decay of the n point correlation functions for certain unbounded models of kac type the methods are based on estimating higher order derivatives of the solution of the witten laplacian equation on 1 forms associated with the hamiltonian of the system we also provide a formula for the taylor coefficients of the pressure that is suitable for a direct proof of the analyticity

finite size scaling of out of time ordered correlators at late times chaotic dynamics in quantum many body systems scrambles local information so that at late times it can no longer be accessed locally this is reflected quantitatively in the out of time ordered correlator of local operators which is expected to decay to zero with time however for systems of finite size out of time ordered correlators do not decay exactly to zero and we show in this paper that the residue value can provide useful insights into the chaotic dynamics in particular we show that when energy is conserved the late time saturation value of out of time ordered correlators for generic traceless local operators scales inverse polynomially with the system size this is in contrast to the inverse exponential scaling expected for chaotic dynamics without energy conservation we provide both analytical arguments and numerical simulations to support this conclusion

phase ordering and persistence in a class of stochastic processes interpolating between the ising and voter models we study the dynamics of a class of two dimensional stochastic processes depending on two parameters which may be interpreted as two different temperatures respectively associated to interfacial and to bulk noise special lines in the plane of parameters correspond to the ising model voter model and majority vote model the dynamics of this class of models may be described formally in terms of reaction diffusion processes for a set of coalescing annihilating and branching random walkers we use the freedom allowed by the space of parameters to measure by numerical simulations the persistence probability of a generic model in the low temperature phase where the system coarsens this probability is found to decay at large times as a power law with a seemingly constant exponent we also discuss the connection between persistence and the nature of the interfaces between domains

the spectral gap for some spin chains with discrete symmetry breaking we prove that for any finite set of generalized valence bond solid gvbs states of a quantum spin chain there exists a translation invariant finite range hamiltonian for which this set is the set of ground states this result implies that there are gvbs models with arbitrary broken discrete symmetries that are described as combinations of lattice translations lattice reflections and local unitary or anti unitary transformations we also show that all gvbs models that satisfy some natural conditions have a spectral gap the existence of a spectral gap is obtained by applying a simple and quite general strategy for proving lower bounds on the spectral gap of the generator of a classical or quantum spin dynamics this general scheme is interesting in its own right and threfore although the basic idea is not new we present it in a system independent setting the results are illustrated with a number of examples

correlation at low temperature ii asymptotics the present paper is a continuation of ref 4 where the truncated two point correlation function for a class of lattice spin systems was proved to have exponential decay at low temperature under a weak coupling assumption in this paper we compute the asymptotics of the correlation function as the temperature goes to zero this paper thus extends ref 3 in two directions the hamiltonian function is allowed to have several local minima other than a unique global minimum and we do not require translation invariance of the hamiltonian function we are in particular able to handle spin systems on a general lattice

opinion dynamics model with weighted influence exit probability and dynamics we introduce a stochastic model of binary opinion dynamics in which the opinions are determined by the size of the neighboring domains the exit probability here shows a step function behavior indicating the existence of a separatrix distinguishing two different regions of basin of attraction this behavior in one dimension is in contrast to other well known opinion dynamics models where no such behavior has been observed so far the coarsening study of the model also yields novel exponent values a lower value of persistence exponent is obtained in the present model which involves stochastic dynamics when compared to that in a similar type of model with deterministic dynamics this apparently counterintuitive result is justified using further analysis based on these results it is concluded that the proposed model belongs to a unique dynamical class

evolutionary dynamics on degree heterogeneous graphs the evolution of two species with different fitness is investigated on degree heterogeneous graphs the population evolves either by one individual dying and being replaced by the offspring of a random neighbor voter model dynamics or by an individual giving birth to an offspring that takes over a random neighbor node invasion process dynamics the fixation probability for one species to take over a population of n individuals depends crucially on the dynamics and on the local environment starting with a single fitter mutant at a node of degree k the fixation probability is proportional to k for voter model dynamics and to 1 k for invasion process dynamics

remarks on decay of correlations and witten laplacians brascamp lieb inequalities and semiclassical limit as it appears in recent articles by helffer or sjostrand and naddaf spencer the analysis in the context of the statistical mechanics of measures of the type exp x dxis connected with the analysis of suitable witten laplacians on 1 forms for illustrating this point of view we present here remarks about the brascamp lieb inequalities and its extensions and prove the decay of the correlation in some cases when is weakly non convex

