One Rudolf Peierls' surprise: the quantum-to-classical transition in the context of solid-state physics

TL;DR

This paper revisits the theory of decoherence in solid-state physics, clarifying conditions under which electrons in a crystal lattice can be considered as coherent quantum systems and exploring the quantum-to-classical transition.

Contribution

It corrects and extends the seminal theory of decoherence due to ionic motion, providing precise conditions and length scales for electron coherence in solids.

Findings

Corrected conditions for electron decoherence in crystals

Calculated length scale for ionic coherence

Discussed physical implications of quantum-to-classical transition

Abstract

In solid state physics, it is an unsaid (tacit) assumption that the Bloch theorem is applicable to a crystal lattice even if it is of the macroscopic dimensions, provided periodicity is maintained. However, in a realistic situation, electrons in a periodic potential of ions constitute an open quantum system and are subjected to decoherence and dissipation. A natural question arises: up to what distances electrons in a periodic potential can be considered as constituting an effective closed quantum system? And what is the cause of decoherence? To answer some of these questions, the seminal theory of Ovchinnikov and Erikhman of decoherence due to ionic motion is revisited and an oversight of the authors is corrected. Correct conditions for decoherence to occur are worked out. Length scale up to which the motion of ions remains coherent is also calculated. Finally, a realistic physical picture is discussed.