Long Term Behaviour of a Reversible System of Interacting Random Walks

This paper studies the long-term behaviour of a system of interacting random walks labelled by vertices of a finite graph. We show that the system undergoes phase transitions, with different behaviour in various regions, depending on model parameters and properties of the underlying graph. We provide the complete classification of the long-term behaviour of the corresponding continuous time Markov chain, identifying whether it is null recurrent, positive recurrent, or transient. The proofs are partially based on the reversibility of the model, which allows us to use the method of electric networks. We also provide some alternative proofs (based on the Lyapunov function method and the renewal theory), which are of interest in their own right, since they do not require reversibility and can be applied to more general situations.

     

Conservative Interacting Particles System with Anomalous Rate of Ergodicity

We analyse certain conservative interacting particle system and establish ergodicity of the system for a family of invariant measures. Furthermore, we show that convergence rate to equilibrium is exponential. This result is of interest because it presents counterexample to the standard assumption of physicists that conservative system implies polynomial rate of convergence. The system in question is stochastic rather than deterministic.     

Statistics of a Stokes-Antistokes Interacting Boson System with Damping

The statistics of a system of four boson modes in Stokes-Antistokes interaction is considered with respect to the influence of damping in one mode. The time evolution of the system is calculated. The mean particle numbers and the factorial moments of photon number distribution are calculated. Numerical results show strong dependence on bath temperature but only weak influence of the bath coupling strength. In the combined Stokes-Antistokes system Antibunching appears if the bath temperature is low.     

Effects of Time Delay on Three Interacting Species System with Noise

We study the effects of time delay in three interacting species system with noise. The time evolution and spatiotemporal pattern in the Lotka-Volterra model of three interacting species with noise and time delay were investigated by means of stochastic simulation. Our results indicate that: (i) Time delay induces the synchronously periodic oscillations of the three species densities; (ii) Time delay cause the spatiotemporal pattern to be concentrated.     

A Tachyonic Scalar Field with Mutually Interacting Components

We investigate the tachyonic cosmological potential V(?) in two different cases of the quasi-exponential expansion of universe and discuss various forms of interaction between the two components—matter and the cosmological constant—of the tachyonic scalar field, which lead to the viable solutions of their respective energy densities. The distinction among the interaction forms is shown to appear in the O _m (x) diagnostic. Further, the role of the high- and low-redshift observations of the Hubble parameter is discussed to determine the proportionality constants and hence the correct form of matter–cosmological constant interaction.     

Bifurcations in a System of Interacting Fronts

We show that the bifurcation scenario in a high-dimensional system with interacting moving fronts can be related to the universal U-sequence which is known from the symbolic analysis of iterated one-dimensional maps. This connection is corroborated for a model of a semiconductor superlattice, which describes the complex dynamics of electron accumulation and depletion fronts. By a suitable Poincaré section we reduce the dynamics to a low-dimensional iterated map, for which in the most elementary case the bifurcation points can be determined analytically.     

Mean Field Analysis of Large-Scale Interacting Populations of Stochastic Conductance-Based Spiking Neurons Using the Klimontovich Method

We investigate the dynamics of large-scale interacting neural populations, composed of conductance based, spiking model neurons with modifiable synaptic connection strengths, which are possibly also subjected to external noisy currents. The network dynamics is controlled by a set of neural population probability distributions (PPD) which are constructed along the same lines as in the Klimontovich approach to the kinetic theory of plasmas. An exact non-closed, nonlinear, system of integro-partial differential equations is derived for the PPDs. As is customary, a closing procedure leads to a mean field limit. The equations we have obtained are of the same type as those which have been recently derived using rigorous techniques of probability theory. The numerical solutions of these so called McKean–Vlasov–Fokker–Planck equations, which are only valid in the limit of infinite size networks, actually shows that the statistical measures as obtained from PPDs are in good agreement with those obtained through direct integration of the stochastic dynamical system for large but finite size networks. Although numerical solutions have been obtained for networks of Fitzhugh–Nagumo model neurons, which are often used to approximate Hodgkin–Huxley model neurons, the theory can be readily applied to networks of general conductance-based model neurons of arbitrary dimension.     

原子与耦合腔相互作用系统中量子态保真度演化

在每个耦合腔中囚禁一个二能级原子并考虑原子与腔场的共振,研究二能级原子与耦合腔的相互作用.数值计算了耦合腔系统中系统、原子和腔场的保真度演化,讨论了腔场间耦合系数变化对保真度演化的影响.结果表明:随着腔场间耦合系数的增大,系统和原子的保真度从不规则振荡逐渐转变为准周期性振荡;腔场的保真度周期性变化;随腔场间耦合系数的增大,原子保真度降低,腔场的保真度增大.     

Entanglement for a Two-Level Atomic System Interacting with Two-Mode Spin States

A key element in the architecture of quantum information processing is a reliable physical interface between fields and qubits. Here, we study the population transfer and entanglement for a two-level atomic system interacting with entangled spin coherent states (ESCSs) considering one- and two-mode interactions. The results show that decrease in the spin number provides a periodic behavior of the entanglement exhibiting the sudden death and birth phenomena. For large values of spin, the atom–field system stabilizes at high value of entanglement during the time evolution exhibiting maximum correlations for both cases of one- and two-mode interactions. Finally, we find an interesting correlation between the entanglement and the population transfer during the time evolution. In particular, we show that the population may be used as an indicator of nonlocal correlations in the system under consideration.     