phase transitions in the q voter model with noise on a duplex clique we study a nonlinear q voter model with stochastic noise interpreted in the social context as independence on a duplex network to study the role of the multilevelness in this model we propose three methods of transferring the model from a mono to a multiplex network they take into account two criteria one related to the status of independence local vs global and one related to peer pressure and vs or in order to examine the influence of the presence of more than one level in the social network we perform simulations on a particularly simple multiplex a duplex clique which consists of two fully overlapped complete graphs cliques solving numerically the rate equation and simultaneously conducting monte carlo simulations we provide evidence that even a simple rearrangement into a duplex topology may lead to significant changes in the observed behavior however qualitative changes in the phase transitions can be observed for only one of the considered rules local and for this rule the phase transition becomes discontinuous for q 5 whereas for a monoplex such behavior is observed for q 6 interestingly only this rule admits construction of realistic variants of the model in line with recent social experiments

topology induced coarsening in language games we investigate how very large populations are able to reach a global consensus out of local microscopic interaction rules in the framework of a recently introduced class of models of semiotic dynamics the so called naming game we compare in particular the convergence mechanism for interacting agents embedded in a low dimensional lattice with respect to the mean field case we highlight that in low dimensions consensus is reached through a coarsening process that requires less cognitive effort of the agents with respect to the mean field case but takes longer to complete in one dimension the dynamics of the boundaries is mapped onto a truncated markov process from which we analytically computed the diffusion coefficient more generally we show that the convergence process requires a memory per agent scaling as n and lasts a time n 1 2 d in dimension d 4 the upper critical dimension while in mean field both memory and time scale as n 3 2 for a population of n agents we present analytical and numerical evidence supporting this picture

exponential decay of correlations implies area law we prove that a finite correlation length i e exponential decay of correlations implies an area law for the entanglement entropy of quantum states defined on a line the entropy bound is exponential in the correlation length of the state thus reproducing as a particular case hastings s proof of an area law for groundstates of 1d gapped hamiltonians

supersymmetry and morse theory it is shown that the morse inequalities can be obtained by consideration of a certain supersymmetric quantum mechanics hamiltonian some of the implications of modern ideas in mathematics for supersymmetric theories are discussed

local interaction scale controls the existence of a nontrivial optimal critical mass in opinion spreading we study a model of opinion formation where the collective decision of a group is said to happen if the fraction of agents having the most common opinion exceeds a threshold value a critical mass we find that there exists a unique nontrivial critical mass giving the most efficient convergence to consensus in addition we observe that for small critical masses the characteristic time scale for the relaxation to consensus splits into two the shorter time scale corresponds to a direct relaxation and the longer one can be explained by the existence of intermediate metastable states similar to those found in p chen and s redner phys rev e 71 036101 2005 this longer time scale is dependent on the precise condition for consensus with a modification of the condition it can go away

on the correlation for kac like models in the convex case the aim of this paper is to stu the behavior asm tends to of a family of measures exp m x dx m on m where m is a potential on m which is a perturbation in a suitable sense of the harmonic potential j x j 2

dynamics of influence on hierarchical structures dichotomous spin dynamics on a pyramidal hierarchical structure the bethe lattice are studied the system embodies a number of classes where a class comprises nodes that are equidistant from the root head node weighted links exist between nodes from the same and different classes the spin hereafter state of the head node is fixed we solve for the dynamics of the system for different boundary conditions we find necessary conditions so that the classes eventually repudiate or acquiesce in the state imposed by the head node the results indicate that to reach unanimity across the hierarchy it suffices that the bottommost class adopts the same state as the head node then the rest of the hierarchy will inevitably comply this also sheds light on the importance of mass media as a means of synchronization between the topmost and bottommost classes surprisingly in the case of discord between the head node and the bottommost classes the average state over all nodes inclines towards that of the bottommost class regardless of the link weights and intraclass configurations hence the role of the bottommost class is signified

irrelevance of information outflow in opinion dynamics models the sznajd model for opinion dynamics has attracted a large interest as a simple realization of the psychological principle of social validation as its most salient feature it has been claimed that the sznajd model is qualitatively different from other ordering processes because it is the only one featuring outflow of information as opposed to inflow we show that this claim is unfounded by presenting a generalized zero temperature glauber type of dynamics which yields results indistinguishable from those of the sznajd model in one dimension we also derive an exact expression for the exit probability of the sznajd model which turns out to coincide with the result of an analytical approach based on the kirkwood approximation this observation raises interesting questions about the applicability and limitations of this approach

social paradoxes of majority rule voting and renormalization group real space renormalization group ideas are used to study a voting problem in political science a model to construct self directed pyramidal structures from bottom up to the top is presented using majority rules it is shown that a minority and even a majority can be systematically self eliminated from top leadership provided the hierarchy has a minimal number of levels in some cases 70 of the population is found to have zero representation after six hierarchical levels results are discussed with respect to the internal operation of political organizations

mapping the q voter model from a single chain to complex networks abstract we propose and compare six different ways of mapping the modified q voter model to complex networks considering square lattices barabasi albert watts strogatz and real twitter networks we ask the question if always a particular choice of the group of influence of a fixed size q leads to different behavior at the macroscopic level using monte carlo simulations we show that the answer depends on the relative average path length of the network and for real life topologies the differences between the considered mappings may be negligible

