Power-law distributions in nonequilibrium open quantum systems
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arXiv
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866908943027011584 |
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| author | Mok, Wai-Keong |
| author_facet | Mok, Wai-Keong |
| contents | Power-law probability distributions are widely used to model extreme statistical events in complex systems, with applications to a vast array of natural phenomena ranging from earthquakes to stock market crashes to pandemics. We show that analogous heavy tails arise naturally in open quantum systems with nonlinear dissipation. Introducing a prototypical family of quantum dynamical models, we analytically prove the emergence of power-law tails in the steady state energy distribution, originating from an amplification of quantum noise whose microscopic fluctuations grow with energy. Moreover, our analysis suggests a general mechanism for heavy-tail statistics in the nonequilibrium steady states of open quantum systems: Nonlinear dissipation generically induces multiplicative quantum noise, enforced by the constraints of quantum mechanics, which is responsible for the heavy-tail behavior. This is supported by numerical simulations of a general class of nonlinear dynamics known as quantum Liénard systems. Remarkably, even when the corresponding classical system is stable, we find power-law tails in both steady-state populations and coherences, which occur for typical parameters without fine-tuning. This phenomenon can potentially be harnessed to develop extreme photon sources for novel applications in light-matter interaction and sensing. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_07275 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Power-law distributions in nonequilibrium open quantum systems Mok, Wai-Keong Quantum Physics Adaptation and Self-Organizing Systems Optics Power-law probability distributions are widely used to model extreme statistical events in complex systems, with applications to a vast array of natural phenomena ranging from earthquakes to stock market crashes to pandemics. We show that analogous heavy tails arise naturally in open quantum systems with nonlinear dissipation. Introducing a prototypical family of quantum dynamical models, we analytically prove the emergence of power-law tails in the steady state energy distribution, originating from an amplification of quantum noise whose microscopic fluctuations grow with energy. Moreover, our analysis suggests a general mechanism for heavy-tail statistics in the nonequilibrium steady states of open quantum systems: Nonlinear dissipation generically induces multiplicative quantum noise, enforced by the constraints of quantum mechanics, which is responsible for the heavy-tail behavior. This is supported by numerical simulations of a general class of nonlinear dynamics known as quantum Liénard systems. Remarkably, even when the corresponding classical system is stable, we find power-law tails in both steady-state populations and coherences, which occur for typical parameters without fine-tuning. This phenomenon can potentially be harnessed to develop extreme photon sources for novel applications in light-matter interaction and sensing. |
| title | Power-law distributions in nonequilibrium open quantum systems |
| topic | Quantum Physics Adaptation and Self-Organizing Systems Optics |
| url | https://arxiv.org/abs/2410.07275 |