Order and disorder in the approach to equilibrium of a classical gas

We study the approach to equilibrium of a classical gas. The initial condition corresponds to a Maxwell velocity distribution, but to a nonequilibrium binary correlation. We consider two cases. In the first, there are initially no spatial correlations, while in the second, initial correlations correspond to long-range spatial order. We show that the gas leaves the Maxwell velocity distribution function in the process of building up equilibrium correlations. The spatial correlations in the equilibrium state are seen to emerge from a self-organization process in the gas. Non-Markovian effects play an essential role in this process by coupling the velocity distribution and the binary correlations. For the case of initial long-range correlations we obtain anti-Boltzmann behavior in the evolution of the velocity distribution as the Boltzmann entropy decreases from the nonequilibrium to the equilibrium state. For this case we also have nontrivial behavior on a short time scale due to the non-Markovian effects. The approach used here is based on the theory of subdynamics as developed in previous publications. The results obtained show the interplay between irreversible processes leading to disorder and to order in a classical gas.     

Decay of entanglement in coupled,driven systems with bipartite decoherence

We analyze a system of two qubits embedded in two different environments. The qubits are coupled to each other and driven on-resonance by two external classical sources. In the secular limit, we obtain exact analytical results for the evolution of the system for several classes of two-qubit mixed initial states. For Werner states we show that the decay of entanglement does not depend on coupling. For other initial states with “X"-type density matrices we find that the sudden death time displays a rich dependence on the coupling energy and state parameters due to the existence of processes of delayed sudden birth of entanglement.     

The Effect of Electromagnetically Induced Transparency in Classical Systems

We develop a classical model of the recently popular parametric effect of electromagnetically induced transparency (EIT), i.e., the formation of a “transparency window” inside a resonance absorption line of a three-level quantum system, which is accompanied by a record strong slowing of the probe wave. Based on this model, we consider the EIT effect for electromagnetic waves at frequencies of the electron-cyclotron resonance in a cold plasma. The parametric (three-wave) interaction of two electromagnetic modes (the frequency of one of these modes is equal to the electron gyrofrequency) with the electrostatic mode is considered. It is shown that the resonance growth in the electron oscillations at the gyrofrequency can be damped due to the parametric coupling with the collective electrostatic oscillations. Similar to analogous quantum systems, the group slowing of the probe electron-cyclotron wave in the transparency window takes place in the case considered.     

Squeezing Exchange and Entanglement between Resonantly Coupled Modes

We study the problem of squeezing exchange between two modes of the electromagnetic field modeled by quantum oscillators for the most general weak bilinear resonance coupling. Also we introduce a new measure of entanglement based on the cross covariances of the quadrature components of interacting modes. We compare the covariance measure with the measures based on the von Neumann and linear entropies of the subsystems, studying their dependences on time, coupling constants, and the initial state in the cases of parametric amplification and parametric conversion. In particular, we show that coherent states remain disentagled for all times and for any choice of coupling constants in the case of parametric converter (with accuracy up to second-order terms with respect to the strength of coupling). Also, we demonstrate that no bilinear coupling can squeeze the initial coherent state or improve the squeezing of the initial squeezed state in the case of a parametric amplifier. A strong sensitivity of the character of evolution to the choice of the set of coupling constants is discovered in the case of a parametric converter.     

Emergent organization of oscillator clusters in coupled self-regulatory chaotic maps

Here we introduce a model of parametrically coupled chaotic maps on a one-dimensional lattice. In this model, each element has its internal self-regulatory dynamics, whereby at fixed intervals of time the nonlinearity parameter at each site is adjusted by feedback from its past evolution. Additionally, the maps are coupled sequentially and unidirectionally, to their nearest neighbor, through the difference of their parametric variations. Interestingly we find that this model asymptotically yields clusters of superstable oscillators with different periods. We observe that the sizes of these oscillator clusters have a power-law distribution. Moreover, we find that the transient dynamics gives rise to a 1/f power spectrum. All these characteristics indicate self-organization and emergent scaling behavior in this system. We also interpret the power-law characteristics of the proposed system from an ecological point of view.      

Nonthermal fixed points: effective weak coupling for strongly correlated systems far from equilibrium

Strongly correlated systems far from equilibrium can exhibit scaling solutions with a dynamically generated weak coupling. We show this by investigating isolated systems described by relativistic quantum field theories for initial conditions leading to nonequilibrium instabilities, such as parametric resonance or spinodal decomposition. The nonthermal fixed points prevent fast thermalization if classical-statistical fluctuations dominate over quantum fluctuations. We comment on the possible significance of these results for the heating of the early Universe after inflation and the question of fast thermalization in heavy-ion collision experiments.     

