# Transportless equilibration in isolated many-body quantum systems

## TL;DR

This paper develops a unified analytical theory for relaxation in isolated quantum systems, emphasizing the role of the initial energy distribution and conditions where transport currents are absent, aligning well with experimental and numerical findings.

## Contribution

It introduces a comprehensive theory of quantum relaxation that accounts for initial energy distributions and the absence of transport, improving upon previous approximations.

## Key findings

- The Fourier transform of the initial energy distribution is crucial for relaxation dynamics.
- Transportless relaxation occurs when the system and initial state lack macroscopic inhomogeneities.
- The theory aligns with various experimental and numerical results.

## Abstract

A general analytical theory of temporal relaxation processes in isolated quantum systems with many degrees of freedom is elaborated, which unifies and substantially amends several previous approximations. Specifically, the Fourier transform of the initial energy distribution is found to play a key role, which is furthermore equivalent to the so-called survival probability in case of a pure initial state. The main prerequisite is the absence of any notable transport currents, caused for instance by some initially unbalanced local densities of particles, energy, and so on. In particular, such a transportless relaxation scenario naturally arises when both the system Hamiltonian and the initial non-equilibrium state do not exhibit any spatial inhomogeneities on macroscopic scales. A further requirement is that the relaxation must not be notably influenced by any approximate (but not exact) constant of motion or metastable state. The theoretical predictions are compared with various experimental and numerical results from the literature.