exit probability of the one dimensional q voter model analytical results and simulations for large networks we discuss the exit probability of the one dimensional q voter model and present tools to obtain estimates about this probability both through simulations in large networks around 10 7 sites and analytically in the limit where the network is infinitely large we argue that the result e q q 1 q that was found in three previous works f slanina k sznajd weron and p przybyla europhys lett 82 18006 2008 r lambiotte and s redner europhys lett 82 18007 2008 for the case q 2 and p przybyla k sznajd weron and m tabiszewski phys rev e 84 031117 2011 for q 2 using small networks around 10 3 sites is a good approximation but there are noticeable deviations that appear even for small systems and that do not disappear when the system size is increased with the notable exception of the case q 2 we also show that under some simple and intuitive hypotheses the exit probability must obey the inequality q q 1 e 1 q in the infinite size limit we believe this settles in the negative the suggestion made s galam and a c r martins europhys lett 95 48005 2001 that this result would be a finite size effect with the exit probability actually being a step function we also show how the result that the exit probability cannot be a step function can be reconciled with the galam unified frame which was also a source of controversy

nonlinear q voter model we introduce a nonlinear variant of the voter model the q voter model in which q neighbors with possible repetition are consulted for a voter to change opinion if the q neighbors agree the voter takes their opinion if they do not have a unanimous opinion still a voter can flip its state with probability epsilon we solve the model on a fully connected network i e in mean field and compute the exit probability as well as the average time to reach consensus by employing the backward fokker planck formalism and scaling arguments we analyze the results in the perspective of a recently proposed langevin equation aimed at describing generic phase transitions in systems with two z2 symmetric absorbing states in particular by deriving explicitly the coefficients of such a langevin equation as a function of the microscopic flipping probabilities we find that in mean field the q voter model exhibits a disordered phase for high epsilon and an ordered one for low epsilon with three possible ways to go from one to the other i a unique generalized voter like transition ii a series of two consecutive transitions one ising like in which the z2 symmetry is broken and a separate one in the directed percolation class in which the system falls into an absorbing state and iii a series of two transitions including an intermediate regime in which the final state depends on initial conditions this third so far unexplored scenario in which a type of ordering dynamics emerges is rationalized and found to be specific of mean field i e fluctuations are explicitly shown to wash it out in spatially extended systems

fast scrambling on sparse graphs given a quantum many body system with few body interactions how rapidly can quantum information be hidden during time evolution the fast scrambling conjecture is that the time to thoroughly mix information among n degrees of freedom grows at least logarithmically in n we derive this inequality for generic quantum systems at infinite temperature bounding the scrambling time by a finite decay time of local quantum correlations at late times using lieb robinson bounds generalized sachdev ye kitaev models and random unitary circuits we propose that a logarithmic scrambling time can be achieved in most quantum systems with sparse connectivity these models also elucidate how quantum chaos is not universally related to scrambling we construct random few body circuits with infinite lyapunov exponent but logarithmic scrambling time we discuss analogies between quantum models on graphs and quantum black holes and suggest methods to experimentally study scrambling with as many as 100 sparsely connected quantum degrees of freedom

stability of frustration free hamiltonians we prove stability of the spectral gap for gapped frustration free hamiltonians under general quasi local perturbations we present a necessary and sufficient condition for stability which we call local topological quantum order and show that this condition implies an area law for the entanglement entropy of the groundstate subspace this result extends previous work by bravyi et al on the stability of topological quantum order for hamiltonians composed of commuting projections with a common zero energy subspace we conclude with a list of open problems relevant to spectral gaps and topological quantum order

mean field analysis of the q voter model on networks we present a detailed investigation of the behavior of the nonlinear q voter model for opinion dynamics at the mean field level we derive analytically for any value of the number q of agents involved in the elementary update the phase diagram the exit probability and the consensus time at the transition point the mean field formalism is extended to the case that the interaction pattern is given by generic heterogeneous networks we finally discuss the case of random regular networks and compare analytical results with simulations

phase transitions in the majority vote model with two types of noises abstract in this work we study the majority vote model with the presence of two distinct noises the first one is the usual noise q that represents the probability that a given agent follows the minority opinion of his her social contacts on the other hand we consider the independent behavior such that an agent can choose his her own opinion 1 or 1 with equal probability independent of the group s norm we study the impact of the presence of such two kinds of stochastic driving in the phase transitions of the model considering the mean field and the square lattice cases our results suggest that the model undergoes a nonequilibrium order disorder phase transition even in the absence of the noise q due to the independent behavior but this transition may be suppressed in addition for both topologies analyzed we verified that the transition is in the same universality class of the equilibrium ising model i e the critical exponents are not affected by the presence of the second noise associated with independence

