Using local uncertainty relations in thermal many body systems, we illustrate that there exist universal speed limit (regardless of interaction range), bounds on acceleration or force/stress, acceleration or material stress rates, diffusion constant, viscosity, other transport coefficients, electromagnetic or other gauge field strengths, correlation functions of arbitrary spatio-temporal derivatives, Lyapunov exponents, thermalization times, and transition times between orthogonal states in non-relativistic quantum thermal systems, and derive analogs of the Ioffe-Regel limit. In the
ℏ→0 limit, all of our bounds either diverge (e.g., our 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 measurements and on how apparent nearly instantaneous effective collapse to an eigenstate may arise in macroscopic interacting many body quantum systems.
We introduce “ local uncertainty relations ” in thermal quantum many-body systems from which fundamental bounds can be derived. These inequalities imply rigorous universal non-relativistic speed limits (independent of interaction range) and, as we focus on in the current work, bounds associated with transport (e.g., the diffusion constant and shear viscosity). Using the chaos bounds and other considerations, we introduce simplified non-rigorous universal transport coefficient inequalities and compare our resulting bounds against experimental data.