A classical Markov process in nonequilibrium quantum statistical mechanics

Abstract

We obtain, from the exact microscopic, reversible, dynamics of an oscillator coupled to a heat bath, a classical, Markov stochastic process, for the energy of the oscillator. Also, the corresponding macroscopic phenomenological equation, describing an irreversible approach to equilibrium, is obtained.

Vlasov hydrodynamics of a quantum mechanical model

“…It is only in certain limited contexts (e.g. [1][2][3]) that the extraction of macroscopic dynamical laws from the microscopic equations of motion of 'large' quantum systems has been rigorously effected. To the best of our knowledge, there are, as yet, no rigorous derivations of hydrodynamics from quantum statistical mechanics.…”

“…that due to Vlasov, for a quantum mechanical model which, though relatively simple, does have some physical significance, as we shall presently explain. The model, Σ {N \ is that of an assembly of N particles of the same species, in [R 3 and where V satisfies certain regularity conditions. As we are concerned with the properties of the model in the limit N -> GO, we formulate the dynamics of a sequence of systems {Σ (N) }.…”

Κβαντικη Τριβη Σε Περιοδικο Δυναμικο

“…'Εκτός τών ανωτέρω μεθόδων έχουν άναπτυχθή καί διάφορα άλλα μοντέλλα χωρίς ιδιαίτερη απή χηση πολλά άπό τά όποια απεδείχθησαν ίσοδύναμα με αυτό τοϋ . Προσπάθειες αντιμετωπίσεως της κβαντι κής τριβής έχουν γίνει διά τής χρήσεως στοχαστικών διαδικασιών (11), (21)(22)(23)(24).…”