light cone matrix product we show how to combine the light cone and matrix product algorithms to simulate quantum systems far from equilibrium for long times for the case of the xxz spin chain at 0 5 we simulate to a time of 22 5 while part of the long simulation time is due to the use of the light cone method we also describe a modification of the infinite time evolving bond decimation algorithm with improved numerical stability and we describe how to incorporate symmetry into this algorithm while statistical sampling error means that we are not yet able to make a definite statement the behavior of the simulation at long times indicates the appearance of either revivals in the order parameter as predicted by hastings and levitov e print arxiv 0806 4283 or of a distinct shoulder in the decay of the order parameter

spectral gap and decay of correlations in u 1 symmetric lattice systems in dimensions d 2 we consider many body systems with a global u 1 symmetry on a class of lattices with the fractal dimension d 2 and their zero temperature correlations whose observables behave as a vector under the u 1 rotation for a wide class of the models we prove that if there exists a spectral gap above the ground state then the correlation functions have a stretched exponentially decaying upper bound this is an extension of the mcbryan spencer method at finite temperatures to zero temperature the class includes quantum spin and electron models on the lattices and our method also allows finite or infinite quasi degeneracy of the ground state the resulting bounds rule out the possibility of the corresponding magnetic and electric long range orders

translation invariant pure state on b j zmd j c and its split property in this paper we prove that a real lattice symmetric reflection positive translation invariant pure state of b j zmd j c admits split property if and only if its two point spatial correlation functions decay exponentially we use amalgamated representation of cuntz algebras to represent two point spatial correlation functions on an augmented hilbert space the underling symmetries and reflection positive property of the pure state make it possible to investigate its split and decaying two point correlation functions properties as spectral properties of a contractive self adjoint operator on the augmented hilbert space haag duality property of the pure state is crucially used in the analysis

efficiency versus speed in quantum heat engines rigorous constraint from lieb robinson bound a long standing open problem whether a heat engine with finite power achieves the carnot efficiency is investgated we rigorously prove a general trade off inequality on thermodynamic efficiency and time interval of a cyclic process with quantum heat engines in a first step employing the lieb robinson bound we establish an inequality on the change in a local observable caused by an operation far from support of the local observable this inequality provides a rigorous characterization of the following intuitive picture that most of the energy emitted from the engine to the cold bath remains near the engine when the cyclic process is finished using this description we prove an upper bound on efficiency with the aid of quantum information geometry our result generally excludes the possibility of a process with finite speed at the carnot efficiency in quantum heat engines in particular the obtained constraint covers engines evolving with non markovian dynamics which almost all previous studies on this topic fail to address

nonequilibrium spin models with ising universal behaviour the properties of a family of nonequilibrium spin models with up down symmetry on a square lattice are determined by a mean field pair approximation and by monte carlo simulation the phase diagram in the parameter space displays a critical line that terminates at a first order critical point it is found that the critical exponents are the same as those of the equilibrium ising model

around a stationary phase theorem in large dimension in this article we want to present a stationary phase theorem appearing in a recent article by j sjostrand ann inst h poincare phys theor in press and explain the role it can play in the context of statistical mechanics this theorem is also technically connected to the semi classical determination of eigenvalues for a schrodinger operator in large dimension and also in the same spirit with small or large temperature expansions

dynamical error bounds for continuum discretisation via gauss quadrature rules a lieb robinson bound approach instances of discrete quantum systems coupled to a continuum of oscillators are ubiquitous in physics often the continua are approximated by a discrete set of modes we derive error bounds on expectation values of system observables that have been time evolved under such discretised hamiltonians these bounds take on the form of a function of time and the number of discrete modes where the discrete modes are chosen according to gauss quadrature rules the derivation makes use of tools from the field of lieb robinson bounds and the theory of orthonormal polynomials

exit probability in a one dimensional nonlinear q voter model we formulate and investigate the nonlinear q voter model which as a special case includes the linear voter and the sznajd model on a one dimensional lattice we derive an analytical formula for the exit probability and show that it agrees perfectly with monte carlo simulations the puzzle that we deal with here may be summarized by a simple question why does the mean field approach give the exact formula for the exit probability in the one dimensional nonlinear q voter model to answer this question we test several hypotheses proposed recently for the sznajd model including the finite size effects the influence of the range of interactions and the importance of the initial step of the evolution on the one hand our work is part of a trend of the current debate on the form of the exit probability in the one dimensional sznajd model but on the other hand it concerns the much broader problem of the nonlinear q voter model

