A Rigorous Theory of Prethermalization without Temperature

TL;DR

This paper establishes a rigorous theoretical framework for prethermalization phenomena that occur without the system approaching a thermal state, highlighting the role of emergent symmetries rather than energy conservation.

Contribution

It introduces a class of systems where prethermal states arise from emergent symmetries without relying on an effective Hamiltonian or energy conservation.

Findings

Prethermal states can be defined by emergent global symmetries.

Prethermal phases of matter can emerge without energy conservation.

Theoretical framework for non-Hamiltonian driven systems.

Abstract

Prethermalization refers to the physical phenomenon where a system evolves toward some long-lived non-equilibrium steady state before eventual thermalization sets in. One general scenario where this occurs is in driven systems with dynamics governed by an effective Hamiltonian (in some rotating frame), such that ergodicity of the latter is responsible for the approach to the prethermal state. This begs the question whether it is possible to have a prethermal state not associated to any effective Hamiltonian. Here, we answer this question in the affirmative. We exhibit a natural class of systems in which the prethermal state is defined by emergent, global symmetries, but where the dynamics that takes the system to this state has no additional conservation laws, in particular energy. We explain how novel prethermal phases of matter can nevertheless emerge under such settings, distinct from those previously discussed.