Large-scale universality in quantum reaction-diffusion from Keldysh field theory
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866916306233589760 |
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| author | Gerbino, Federico Lesanovsky, Igor Perfetto, Gabriele |
| author_facet | Gerbino, Federico Lesanovsky, Igor Perfetto, Gabriele |
| contents | We consider the quantum reaction-diffusion dynamics in $d$ spatial dimensions of a Fermi gas subject to binary annihilation reactions $A+A \to \emptyset$. These systems display collective nonequilibrium long-time behavior, which is signalled by an algebraic decay of the particle density. Building on the Keldysh formalism, we devise a field theoretical approach for the reaction-limited regime, where annihilation reactions are scarce. By means of a perturbative expansion of the dissipative interaction, we derive a description in terms of a large-scale universal kinetic equation. Our approach shows how the time-dependent generalized Gibbs ensemble assumption, which is often employed for treating low-dimensional nonequilibrium systems, emerges from systematic diagrammatics. It also allows to exactly compute -- for arbitrary spatial dimension -- the decay exponent of the particle density. The latter is based on the large-scale description of the quantum dynamics and it differs from the mean-field prediction even in dimension larger than one. We moreover consider spatially inhomogeneous setups involving an external potential. In confined systems the density decay is accelerated towards the mean-field algebraic behavior, while for deconfined scenarios the power-law decay is replaced by a slower non-algebraic decay. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2307_14945 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Large-scale universality in quantum reaction-diffusion from Keldysh field theory Gerbino, Federico Lesanovsky, Igor Perfetto, Gabriele Statistical Mechanics Quantum Gases We consider the quantum reaction-diffusion dynamics in $d$ spatial dimensions of a Fermi gas subject to binary annihilation reactions $A+A \to \emptyset$. These systems display collective nonequilibrium long-time behavior, which is signalled by an algebraic decay of the particle density. Building on the Keldysh formalism, we devise a field theoretical approach for the reaction-limited regime, where annihilation reactions are scarce. By means of a perturbative expansion of the dissipative interaction, we derive a description in terms of a large-scale universal kinetic equation. Our approach shows how the time-dependent generalized Gibbs ensemble assumption, which is often employed for treating low-dimensional nonequilibrium systems, emerges from systematic diagrammatics. It also allows to exactly compute -- for arbitrary spatial dimension -- the decay exponent of the particle density. The latter is based on the large-scale description of the quantum dynamics and it differs from the mean-field prediction even in dimension larger than one. We moreover consider spatially inhomogeneous setups involving an external potential. In confined systems the density decay is accelerated towards the mean-field algebraic behavior, while for deconfined scenarios the power-law decay is replaced by a slower non-algebraic decay. |
| title | Large-scale universality in quantum reaction-diffusion from Keldysh field theory |
| topic | Statistical Mechanics Quantum Gases |
| url | https://arxiv.org/abs/2307.14945 |