on the spectrum of semi classical witten laplacians and schrodinger operators in large dimension we investigate the low lying spectrum of witten laplacians on forms of arbitrary degree in the semi classical limit and uniformly in the space dimension we show that under suitable assumptions implying that the phase function has a unique local minimum one obtains a number of clusters of discrete eigenvalues at the bottom of the spectrum moreover we are able to count the number of eigenvalues in each cluster we apply our results to certain sequences of schrodinger operators having strictly convex potentials and show that some well known results of semi classical analysis hold also uniformly in the dimension

witten laplacian method for the decay of correlations the aim of this paper is to apply direct methods to the study of integrals that appear naturally in statistical mechanics and euclidean field theory we provide weighted estimates leading to the exponential decay of the two point correlation functions for certain classical convex unbounded models the methods involve the study of the solutions of the witten laplacian equations associated with the hamiltonian of the system

correlation at low temperature i exponential decay abstract the present paper generalizes the analysis in ann h poincare 1 2000 59 math j ams 8 1997 123 of the correlations for a lattice system of real valued spins at low temperature the gibbs measure is assumed to be generated by a fairly general hamiltonian function with pair interaction the novelty as compared to 2 20 is that the single site self energies of the spins are not required to have only a single local minimum and no other extrema our derivation of exponential decay of correlations goes through the spectral analysis of a deformed laplacian closely related to the witten laplacian studied in 2 20 we prove that this laplacian has a spectral gap above zero and argue that this implies exponential decay of the correlations

a remark on the cluster theorem an improved version of the cluster theorem of relativistic quantum field theory with the correct exponential decay is derived by function theoretical methods

hipsters on networks how a minority group of individuals can lead to an antiestablishment majority the spread of opinions memes diseases and alternative facts in a population depends both on the details of the spreading process and on the structure of the social and communication networks on which they spread one feature that can change spreading dynamics substantially is heterogeneous behavior among different types of individuals in a social network in this paper we explore how antiestablishment nodes e g hipsters influence the spreading dynamics of two competing products we consider a model in which spreading follows a deterministic rule for updating node states which indicate which product has been adopted in which an adjustable probability p hip of the nodes in a network are hipsters who choose to adopt the product that they believe is the less popular of the two the remaining nodes are conformists who choose which product to adopt by considering which products their immediate neighbors have adopted we simulate our model on both synthetic and real networks and we show that the hipsters have a major effect on the final fraction of people who adopt each product even when only one of the two products exists at the beginning of the simulations a small fraction of hipsters in a network can still cause the other product to eventually become the more popular one to account for this behavior we construct an approximation for the steady state adoption fractions of the products on k regular trees in the limit of few hipsters additionally our simulations demonstrate that a time delay in the knowledge of the product distribution in a population as compared to immediate knowledge of product adoption among nearest neighbors can have a large effect on the final distribution of product adoptions using a local tree approximation we derive an analytical estimate of the spreading of products and obtain good agreement if a sufficiently small fraction of the population consists of hipsters in all networks we find that either of the two products can become the more popular one at steady state depending on the fraction of hipsters in the network and on the amount of delay in the knowledge of the product distribution our simple model and analysis may help shed light on the road to success for antiestablishment choices in elections as such success and qualitative differences in final outcomes between competing products political candidates and so on can arise rather generically in our model from a small number of antiestablishment individuals and ordinary processes of social influence on normal individuals

stochastic analysis on product manifolds dirichlet operators on differential forms abstract we define a de rham complex over a product manifold infinite product of compact manifolds and dirichlet operators on differential forms associated with differentiable measures in particular gibbs measures which generalize the notions of bochner and de rham laplacians we give probabilistic representations for corresponding semigroups and study properties of the corresponding stochastic dynamics

local random quantum circuits are approximate polynomial designs numerical results we numerically investigate the statement that local random quantum circuits acting on n qubits composed of polynomially many nearest neighbor two qubit gates form an approximate unitary poly n design brandao et al 2012 arxiv 1208 0692 using a group theory formalism spectral gaps that give a ratio of convergence to a given t design are evaluated for a different number of qubits n up to 20 and degrees t t 2 3 4 and 5 improving previously known results for n 2 in the case of t 2 and 3 their values lead to the conclusion that the previously used lower bound that bounds spectral gaps values may give very little information about the real situation and in most cases only tells us that a gap is closed we compare our results to another lower bounding technique again showing that its results may not be tight

a multi dimensional lieb schultz mattis theorem for a large class of finite range quantum spin models with half integer spins we prove that uniqueness of the ground state implies the existence of a low lying excited state for systems of linear size l with arbitrary finite dimension we obtain an upper bound on the excitation energy i e the gap above the ground state of the form c log l l this result can be regarded as a multi dimensional lieb schultz mattis theorem 14 and provides a rigorous proof of the main result in 8

