Solvable Models of Heat Transport in Quantum Mechanics

TL;DR

This paper explores solvable quantum models to understand heat transport, revealing how toy models like RMT and conformal models capture key features and connect to the more realistic DSSYK model.

Contribution

It introduces solvable models including RMT, conformal, and DSSYK, to analyze heat transport and connect toy models with realistic quantum systems.

Findings

Toy models replicate transient peaks and NESS features.

Exact results for transient dynamics and thermal conductivity.

DSSYK model bridges toy models and realistic quantum heat transport.

Abstract

We investigate solvable models of heat transport between a pair of quantum mechanical systems initialized at two different temperatures. At time $t=0$, a weak interaction is switched on between the systems, and we study the resulting energy transport. Focusing on the heat current as the primary observable, we analyze both the transient dynamics and the long-time behavior of the system. We demonstrate that simple toy models - including Random Matrix Theory like models ({\it RMT models}) and Schwarzian like models ({\it conformal models}) - can capture many generic features of heat transport, such as transient current peaks and the emergence of non-equilibrium steady state (NESS). For these models, we derive a variety of exact results characterizing the short time transients, long time approach to NESS and thermal conductivity. Finally, we show how these features appear in a more realistic solvable model, the Double-Scaled SYK (DSSYK) model. We demonstrate that the DSSYK model interpolates between the seemingly distinct toy models discussed earlier, with the toy models in turn providing a useful lens through which to understand the rich features of DSSYK.