Disentanglement Dynamics in Nonequilibrium Environments

We theoretically study the non-Markovian disentanglement dynamics of a two-qubit system coupled to nonequilibrium environments with nonstationary and non-Markovian random telegraph noise statistical properties. The reduced density matrix of the two-qubit system can be expressed as the Kraus representation in terms of the tensor products of the single qubit Kraus operators. We derive the relation between the entanglement and nonlocality of the two-qubit system which are both closely associated with the decoherence function. We identify the threshold values of the decoherence function to ensure the existences of the concurrence and nonlocal quantum correlations for an arbitrary evolution time when the two-qubit system is initially prepared in the composite Bell states and the Werner states, respectively. It is shown that the environmental nonequilibrium feature can suppress the disentanglement dynamics and reduce the entanglement revivals in non-Markovian dynamics regime. In addition, the environmental nonequilibrium feature can enhance the nonlocality of the two-qubit system. Moreover, the entanglement sudden death and rebirth phenomena and the transition between quantum and classical nonlocalities closely depend on the parameters of the initial states and the environmental parameters in nonequilibrium environments.     

Equilibrium Sampling From Nonequilibrium Dynamics

We present some applications of an Interacting Particle System (IPS) methodology to the field of Molecular Dynamics. This IPS method allows several simulations of a nonequilibrium random process to keep closer to equilibrium at each time, thanks to a selection mechanism based on the relative virtual work induced on the system. It is therefore an efficient improvement of usual nonequilibrium simulations, which can be used to compute canonical averages, free energy differences, and typical transitions paths. AMS: 65C05 65C35 80A10     

New developments in the Nonequilibrium Dynamics of spin glasses

We present an overview of recent developments in the nonequilibrium dynamics of spin glasses. The prevailing theoretical pictures are described and discussed in light of numerical results and experimental observations. We focus on aging phenomena like waiting-time-dependent length scales, scaling of two-time quantities, more complex temperature protocols during aging, and the violation of the fluctuation–dissipation theorem. Finally, aging in quantum spin glass models coupled to a dissipative bath is discussed.     

A Bit Shift Image Encryption Algorithm Based on Double Chaotic Systems

A chaotic system refers to a deterministic system with seemingly random irregular motion, and its behavior is uncertain, unrepeatable, and unpredictable. In recent years, researchers have proposed various image encryption schemes based on a single low-dimensional or high-dimensional chaotic system, but many algorithms have problems such as low security. Therefore, designing a good chaotic system and encryption scheme is very important for encryption algorithms. This paper constructs a new double chaotic system based on tent mapping and logistic mapping. In order to verify the practicability and feasibility of the new chaotic system, a displacement image encryption algorithm based on the new chaotic system was subsequently proposed. This paper proposes a displacement image encryption algorithm based on the new chaotic system. The algorithm uses an improved new nonlinear feedback function to generate two random sequences, one of which is used to generate the index sequence, the other is used to generate the encryption matrix, and the index sequence is used to control the generation of the encryption matrix required for encryption. Then, the encryption matrix and the scrambling matrix are XORed to obtain the first encryption image. Finally, a bit-shift encryption method is adopted to prevent the harm caused by key leakage and to improve the security of the algorithm. Numerical experiments show that the key space of the algorithm is not only large, but also the key sensitivity is relatively high, and it has good resistance to various attacks. The analysis shows that this algorithm has certain competitive advantages compared with other encryption algorithms.     

Resonant Forcing of Chaotic Dynamics

We study resonances of multidimensional chaotic map dynamics. We use the calculus of variations to determine the additive forcing function that induces the largest response, that is, the greatest deviation from the unperturbed dynamics. We include the additional constraint that only select degrees of freedom be forced, corresponding to a very general class of problems in which not all of the degrees of freedom in an experimental system are accessible to forcing. We find that certain Lagrange multipliers take on a fundamental physical role as the efficiency of the forcing function and the effective forcing experienced by the degrees of freedom which are not forced directly. Furthermore, we find that the product of the displacement of nearby trajectories and the effective total forcing function is a conserved quantity. We demonstrate the efficacy of this methodology with several examples.     

Nonequilibrium Dynamics of Quantum Fields in Inflationary Cosmology

We summarize a recent study (with B. L. Hu) ofthe nonequilibrium dynamics of an unbroken-symmetryinflaton field during postinflationary reheating, duringwhich the energy density contained in the expectation value of the inflaton field is rapidlytransferred to inhomogeneous quantum modes of theinflaton field. The coupled dynamics of the expectationvalue (mean field) of a scalar inflaton field with anunbroken global O(N) symmetry and its quantum varianceis studied using the leading-order, large-Napproximation in a spatially flatFriedmann–Robertson–Walker (FRW) backgroundspacetime. The initial conditions for the mean field, variance, and Hubbleparameter were chosen to be consistent with conditionsat the end of slow roll in chaotic inflation.Backreaction of the dynamics of the mean field on thespacetime is incorporated self-consistently using thesemiclassical Einstein equation. The coupled dynamicalequations for the mean field, variance, and scale factorare solved for various choices of the mean field amplitude at the end of the slow-roll period,in order to determine the effect of spacetime curvatureon preheating, the parametricresonance-induced, rapid transfer of energy from themean field to the inhomogeneous inflaton modes. Itis shown that cosmic expansion can dramatically effectthe efficiency of preheating in the particular modelstudied.     