making almost commuting matrices commute suppose two hermitian matrices a b almost commute vert a b vert leq delta are they close to a commuting pair of hermitian matrices a b with vert a a vert vert b b vert leq epsilon a theorem of h lin 3 shows that this is uniformly true in that for every epsilon 0 there exists a 0 independent of the size n of the matrices for which almost commuting implies being close to a commuting pair however this theorem does not specify how depends on epsilon we give uniform bounds relating and epsilon the proof is constructive giving an explicit algorithm to construct a and b we provide tighter bounds in the case of block tridiagonal and tridiagonal matrices within the context of quantum measurement this implies an algorithm to construct a basis in which we can make a projective measurement that approximately measures two approximately commuting operators simultaneously finally we comment briefly on the case of approximately measuring three or more approximately commuting operators using povms positive operator valued measures instead of projective measurements

universal and nonuniversal features of the generalized voter class for ordering dynamics in two dimensions by considering three different spin models belonging to the generalized voter class for ordering dynamics in two dimensions dornic et al phys rev lett 87 045701 2001 we show that they behave differently from the linear voter model when the initial configuration is an unbalanced mixture of up and down spins in particular we show that for nonlinear voter models the exit probability probability to end with all spins up when starting with an initial fraction x of them assumes a nontrivial shape this is the first time a nontrivial exit probability is observed in two dimensional systems the change is traced back to the strong nonconservation of the average magnetization during the early stages of dynamics also the time needed to reach the final consensus state tn x has an anomalous nonuniversal dependence on x

effect of initial concentration and spatial heterogeneity of active agent distribution on opinion dynamics abstract we analyze the effect of spatial heterogeneity in the initial spin distribution on spin dynamics in a three state square lattice divided into spatial cells districts in the spirit of the statistical mechanics of social impact we introduce a dominant influence rule dir according to which in a single update step a chosen node adopts the state determined by the influence of its discussion group formed by the node itself and its neighbors within one or more coordination spheres in contrast to models based on some form of majority rule mr a system governed by the dir is easily trapped in a stable non consensus state if all nodes of the discussion group have the same weight of influence to ensure that a consensus in the dir system is necessarily reached we need to put a stochastic process in the update rule further the stochastic dir model is used as a starting point for understanding the effect of spatial heterogeneity of active agent non zero spin distribution on the exit probabilities initially the positive and negative spins active agents are assigned to some nodes with non uniform spatial distributions while the rest of the nodes remain in the state with spin zero uncommitted voters by varying the relative means and skewness of the initial spin distributions we observe critical behaviors of exit probabilities in finite size systems the critical exponents are obtained by monte carlo simulations the results of numerical simulations are discussed in the context of social dynamics

many body localization in the droplet spectrum of the random xxz quantum spin chain abstract we study many body localization properties of the disordered xxz spin chain in the ising phase disorder is introduced via a random magnetic field in the z direction we prove a strong form of dynamical exponential clustering for eigenstates in the droplet spectrum for any pair of local observables separated by a distance l the sum of the associated correlators over these states decays exponentially in l in expectation this exponential clustering persists under the time evolution in the droplet spectrum our result applies to the large disorder regime as well as to the strong ising phase at fixed disorder with bounds independent of the support of the observables

phase transitions in the q voter model with two types of stochastic driving we study a nonlinear q voter model with stochastic driving on a complete graph we investigate two types of stochasticity that using the language of social sciences can be interpreted as different kinds of nonconformity from a social point of view it is very important to distinguish between two types nonconformity so called anticonformity and independence a majority of work has suggested that these social differences may be completely irrelevant in terms of microscopic modeling that uses tools of statistical physics and that both types of nonconformity play the role of so called social temperature in this paper we clarify the concept of social temperature and show that different types of noise may lead to qualitatively different emergent properties in particular we show that in the model with anticonformity the critical value of noise increases with parameter q whereas in the model with independence the critical value of noise decreases with q moreover in the model with anticonformity the phase transition is continuous for any value of q whereas in the model with independence the transition is continuous for q 5 and discontinuous for q 5

splitting the voter potts model critical point recently some two dimensional models with double symmetric absorbing states were shown to share the same critical behavior that was called the voter universality class we show that for an absorbing states potts model with finite but further than nearest neighbor range of interactions the critical point is split into two critical points one of the ising type and the other of the directed percolation universality class similar splitting takes place in the three dimensional nearest neighbor model

dobrushin uniqueness theorem and logarithmic sobolev inequalities we formulate a condition on a local specification e on a countable product space m m being a riemannian manifold or a discrete set 1 1 assuring that the corresponding set of gibbs measures consists of a unique measure satisfying a logarithmic sobolev inequality

