Thermalization in Quantum Systems: An Emergent Approach

TL;DR

This paper presents an emergent approach to quantum thermalization, showing how localized atomic motions in solids lead to classical-like thermal behavior and deriving the Planck distribution dynamically from quantum dynamics.

Contribution

It introduces a novel emergent framework for quantum thermalization that explains classical behavior and derives the Planck distribution from Schrödinger dynamics.

Findings

Localization persists in excited states of solids.

Thermalization arises from long-term localized atomic motions.

Dynamical derivation of the Planck distribution from quantum mechanics.

Abstract

The problems with an emergent approach to quantum statistical mechanics are discussed and shown to follow from some of the same sources as those of quantum measurement. A wavefunction of an N atom solid is described in the ground and excited eigenstates with explicit modifications for phonons. Using the particular subclass of wavefunctions that can correspond to classical solids we investigate the localization properties of atomic centers of mass motion and contrast it with more general linear combinations of phonon states. The effectively large mass of longer modes means that localization present in the ground state persists on excitation of the material by macroscopic coherent disturbances. The "thermalization" that arises then follows from the long term well defined motion of these localized peaks in their 3N dimensional harmonic wells in the same fashion as that of a classical solid in phase space. Thermal production of photons then create an internal radiation field and provides the first dynamical derivation of the Planck distribution from material motions. Significantly, this approach resolves a long standing paradox of thermalization of many body quantum systems from Schr\"{o}dinger dynamics alone.