Nonequilibrium Linear Response for Markov Dynamics,II: Inertial Dynamics

We continue our study of the linear response of a nonequilibrium system. This Part II concentrates on models of open and driven inertial dynamics but the structure and the interpretation of the result remain unchanged: the response can be expressed as a sum of two temporal correlations in the unperturbed system, one entropic, the other frenetic. The decomposition arises from the (anti)symmetry under time-reversal on the level of the nonequilibrium action. The response formula involves a statistical averaging over explicitly known observables but, in contrast with the equilibrium situation, they depend on the model dynamics in terms of an excess in dynamical activity. As an example, the Einstein relation between mobility and diffusion constant is modified by a correlation term between the position and the momentum of the particle.     

Nonequilibrium dynamics in lattice ecosystems: Chaotic stability and dissipative structures

A generalized coupled map lattice (CML) model of ecosystem dynamics is presented. We consider the spatiotemporal behavior of a prey-predator map, a model of host-parasitoid interactions, and two-species competition. The latter model can show phase separation of domains (Turing-like structures) even when chaos is present. We also use this CML model to explore the time evolution and structural properties of ecological networks built with a set of N competing species. The May-Wigner criterion is applied as a measure of stability, and some regularities in the stable networks observed are discussed.     

Microscopic Reversibility for Nonequilibrium Classical Open Systems

We rigorously show that the probability to have a specific trajectory of an externally perturbed classical open system satisfies a universal symmetry for Hamiltonian dynamics. It connects the ratio between the probabilities of time forward and reversed trajectories to a degree of the time reversal asymmetry of the final phase space distribution in a model-independent framework. Especially, it amounts to a nonequilibrium generalization of the detailed balance between the probabilities of the forward and reversed trajectories under the condition that the initial phase space distribution is described by an equilibrium ensemble. An expression of the microscopic reversibility for the subsystem is also derived based on this relation.     

Universal Dynamics,¶a Unified Theory of Complex Systems.¶Emergence, Life and Death

A universal framework is proposed, where all laws are regularities of relations between things or agents. Parts of the world at one or all times are modelled as networks called \system s with a minimum of axiomatic properties. A notion of locality is introduced by declaring some relations direct (or links). Dynamics is composed of basic constituents called mechanisms. They are conditional actions of basic local structural transformations (“enzymes”): indirect relations become direct (friend of friend becomes friend), links are removed, objects copied. This defines a kind of universal chemistry. I show how to model basic life processes in a self contained fashion as a kind of enzymatic computation. The framework also accommodates the gauge theories of fundamental physics. Emergence creates new functionality by cooperation – nonlocal phenomena arise out of local interactions. I explain how this can be understood in a reductionist way by multiscale analysis (e.g. renormalization group). Received: 20 April 2000 / Accepted: 20 April 2000     

Universal Single-Mode Lasing in Fully Chaotic Billiard Lasers

By numerical simulations and experiments of fully chaotic billiard lasers, we show that single-mode lasing states are stable, whereas multi-mode lasing states are unstable when the size of the billiard is much larger than the wavelength and the external pumping power is sufficiently large. On the other hand, for integrable billiard lasers, it is shown that multi-mode lasing states are stable, whereas single-mode lasing states are unstable. These phenomena arise from the combination of two different nonlinear effects of mode-interaction due to the active lasing medium and deformation of the billiard shape. Investigations of billiard lasers with various shapes revealed that single-mode lasing is a universal phenomenon for fully chaotic billiard lasers.     

Computation of Current Cumulants for Small Nonequilibrium Systems

We analyze a systematic algorithm for the exact computation of the current cumulants in stochastic nonequilibrium systems, recently discussed in the framework of full counting statistics for mesoscopic systems. This method is based on identifying the current cumulants from a Rayleigh-Schrödinger perturbation expansion for the generating function. Here it is derived from a simple path-distribution identity and extended to the joint statistics of multiple currents. For a possible thermodynamical interpretation, we compare this approach to a generalized Onsager-Machlup formalism. We present calculations for a boundary driven Kawasaki dynamics on a one-dimensional chain, both for attractive and repulsive particle interactions.     

Frequency—Locking in Coupled Chaotic Systems

A novel approach is presented for measuring the phase synchronization(frequency-Locking)of coupled N nonidentical oscillators,which can characterize frequency-locking for chaotic systems without well-defined phase by measuring the mean frequency.Numerical simulations confirm the existence of frequency-locking.The relations between the mean frequency and the coupling strength and the frequency mismatch are given.For the coupled hyperchaotic systems.the frequency-locking can be better characterized by more than one mean frequency curves.