Elementary explanation of the inexistence of decoherence at zero temperature for systems with purely elastic scattering

Yoseph Imry

Published 2002-02-04Version 1

This note has no new results and is therefore not intended to be submitted to a "research" journal in the foreseeable future, but to be available to the numerous individuals who are interested in this issue. Several of those have approached the author for his opinion, which is summarized here in a hopefully pedagogical manner, for convenience. It is demonstrated, using essentially only energy conservation and elementary quantum mechanics, that true decoherence by a normal environment approaching the zero-temperature limit is impossible for a test particle which can not give or lose energy. Prime examples are: Bragg scattering, the M\"ossbauer effect and related phenomena at zero temperature, as well as quantum corrections for the transport of conduction electrons in solids. The last example is valid within the scattering formulation for the transport. Similar statements apply also to interference properties in equilibrium.