Inevitable Power-law Behavior of Isolated Many-Body Quantum Systems and How It Anticipates Thermalization

TL;DR

This paper demonstrates that isolated many-body quantum systems universally exhibit a power-law decay in their return probability over time, which can predict their thermalization behavior regardless of system specifics.

Contribution

It provides a general analytical and numerical framework showing the inevitable power-law decay in quantum relaxation, linking decay exponent to system properties and thermalization.

Findings

Power-law decay $ o t^{- ext{gamma}}$ in return probability is universal.

Decay exponent $ ext{gamma}$ encodes spectral and initial state information.

Decay behavior predicts whether the system thermalizes or not.

Abstract

Despite being ubiquitous, out-of-equilibrium quantum systems are much less understood than systems at equilibrium. Progress in the field has benefited from a symbiotic relationship between theoretical studies and new experiments on coherent dynamics. The present work strengthens this connection by providing a general picture of the relaxation process of isolated lattice many-body quantum systems that are routinely studied in experiments with cold atoms, ions traps, and nuclear magnetic resonance. We show numerically and analytically that the long-time decay of the probability for finding the system in its initial state necessarily shows a power-law behavior $\propto t^{ - \gamma }$. This happens independently of the details of the system, such as integrability, level repulsion, and the presence or absence of disorder. Information about the spectrum, the structure of the initial state, and the number of particles that interact simultaneously is contained in the value of $\gamma$. From it, we can anticipate whether the initial state will or will not thermalize.