Non-coherent evolution of closed weakly interacting system leads to equidistribution of probabilities of microstates

• URL: http://arxiv.org/abs/2402.14971v3
• Date: Mon, 27 May 2024 18:12:54 GMT
• Title: Non-coherent evolution of closed weakly interacting system leads to equidistribution of probabilities of microstates
• Authors: A. P. Meilakhs,
• Abstract summary: We show that for weakly interacting systems such evolution is a Markovian process. We search for time dependence of mean numbers of particles in single-particle states and find that under made assumptions it is governed by Boltzmann integral collision. In this theory, the non-coherence is the mechanism that transforms time-reversible unitary evolution into time-irreversible evolution.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We introduce a concept of non-coherent evolution of macroscopic quantum systems. We show that for weakly interacting systems such evolution is a Markovian stochastic process. The rates of transitions between states of the system, that characterize the process, are found by Fermi's golden rule. Such evolution is time-irreversible and leads to the equidistribution of probabilities across every state of the system. Further, we search for time dependence of mean numbers of particles in single-particle states and find that under made assumptions it is governed by Boltzmann collision integral. In this theory, the non-coherence is the mechanism that transforms time-reversible unitary evolution into time-irreversible stochastic evolution. Thus we present the possible solution for the famous time-arrow problem.

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