Decoherence, the Density Matrix, the Thermal State and the Classical World

Abstract

Decoherence has been the basis for understanding the emergence of the classical world from its quantum underpinnings. Unfortunately the calculations establishing decoherence overshoot and, based on assumptions that break down, predict that with the passage of time the off-diagonal elements of the density matrix become arbitrarily small. It has been recognized by some authors that the thermal state, assumed to hold for systems in equilibrium, places a bound on off diagonal terms. In this article we establish-preserving the conservation of energy, as is not the case for previous work-that indeed the thermal state is an attractor under scattering. Moreover, the bound on the off-diagonal terms present in the thermal state does not contradict everyday experience.

Initial-state dependence of thermodynamic dissipation for any quantum process

“…The case of strong coupling is more tricky because of the possibility of steady-state coherences in the system's energy eigenbasis [36]. Nevertheless, there are small quantum systems of significant interest that are rigorously shown to approach the Gibbs state as an attractor, even with strong interactions [37,38].…”

Reconciling Kinetic and Quantum Theory

“…In this article we do not fully solve the problem, but report ideas that lead to a resolution of sorts. In an appendix to a previous paper [5] we assumed the wave function was gaussian and that measurement caused a resumption of localization. In that heuristic treatment the size of a wave packet was on the order of √ th where the thermal wavelength is th = ℏ∕…”

What Is the Size and Shape of a Wave Packet?

“…I do not deal with the effects of temperature (cf. [5]), nor with off-diagonal elements of the density matrix [6,7]. I am concerned with pure quantum behavior.…”