We systematically investigate master equations involving double-bracket dissipators in the classical limit. Dissipators defined by double commutators arise naturally in dephasing dynamics, while those defined by double anticommutators are typically associated with noisy Hamiltonians. The classical limit of such master equations is derived by reformulating the dissipative open dynamics in phase space using the Wigner-Weyl transform and Moyal bracket formalism, and by identifying the leading-order terms in a systematic
ℏ-expansion. We first analyze a double-commutator master equation associated with energy diffusion, and then turn to master equations containing a double anticommutator with the system Hamiltonian, recently derived in the context of noisy non-Hermitian systems. For both classes of double-bracket equations, we establish a gradient-flow representation of the dynamics within both the quantum and semiclassical formalisms. We further study the semiclassical evolution generated by double-bracket master equations for the harmonic (integrable) and driven anharmonic (chaotic) oscillators, considering both classical and quantum initial states. The dynamics are characterized through several observables, including mean position, momentum, and energy. The quantumness of the time-evolved state is assessed via the Wigner logarithmic negativity, and the interplay between double-bracket dissipation and chaotic dynamics is examined in detail. Finally, we extend our analysis to generalized master equations involving higher-order nested brackets, which arise naturally as a time-continuous formulation of spectral filtering techniques widely used in the numerical simulation of quantum systems.
We study the correspondence between quantum and classical dynamics with Wigner and Husimi distribution functions, respectively. The nature of quantum-mechanical regular and irregular behaviors is discussed with the use of Wigner and Husimi distribution functions. By numerical studies of the chaotic state, the Husimi distribution function is found to be a better representation than the Wigner distribution function, because coarse graining is usually involved implicitly in an observational process using the Wigner distribution function.
The paper deals with dynamics of a quantum chaotic system under influence of an environment. The effect of an environment is known to destroy the quantum coherence and can convert the quantum dynamics of a system to classical. We use a semiclassical technique for studying the process of decoherence. The condition for transition from quantum to classical dynamics is obtained in general form and checked numerically for a particular chaotic system, known as quantum the standard map on a torus. The relevance of the obtained results to the problem of correspondence between quantum and classical mechanics is briefly discussed. (c) 1996 American Institute of Physics.