Exactly Solvable Model of a Two-Level Quantum System Interacting with Spin Environment

An exactly solvable model of a two-level quantum system interacting with spin environment is considered. The interaction is assumed to be such that the state of the environment is conserved. Dynamics of the reduced density matrix of the two-level system is calculated for arbitrary coupling strength. The stationary state of the spin is obtained explicitly in the t limit.     

Entanglement Evolution of a 2-Qutrit System Interacting with a Fermionic Bath

Based on the algebraic entanglement measure proposed [G. Vidal et al., Phys. Rev. A 65 (2002) 032314],we study the entanglement evolution of both pure quantum states and mixed ones of 2-qutrit system in a symmetrybroken environment consisting of a fermionic bath. Entanglement of states will decrease or remain constant under the influence of environment, and the class of states which remain unchanged has been found out.     

Entanglement Evolution of a 2-Qutrit System Interacting with a Fermionic Bath

Based on the algebraic entanglement measure proposed [G. Vidal et al., Phys. Rev. A 65 （2002） 032314],we study the entanglement evolution of both pure quantum states and mixed ones of 2-qutrit system in a symmetrybroken environment consisting of a fermionic bath. Entanglement of states will decrease or remain constant under the influence of environment, and the class of states which remain unchanged has been found out.     

Entropy Dynamics in the System of Interacting Qubits

The classical second law of thermodynamics demands that an isolated system evolves with a nondiminishing entropy. This holds as well in quantum mechanics if the evolution of the energy-isolated system can be described by a unital quantum channel. At the same time, the entropy of a system evolving via a nonunital channel can, in principle, decrease. Here, we analyze the behavior of entropy in the context of the H-theorem. As exemplary phenomena, we discuss the action of a Maxwell demon (MD) operating a qubit and the processes of heating and cooling in a two-qubit system. Further we discuss how small initial correlations between a quantum system and a reservoir affect the entropy increase during the quantum-system evolution.     

原子与热库相互作用系统中的三体纠缠特性

利用Ket-Bra纠缠态方法,求解了原子与热库相互作用系统中的密度矩阵主方程,得到了密度矩阵的演化表达式.考虑三个二能级原子独立与热库相互作用的情况,利用负本征值度量三体纠缠,研究了系统中原子间的三体纠缠特性.采用数值计算方法,讨论了热库平均光子数和原子自发辐射率对原子间三体纠缠特性的影响.研究结果表明:随原子自发辐射率和热库平均光子数的增大,原子间的三体纠缠衰减加快.     

三个两能级原子与数态场相互作用的纠缠特性

通过计算并发度和线性熵研究了初始处于GHZ态的三个两能级原子与数态场相互作用系统的纠缠动力学特性,讨论了场的初始光子数对并发度和线性熵的影响.结果表明,腔内两原子之间的纠缠出现突然产生现象,而且可以通过改变场的初始光子数来控制产生纠缠的阈值时间和纠缠的最大值.对腔外原子的探测导致了并发度随时间的演化呈现周期性规律,场的光子数的增加不但减小了并发度的最大值,而且缩短了并发度的演化周期.     

三个两能级原子与数态场相互作用的纠缠特性

通过计算并发度和线性熵研究了初始处于GHZ态的三个两能级原子与数态场相互作用系统的纠缠动力学特性,讨论了场的初始光子数对并发度和线性熵的影响.结果表明,腔内两原子之间的纠缠出现突然产生现象,而且可以通过改变场的初始光子数来控制产生纠缠的阈值时间和纠缠的最大值.对腔外原子的探测导致了并发度随时间的演化呈现周期性规律,场的光子数的增加不但减小了并发度的最大值,而且缩短了并发度的演化周期.     

On the Motion of a Charged Particle Interacting with an Infinitely Extended System

 We study the time evolution of a charged particle moving in a medium under the action of a constant electric field E. In the framework of fully Hamiltonian models, we discuss conditions on the particle/medium interaction which are necessary for the particle to reach a finite limit velocity. We first consider the case when the charged particle is confined in an unbounded tube of ℝ³. The electric field E is directed along the symmetry axis of the tube and the particle also interacts with an infinitely many particle system. The background system initial conditions are chosen in a set which is typical for any reasonable thermodynamic (equilibrium or non-equilibrium) state. We prove that, for large E and bounded interactions between the charged particle and the background, the velocity v(t) of the charged particle does not reach a finite limit velocity, but it increases to infinite as: |v(t)−Et|≤C ₀ (1+t), where C ₀ is a constant independent of E. As a corollary we obtain that, if the initial conditions of the background system are distributed according to any Gibbs state, then the average velocity of the charged particle diverges as time goes to infinite. This result is obtained for E large enough in comparison with the mean energy of the Gibbs state. We next study the one-dimensional case, in which the estimates can be improved. We finally discuss, at an heuristic level, the existence of a finite limit velocity for unbounded interactions, and give some suggestions about the case of small electric fields. Received: 7 March 2002 / Accepted: 23 September 2002 Published online: 8 January 2003 RID="*" ID="*" Work partially supported by the GNFM-INDAM and the Italian Ministry of the University. Communicated by J.L. Lebowitz