Thermalization is typical in large classical and quantum harmonic systems
Fuente:
arXiv
Salvato in:
| Autori principali: | , , , , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2024
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866918105065717760 |
|---|---|
| author | Cattaneo, Marco Baldovin, Marco Lucente, Dario Muratore-Ginanneschi, Paolo Vulpiani, Angelo |
| author_facet | Cattaneo, Marco Baldovin, Marco Lucente, Dario Muratore-Ginanneschi, Paolo Vulpiani, Angelo |
| contents | We establish an analytical criterion for dynamical thermalization within harmonic systems, applicable to both classical and quantum models. Specifically, we prove that thermalization of various observables, such as particle energies in physically relevant random quadratic Hamiltonians, is typical for large systems ($N \gg 1$) with initial conditions drawn from the microcanonical distribution. Moreover, we show that thermalization can also arise from non-typical initial conditions, where only a finite fraction of the normal modes is excited. A different choice of initial conditions, such as all the initial energy localized in a single particle, instead leads to energy equipartition without thermalization. Since the models we consider are integrable, our findings provide a general dynamical basis for an approach to thermalization that bypasses chaos and ergodicity, focusing instead on the physical requirement that thermodynamic observables depend on a large number of normal modes, and build a bridge between the classical and quantum theories of thermalization. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_06489 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Thermalization is typical in large classical and quantum harmonic systems Cattaneo, Marco Baldovin, Marco Lucente, Dario Muratore-Ginanneschi, Paolo Vulpiani, Angelo Statistical Mechanics Quantum Physics We establish an analytical criterion for dynamical thermalization within harmonic systems, applicable to both classical and quantum models. Specifically, we prove that thermalization of various observables, such as particle energies in physically relevant random quadratic Hamiltonians, is typical for large systems ($N \gg 1$) with initial conditions drawn from the microcanonical distribution. Moreover, we show that thermalization can also arise from non-typical initial conditions, where only a finite fraction of the normal modes is excited. A different choice of initial conditions, such as all the initial energy localized in a single particle, instead leads to energy equipartition without thermalization. Since the models we consider are integrable, our findings provide a general dynamical basis for an approach to thermalization that bypasses chaos and ergodicity, focusing instead on the physical requirement that thermodynamic observables depend on a large number of normal modes, and build a bridge between the classical and quantum theories of thermalization. |
| title | Thermalization is typical in large classical and quantum harmonic systems |
| topic | Statistical Mechanics Quantum Physics |
| url | https://arxiv.org/abs/2409.06489 |