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Acta Phys. Polon.

STATISTICAL AND THERMODYNAMICAL DESCRIPTION OF CORRELATED SYSTEMS. IV. TIME-DEPENDENT DISTRIBUTIONS

A. Fuliński

Published Aug 1, 1963• 0 citations
OpenAlex

Abstract

The solution of master equations describing the evolution in time of correlated subsystems forming an isolated system is given. It is found that near the equilibrium or stationary state the probabilities of finding of the subsystems in their quantized states and the correlation coefficients are the exponential functions of momentary values of observables, and do not depend on the initial state of the system. (auth)

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The solution of master equations describing the evolution in time of correlated subsystems forming an isolated system is given. It is found that near the equilibrium or stationary state the probabilities of finding of the subsystems in their quantized states and the correlation coefficients are the exponential functions of momentary values of observables, and do not depend on the initial state of the system. (auth)
The non-equilibrium dynamics of isolated quantum systems represent a theoretical and experimental challenge raising many fundamental questions with applications to different fields of modern physics. In these proceedings, we briefly review some of the recent findings on the subject, with particular emphasis to the existence of stationary expectation values of local observables and to their statistical mechanics description. It turns out that the appropriate statistical ensemble describing these asymptotic values depends on whether the Hamiltonian governing the time evolution is integrable or not.
We derive the general form of a master equation describing the reduced time evolution of a sequence of subsystems "propagating" in an environment which can be described as a sequence of subenvironments. The interaction between subsystems and subenvironments is described in terms of a collision model, with the irreversible dynamics of the subenvironments between collisions explicitly taken into account. In the weak coupling regime, we show that the collisional model produces a correlated Markovian evolution for the joint density matrix of the multipartite system. The associated Lindblad superoperator contains pairwise terms describing cross correlation between the different subsystems. Such a model can describe a broad range of physical situations, ranging from quantum channels with memory to photon propagation in concatenated quantum optical systems.
Abstract We discuss the classical statistics of isolated subsystems. Only a small part of the information contained in the classical probability distribution for the subsystem and its environment is available for the description of the isolated subsystem. The “coarse graining of the information” to micro‐states implies probabilistic observables. For two‐level probabilistic observables only a probability for finding the values one or minus one can be given for any micro‐state, while such observables could be realized as classical observables with sharp values on a substate level. For a continuous family of micro‐states parameterized by a sphere all the quantum mechanical laws for a two‐state system follow under the assumption that the purity of the ensemble is conserved by the time evolution. The correlation functions of quantum mechanics correspond to the use of conditional correlation functions in classical statistics. We further discuss the classical statistical realization of entanglement within a system corresponding to four‐state quantum mechanics. We conclude that quantum mechanics can be derived from a classical statistical setting with infinitely many micro‐states.
There are numerous examples in physics that can be modeled by the interaction between a small system of interest and a reservoir. The interaction typically leads to the irreversible decay of the system variables. As the system evolves into an equilibrium state, various parameters such as mean values, probabilities, and variances change until the final steady state is reached. The evolution of a system coupled to a reservoir with a short memory is often described by a master equation for the reduced density operator of the system. Master equations are important in physics because of their generality and hence wide range of applicability [1].