Exact universal chaos, speed limit, acceleration, Planckian transport coefficient, collapse to equilibrium, and other bounds in thermal quantum systems

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 spatiotemporal 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 h over bar -> 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. (C) 2022 Elsevier Inc. All rights reserved.

Automated summary

In this study, we introduce local uncertainty relations in thermal many-body systems and derive basic bounds based on these relations. The derived bounds cover various aspects such as speed limits, acceleration or force/stress, transport coefficients, correlation functions, Lyapunov exponents, etc. These bounds hold at all temperatures and regardless of interaction range, and they are relatively close to experimental data. The results shed light on the nearly instantaneous collapse to energy eigenstates in macroscopic interacting many-body quantum systems and the inhibitory effect of random off-diagonal matrix elements of local operators on their dynamics.