On the Theory of “Inversionless” Free-Electron Maser

We develop a linear theory of cyclotron parametric instability in systems that are classical analogs of quantum inversionless lasers. Interaction of bichromatic radiation with an ensemble of classical electron oscillators having a modulated distribution function is considered taking into account that the cyclotron-resonance conditions is valid both for each of the two spectral components at high harmonics and for their beat wave. It is shown that the ballistic restructuring of the modulated fraction of the electrons leads to stabilization of the instability. In this case, a peculiar nonreciprocal regime of the parametric particle-field interaction is realized in which the evolution of the high-frequency wave is independent of the low-frequency mode, though the former wave affects the behavior of the latter one.     

Relaxation of Bose-condensate oscillations in a mesoscopic system at <Emphasis Type="Italic">T</Emphasis>=0

A general system of nonlinear equations describing the nondissipative evolution of an oscillating Bose condensate is presented. The relaxation of the transverse oscillations of the condensate in a trap of cylindrical symmetry is considered. The evolution is due to the parametric resonance coupling the transverse mode with the longitudinal ones. Nonlinear rescattering in the subsystem of discrete longitudinal modes leads to the suppression of back energy recovery, generating the nondissipative nonmonotonic relaxation of the transverse oscillations of the condensate.     

集合预报物理基础的探讨

将集合预报中的每次积分算程视为非平衡统计物理理论中的准粒子轨迹，由此对Lorenz模型 进行了数值试验，计算了初值位于不同性质平衡态附近时准粒子数处于基态和第一激发态随 时间的演化.结果证明：(1)若动力系统在整个相空间内存在稳定的平衡态，在稳定的平衡态 附近，系统随时间长期演化行为是可预测的.(2)若动力系统在整个相空间内不存在任何稳定 的平衡态，初值位于远离非稳定的平衡态，则在1—2周内准粒子多数分布在低能量态，即预 报是最可几率的.(3)若初始状态位于非稳定平衡态附近，系统随时间的演化几乎是不可预测 的.这从理论上说明了作大量积分算程的集合预报其效果会比单一初值的单程积分要好.这就 从物理上对集合预报能提高准确率提供了一种解释. 关键词： 集合预报 Lorenz模型 正则分布 概率密度分布     

Classical Representation of a Quantum System at Equilibrium

A quantum system at equilibrium is represented by a corresponding classical system, chosen to reproduce the thermodynamic and structural properties. The objective is to develop a means for exploiting strong coupling classical methods (e.g., MD, integral equations, DFT) to describe quantum systems. The classical system has an effective temperature, local chemical potential, and pair interaction that are defined by requiring equivalence of the grand potential and its functional derivatives with respect to the external and pair potentials for the classical and quantum systems. Practical inversion of this mapping for the classical properties is effected via the hypernetted chain approximation, leading to representations as functionals of the quantum pair correlation function. As an illustration, the parameters of the classical system are determined approximately such that ideal gas and weak coupling RPA limits are preserved (© 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Trace Distance and Level Crossing in Spin-Bosen Model with Added Classical Driving Fields

By making use of the trace distance as a measure we investigate the influence of classical driving fields on a open quantum system when the system and its environment are initially in a correlated state. It is shown that the amount of trace distance is sensitive to the classical driving fields which implies that the information flowing between open system and its environment can be controlled by the classical driving fields. Furthermore, we also explore the dependence of the trace distance on the initial parameters when the total system is considered in the thermal equilibrium state. We find that the trace distance on the coupling strength can be used to demonstrate the level crossing of the ground state of the system. In particular, the classical driving fields have significant effect on the level crossing of the ground state.     

Manifestation of Arnol'd diffusion in quantum systems

We study an analog of the classical Arnol'd diffusion in a quantum system of two coupled nonlinear oscillators one of which is governed by an external periodic force with two frequencies. In a classical model this very weak diffusion happens in a narrow stochastic layer along the coupling resonance and leads to an increase of the total energy of the system. We show that quantum dynamics of wave packets mimics, up to some extent, global properties of the classical Arnol'd diffusion. This specific diffusion represents a new type of quantum dynamics and may be observed, for example, in 2D semiconductor structures (quantum billiards) perturbed by time-periodic external fields.     

Stochastic gain in population dynamics

We introduce an extension of the usual replicator dynamics to adaptive learning rates. We show that a population with a dynamic learning rate can gain an increased average payoff in transient phases and can also exploit external noise, leading the system away from the Nash equilibrium, in a resonancelike fashion. The payoff versus noise curve resembles the signal to noise ratio curve in stochastic resonance. Seen in this broad context, we introduce another mechanism that exploits fluctuations in order to improve properties of the system. Such a mechanism could be of particular interest in economic systems.     

