On the Conditions for a Quantum Violent Relaxation
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2023
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| _version_ | 1866911006727340032 |
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| author | Giachetti, Guido Defenu, Nicolò |
| author_facet | Giachetti, Guido Defenu, Nicolò |
| contents | In general, classical fully-connected systems are known to undergo violent relaxation. This phenomenon refers to the relaxation of observables to stationary, non-thermal, values on a finite timescale, despite their long-time dynamics being dominated by mean-field effects in the thermodynamic limit. Here, we analyze the ``quantum" violent relaxation by studying the dynamics of generic many-body systems with two-body, all-to-all, interactions in the thermodynamic limit. We show that, in order for violent relaxation to occur very specific conditions on the spectrum of the mean-field effective Hamiltonian have to be met. These conditions are hardly met and ``quantum" violent relaxation is observed rarely with respect to its classical counterpart. Our predictions are validated by the study of a spin model which, depending on the value of the coupling, shows a transition between violent-relaxation and a generic prethermal phase. We also analyze a spin version of the quantum Hamiltonian-Mean-Field model, which is shown not to exhibit violent-relaxation. Finally, we discuss how the violent-relaxation picture emerges back in the classical limit. Our results demonstrate how, even in the mean-field regime, quantum effects have a rather dramatic impact on the dynamics, paving the way to a better understanding of light-matter coupled systems. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2312_14768 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | On the Conditions for a Quantum Violent Relaxation Giachetti, Guido Defenu, Nicolò Quantum Physics Statistical Mechanics In general, classical fully-connected systems are known to undergo violent relaxation. This phenomenon refers to the relaxation of observables to stationary, non-thermal, values on a finite timescale, despite their long-time dynamics being dominated by mean-field effects in the thermodynamic limit. Here, we analyze the ``quantum" violent relaxation by studying the dynamics of generic many-body systems with two-body, all-to-all, interactions in the thermodynamic limit. We show that, in order for violent relaxation to occur very specific conditions on the spectrum of the mean-field effective Hamiltonian have to be met. These conditions are hardly met and ``quantum" violent relaxation is observed rarely with respect to its classical counterpart. Our predictions are validated by the study of a spin model which, depending on the value of the coupling, shows a transition between violent-relaxation and a generic prethermal phase. We also analyze a spin version of the quantum Hamiltonian-Mean-Field model, which is shown not to exhibit violent-relaxation. Finally, we discuss how the violent-relaxation picture emerges back in the classical limit. Our results demonstrate how, even in the mean-field regime, quantum effects have a rather dramatic impact on the dynamics, paving the way to a better understanding of light-matter coupled systems. |
| title | On the Conditions for a Quantum Violent Relaxation |
| topic | Quantum Physics Statistical Mechanics |
| url | https://arxiv.org/abs/2312.14768 |