A new description of dissipative systems in quantum statistical mechanics

Vyacheslav Sergeevich Kirchanov

Vyacheslav Sergeevich Kirchanov

Bernardo Spagnolo, Alexander A. Dubkov, Davide Valenti

Abstract The main aim of this special issue is to report recent advances and new trends in nonequilibrium statistical mechanics of classical and quantum systems, from both theoretical and experimental points of view, within an interdisciplinary context. In particular, the nonlinear relaxation processes in the dynamics of out-of-equilibrium systems and the role of the metastability and environmental noise will be overviewed. Three main areas of nonequilibrium statistical mechanics will be covered: slow relaxation phenomena and dissipative dynamics; long-range interactions and classical systems; quantum systems. New trends such as quantum thermodynamics and novel types of quantum phase transitions occurring in nonequilibrium steady states and topological phase transitions will be also highlighted.

M. Courbage

Mei Xiaochun

Based on the concept of ensemble, it is proved in the manuscript that the probability amplitude function can also been used to describe the classical statistical system. The motion equations of probability amplitude functions of classical statistical system are obtained, which are similar to that in quantum mechanics. It is also proved in the meantime that microsystems that obey quantum mechanics can also be described in the forms of classical statistical mechanics and deterministic classical mechanics. The quantum revised formula of classical interaction force and the revised Liouville's equations are also obtained. In this way, the transformation of two descriptive forms between classical mechanics and quantum mechanics is achieved. A new and rational interpretation about quantum mechanics, including the meaning of wave function, the potential barrier penetration of microparticles, the Uncertainty relation, the wave-particle duality, the essence of spin and the Bell's inequality and so on, is provided in the paper. Based on the transformation, two fundamental hypotheses are put forward as the basic postulates of classical statistical physics. The equal probability hypothesis in the equilibrium states is given up. The united description of nonequilibrium state mechanics and equilibrium state statistical mechanics is reached, and the so-called reversibility paradox can also be eliminated.

Irène Burghardt, Klaus B. Møller

This paper explores the hydrodynamic description of quantum densities evolving under the effects of dissipation. For illustration, we refer to analytical solutions for a harmonic system and Markovian dissipation, and derive expressions for the hydrodynamic moments and a hydrodynamic force that represents a generalization of the quantum force of Bohmian dynamics. Beyond this, we draw general conclusions on the dynamical transition, induced by dissipation, to a classical-like regime. In this context, the relation between the quantum-mechanical hydrodynamic picture and its classical-statistical analogue is investigated. This has some bearing upon mixed quantum-classical schemes emerging from the hydrodynamic description.