Effective grand-canonical description of condensation in negative-temperature regimes
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866912227580182528 |
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| author | Iubini, Stefano Politi, Antonio |
| author_facet | Iubini, Stefano Politi, Antonio |
| contents | The observation of negative-temperature states in the localized phase of the Discrete Nonlinear Schrödinger (DNLS) equation has challenged statistical mechanics for a long time. For isolated systems, they can emerge as stationary extended states through a large-deviation mechanism occurring for finite sizes, while they are formally unstable in grand-canonical setups, being associated to an unlimited growth of the condensed fraction. Here, we show that negative-temperature states in open setups are metastable and their lifetime $τ$ is exponentially long with the temperature, $τ\approx \exp(λ|T|)$ (for $T<0$). A general expression for $λ$ is obtained in the case of a simplified stochastic model of non-interacting particles. In the DNLS model, the presence of an adiabatic invariant, makes $λ$ even larger because of the resulting freezing of the breather dynamics. This mechanism, based on the existence of two conservation laws, provides a new perspective over the statistical description of condensation processes. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_15140 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Effective grand-canonical description of condensation in negative-temperature regimes Iubini, Stefano Politi, Antonio Statistical Mechanics The observation of negative-temperature states in the localized phase of the Discrete Nonlinear Schrödinger (DNLS) equation has challenged statistical mechanics for a long time. For isolated systems, they can emerge as stationary extended states through a large-deviation mechanism occurring for finite sizes, while they are formally unstable in grand-canonical setups, being associated to an unlimited growth of the condensed fraction. Here, we show that negative-temperature states in open setups are metastable and their lifetime $τ$ is exponentially long with the temperature, $τ\approx \exp(λ|T|)$ (for $T<0$). A general expression for $λ$ is obtained in the case of a simplified stochastic model of non-interacting particles. In the DNLS model, the presence of an adiabatic invariant, makes $λ$ even larger because of the resulting freezing of the breather dynamics. This mechanism, based on the existence of two conservation laws, provides a new perspective over the statistical description of condensation processes. |
| title | Effective grand-canonical description of condensation in negative-temperature regimes |
| topic | Statistical Mechanics |
| url | https://arxiv.org/abs/2406.15140 |