Dynamics of an atom coupled through a parametric frequency converter with quantum and classical fields

In this communication we introduce a model of a two-level system which represents the interaction between an atom and external quantum and classical electric fields through a parametric frequency converter. We show that the system can be reduced to an effective Jaynes-Cummings model by adequate adjustment of the field coupling in the frequency converter. The atom dynamics and the atom-quantum field entanglement are then shown to be controlled through the classical field.     

Chaotic delocalization of two interacting particles in the classical Harper model

We study the problem of two interacting particles in the classical Harper model in the regime when one-particle motion is absolutely bounded inside one cell of periodic potential. The interaction between particles breaks integrability of classical motion leading to emergence of Hamiltonian dynamical chaos. At moderate interactions and certain energies above the mobility edge this chaos leads to a chaotic propulsion of two particles with their diffusive spreading over the whole space both in one and two dimensions. At the same time the distance between particles remains bounded by one or two periodic cells demonstrating appearance of new composite quasi-particles called chaons. The effect of chaotic delocalization of chaons is shown to be rather general being present for Coulomb and short range interactions. It is argued that such delocalized chaons can be observed in experiments with cold atoms and ions in optical lattices.     

Quantum corrections to the entropy in a driven quantum Brownian motion model

The quantum Brownian motion model is a typical model in the study of nonequilibrium quantum thermodynamics. Entropy is one of the most fundamental physical concepts in thermodynamics.In this work, by solving the quantum Langevin equation, we study the von Neumann entropy of a particle undergoing quantum Brownian motion. We obtain the analytical expression of the time evolution of the Wigner function in terms of the initial Wigner function. The result is applied to the thermodynamic equilibrium initial state, which reproduces its classical counterpart in the high temperature limit. Based on these results, for those initial states having well-defined classical counterparts, we obtain the explicit expression of the quantum corrections to the entropy in the weak coupling limit. Moreover, we find that for the thermodynamic equilibrium initial state, all terms odd in h are exactly zero. Our results bring important insights to the understanding of entropy in open quantum systems.     

“Inversionless” stimulated emission of radiation by nonequilibrium ensembles of classical oscillators

We find classical analogs of quantum systems capable of stimulated emission of radiation in the absence of inversion. We show that cyclotron parametric instability in low-frequency modulation of the distribution function of resonant particles can amplify a bichromatic high-frequency field when amplification of each spectral component separately is impossible. We point to similar modes for a Cherenkov resonance and a model system with lumped parameters. Finally, we suggest using this effect for converting microwave radiation to a higher frequency. Zh. éksp. Teor. Fiz. 112, 1176–1196 (October 1997)     

磁声参量振荡的理论

在本文中,我们从磁-弹性耦合的宏观表达式,通过经典场论的方法,求得弹性振动和磁振璗的耦合方程,用来分析了伴随波长约等于铁氧体样品的线度的声振动而存在的磁振璗(磁声模)。文中指出,Spencer和LeCraw所发现的磁声效应是磁声模和静磁模在注入场的激发下产生的参量振璗现象(也可以说是热声子的电磁讯号的放大)。我们引用Berk等人在讨论一种半静磁操作放大器的文章中给出的公式,算出Spencer-LeCraw实验所需要的功率,其结果与记录的数据相接近。我们提出了使任一静磁模配合磁声模产生振璗的调谐条件以及降低激发功率和观测几十到几百兆赫的声频的办法。通过磁声模和静磁模的交变场向量的空间对称性的分析,我们推导出磁声参量振璗的选择定则:对于球体三个主要弹性振动模(旋转模、向径模和椭球模),(1)静磁模(n,m,r)的Walker指标n是偶数者不产生磁声效应;(2)指标m是奇数者不与旋转模产生磁声效应,m是偶数者不与向径模或椭球模产生磁声效应。我们也举出第一类本征振动中有只可能和n是偶数、m是奇数的静磁模产生参量振璗的例子。Spencer-LeCraw局限于使静磁场调谐在(110)模上,所观察到的现象仅仅是本文所给出理论预见的一个特殊情况。他们发现了椭球模和向径模的频率显著地出现,但并无旋转模的频率,这是上述的选择定则的具体验证。最后,我们指出,热声子的参量放大可形成铁氧体微波放大器的噪声的来源。     

基于荧光非共线光参量放大光谱技术的溶剂化动力学研究中的光谱矫正

利用荧光非共线光参量放大光谱技术测量了DCM染料乙醇溶液的溶剂化动力学过程. 实验结果表明,瞬态荧光光谱经过光谱矫正后,可以产生准确的溶剂化相关函数以及溶剂化过程中瞬态光谱峰值频率移动. 本文的工作表明荧光非共线光参量放大光谱技术有益同时关注荧光强度动力学以及光谱谱型演化的研究领域.