quantum states on harmonic lattices we investigate bosonic gaussian quantum states on an infinite cubic lattice in arbitrary spatial dimensions we derive general properties of such states as ground states of quadratic hamiltonians for both critical and non critical cases tight analytic relations between the decay of the interaction and the correlation functions are proven and the dependence of the correlation length on band gap and effective mass is derived we show that properties of critical ground states depend on the gap of the point symmetrized rather than on that of the original hamiltonian for critical systems with polynomially decaying interactions logarithmic deviations from polynomially decaying correlation functions are found

ordering dynamics in the voter model with aging abstract we study theoretically and numerically the voter model with memory dependent dynamics at the mean field level the internal age related to the time an individual spends holding the same state is added to the set of binary states of the population such that the activation probability p i for attempting a change of state has an explicit dependence on the internal age i we derive a closed set of integro differential equations describing the time evolution of the fraction of individuals with a given state and internal age and from it we obtain analytical results characterizing the behavior of the system close to the absorbing states in general different internal age dependent activation probabilities p i have different effects on the dynamics in the case of aging i e p i being a decreasing function of its argument i either the system reaches consensus or it gets trapped in a frozen state depending on whether the limiting value p is zero or positive and on the rate at which p i approaches p moreover when the system reaches consensus the fraction x t of nodes not holding the consensus state may decay exponentially with time or as a power law depending again on the specific details of the functional form of p i for the case of anti aging when the activation probability p i is an increasing function of i the system always reaches a steady state with coexistence of opinions exact conditions for having one or another behavior together with the equations and explicit expressions for the power law exponents are provided

quantum harmonic oscillator systems with disorder we study many body properties of quantum harmonic oscillator lattices with disorder a sufficient condition for dynamical localization expressed as a zero velocity lieb robinson bound is formulated in terms of the decay of the eigenfunction correlators for an effective one particle hamiltonian we show how state of the art techniques for proving anderson localization can be used to prove that these properties hold in a number of standard models we also derive bounds on the static and dynamic correlation functions at both zero and positive temperature in terms of one particle eigenfunction correlators in particular we show that static correlations decay exponentially fast if the corresponding effective one particle hamiltonian exhibits localization at low energies regardless of whether there is a gap in the spectrum above the ground state or not our results apply to finite as well as to infinite oscillator systems the eigenfunction correlators that appear are more general than those previously studied in the literature in particular we must allow for functions of the hamiltonian that have a singularity at the bottom of the spectrum we prove exponential bounds for such correlators for some of the standard models

quantum dynamics with mean field interactions a new approach we propose a new approach for the study of the time evolution of a factorized n particle bosonic wave function with respect to a mean field dynamics with a bounded interaction potential the new technique which is based on the control of the growth of the correlations among the particles leads to quantitative bounds on the difference between the many particle schrodinger dynamics and the one particle nonlinear hartree dynamics in particular the one particle density matrix associated with the solution to the n particle schrodinger equation is shown to converge to the projection onto the one dimensional subspace spanned by the solution to the hartree equation with a speed of convergence of order 1 n for all fixed times

multistable binary decision making on networks we propose a simple model for a binary decision making process on a graph motivated by modeling social decision making with cooperative individuals the model is similar to a random field ising model or fiber bundle model but with key differences on heterogeneous networks for many types of disorder and interactions between the nodes we predict discontinuous phase transitions with mean field theory which are largely independent of network structure we show how these phase transitions can also be understood by studying microscopic avalanches and describe how network structure enhances fluctuations in the distribution of avalanches we suggest theoretically the existence of a glassy spectrum of equilibria associated with a typical phase even on infinite graphs so long as the first moment of the degree distribution is finite this behavior implies that the model is robust against noise below a certain scale and also that phase transitions can switch from discontinuous to continuous on networks with too few edges numerical simulations suggest that our theory is accurate

dynamics of majority rule in two state interacting spin systems we introduce a two state opinion dynamics model where agents evolve by majority rule in each update a group of agents is specified whose members then all adopt the local majority state in the mean field limit where a group consists of randomly selected agents consensus is reached in a time that scales ln n where n is the number of agents on finite dimensional lattices where a group is a contiguous cluster the consensus time fluctuates strongly between realizations and grows as a dimension dependent power of n the upper critical dimension appears to be larger than 4 the final opinion always equals that of the initial majority except in one dimension

lieb robinson bounds and the exponential clustering theorem we give a lieb robinson bound for the group velocity of a large class of discrete quantum systems which can be used to prove that a non vanishing spectral gap implies exponential clustering in the ground state of such systems

