Exact Universal Chaos, Speed Limit, Acceleration, Planckian Transport Coefficient, "Collapse" to equilibrium, and Other Bounds in Thermal Quantum Systems

TL;DR

This paper introduces universal bounds and limits in thermal quantum systems using local uncertainty relations, covering speed, acceleration, transport, and thermalization, applicable at all temperatures and supported by experimental data.

Contribution

It derives a comprehensive set of universal bounds in thermal quantum systems, including speed limits, transport coefficients, and thermalization times, using a novel approach based on local uncertainty relations.

Findings

Universal non-relativistic speed limits regardless of interaction range

Bounds on transport coefficients like diffusion constant and viscosity

Analogues of the Ioffe-Regel limit and implications for quantum thermalization

Abstract

We introduce "local uncertainty relations" in thermal many body systems. Using these relations, we derive basic bounds. These results include the demonstration of universal non-relativistic speed limits (regardless of interaction range), bounds on acceleration or force/stress, acceleration or material stress rates, transport coefficients (including the diffusion constant and viscosity), electromagnetic or other gauge field strengths, correlation functions of arbitrary spatio-temporal derivatives, Lyapunov exponents, and thermalization times. We further derive analogs of the Ioffe-Regel limit. These bounds are relatively tight when compared to various experimental data. In the $\hbar \to 0$ limit, all of our bounds either diverge (e.g., the derived speed and acceleration limit) or vanish (as in, e.g., our viscosity and diffusion constant bounds). Our inequalities hold at all temperatures and, as corollaries, imply general power law bounds on response functions at both asymptotically high and low temperatures. Our results shed light on how apparent nearly instantaneous effective "collapse" to energy eigenstates may arise in macroscopic interacting many body quantum systems. We comment on how random off-diagonal matrix elements of local operators (in the eigenbasis of the Hamiltonian) may inhibit their dynamics.