Power-law distributions in nonequilibrium open quantum systems

TL;DR

This paper demonstrates that power-law distributions naturally emerge in the steady states of open quantum systems with nonlinear dissipation, due to multiplicative quantum noise, with implications for extreme photon sources.

Contribution

It analytically and numerically shows how nonlinear dissipation induces heavy tails in quantum steady states through amplified quantum noise, a mechanism previously unrecognized.

Findings

Power-law tails appear in steady-state energy distributions of open quantum systems.

Heavy tails occur even when classical analogs are stable, without fine-tuning.

Numerical simulations support the analytical mechanism across various nonlinear quantum models.

Abstract

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 Li\'{e}nard 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.