spectral gap and exponential decay of correlations we study the relation between the spectral gap above the ground state and the decay of the correlations in the ground state in quantum spin and fermion systems with short range interactions on a wide class of lattices we prove that if two observables anticommute with each other at large distance then the nonvanishing spectral gap implies exponential decay of the corresponding correlation when two observables commute with each other at large distance the connected correlation function decays exponentially under the gap assumption if the observables behave as a vector under the u 1 rotation of a global symmetry of the system we use previous results on the large distance decay of the correlation function to show the stronger statement that the correlation function itself rather than just the connected correlation function decays exponentially under the gap assumption on a lattice with a certain self similarity in fractal dimensions d 2 in particular if the system is translationally invariant in one of the spatial directions then this self similarity condition is automatically satisfied we also treat systems with long range power law decaying interactions

exact results for kinetics of catalytic reactions the kinetics of an irreversible catalytic reaction on substrate of arbitrary dimension is examined in the limit of infinitesimal reaction rate reaction controlled limit we solve the dimer dimer surface reaction model or voter model exactly in arbitrary dimension d the density of reactive interfaces is found to exhibit a power law decay for d 2 and a slow logarithmic decay in two dimensions we discuss the relevance of these results for the monomer monomer surface reaction model

voter models on heterogeneous networks we study simple interacting particle systems on heterogeneous networks including the voter model and the invasion process these are both two state models in which in an update event an individual changes state to agree with a neighbor for the voter model an individual imports its state from a randomly chosen neighbor here the average time t n to reach consensus for a network of n nodes with an uncorrelated degree distribution scales as n ensuremath mu 1 2 ensuremath mu 2 where ensuremath mu k is the k text th moment of the degree distribution quick consensus thus arises on networks with broad degree distributions we also identify the conservation law that characterizes the route by which consensus is reached parallel results are derived for the invasion process in which the state of an agent is exported to a random neighbor we further generalize to biased dynamics in which one state is favored the probability for a single fitter mutant located at a node of degree k to overspread the population char22 the fixation probability char22 is proportional to k for the voter model and to 1 k for the invasion process

metastability in stochastic dynamics of disordered mean field models we study a class of markov chains that describe reversible stochastic dynamics of a large class of disordered mean field models at low temperatures our main purpose is to give a precise relation between the metastable time scales in the problem to the properties of the rate functions of the corresponding gibbs measures we derive the analog of the wentzell freidlin theory in this case showing that any transition can be decomposed with probability exponentially close to one into a deterministic sequence of admissible transitions for these admissible transitions we give upper and lower bounds on the expected transition times that differ only by a constant factor the distributions of the rescaled transition times are shown to converge to the exponential distribution we exemplify our results in the context of the random field curie weiss model

anticonformity or independence insights from statistical physics the aim of this paper is to examine how different types of social influence introduced on the microscopic individual level manifest on the macroscopic level i e in the society the inspiration for this task came mainly from two sources social psychology that recognize two different types of nonconformity anticonformity and independence and the observation related to the agent based modeling that was verbalized in 2002 by macy and willer that there was a little effort to provide analysis of how results differ depending on the model designs to achieve the goal we propose a generalized model of opinion dynamics that as a special cases reduces to the linear voter model sznajd model q voter model and the majority rule we use the model to examine the differences that appear at the macroscopic level under the influence of two types of nonconformity introduced on the microscopic level we answer the question if the observed differences are universal or model dependent

universal time fluctuations in near critical out of equilibrium quantum dynamics out of equilibrium quantum systems display complex temporal patterns such time fluctuations are generically exponentially small in the system volume and therefore can be safely ignored in most of the cases however if one consider small quench experiments time fluctuations can be greatly enhanced we show that time fluctuations may become stronger than other forms of equilibrium quantum fluctuations if the quench is performed close to a critical point for sufficiently relevant operators the full distribution function of dynamically evolving observable expectation values becomes a universal function uniquely characterized by the critical exponents and the boundary conditions at regular points of the phase diagram and for nonsufficiently relevant operators the distribution becomes gaussian our predictions are confirmed by an explicit calculation on the quantum ising model

a complete renormalization group trajectory between two fixed points we give a rigorous nonperturbative construction of a massless discrete trajectory for wilson s exact renormalization group the model is a three dimensional euclidean field theory with a modified free propagator the trajectory realizes the mean field to critical crossover from the ultraviolet gaussian fixed point to an analog recently constructed by brydges mitter and scoppola of the wilson fisher nontrivial fixed point

witten laplacian method for generalized models of kac type we first study the exponential decay of correlations for classical models of kac type using recent results j jon on spectral properties of witten laplacians their range of projections and brascamp lieb inequality integral equ oper theory 36 3 288 324 2000 10 1007 bf01213926 about the witten laplacians we improve the bounds obtained a lo witten laplacian methods for the decay of correlations j stat phys 132 2 355 396 2008 10 1007 s10955 008 9547 6 to justify the conjecture that the critical point in the d 1 dimensional kac model is given by c 1 4d we also provide a new approach for proving the exponential decay of the usual truncated correlations which is more direct than the existing ones in the sense that it does not use any cluster type expansions