Non-coherent evolution of closed weakly interacting system leads to equidistribution of probabilities of microstates
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arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866911513178013696 |
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| author | Meilakhs, A. P. |
| author_facet | Meilakhs, A. P. |
| contents | 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 transition rates between system states, which characterize the process, are determined by Fermi's golden rule. Such evolution is time-irreversible and leads to the equidistribution of probabilities across every state of the system. Furthermore, we investigate the time dependence of the mean numbers of particles in single-particle states and find that, under the given assumptions, it is governed by the Boltzmann collision integral. The proposed mechanism that transforms time-reversible unitary evolution into time-irreversible stochastic evolution is non-coherence. In the presented theory, the non-coherence is not associated with interaction with a heat bath, but rather with the finite spectral width of quantum states. This understanding of non-coherence is analogous to the one used in wave optics. Thus, we present a novel approach to the famous arrow of time problem. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_14971 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Non-coherent evolution of closed weakly interacting system leads to equidistribution of probabilities of microstates Meilakhs, A. P. Quantum Physics Other Condensed Matter 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 transition rates between system states, which characterize the process, are determined by Fermi's golden rule. Such evolution is time-irreversible and leads to the equidistribution of probabilities across every state of the system. Furthermore, we investigate the time dependence of the mean numbers of particles in single-particle states and find that, under the given assumptions, it is governed by the Boltzmann collision integral. The proposed mechanism that transforms time-reversible unitary evolution into time-irreversible stochastic evolution is non-coherence. In the presented theory, the non-coherence is not associated with interaction with a heat bath, but rather with the finite spectral width of quantum states. This understanding of non-coherence is analogous to the one used in wave optics. Thus, we present a novel approach to the famous arrow of time problem. |
| title | Non-coherent evolution of closed weakly interacting system leads to equidistribution of probabilities of microstates |
| topic | Quantum Physics Other Condensed Matter |
| url | https://arxiv.org/abs/2402.14971 |