Macroscopic Superpositions, Decoherent Histories and the Emergence of Hydrodynamic Behaviour

TL;DR

This paper explains how macroscopic local densities in large systems appear classical due to decoherence from conservation laws, leading to hydrodynamic behavior, with explicit analysis in oscillator chains.

Contribution

It demonstrates that decoherence of local densities arises from conservation laws rather than environment, elucidating the emergence of hydrodynamics from quantum mechanics.

Findings

Decoherence of local densities is primarily due to conservation laws.

Hydrodynamic equations emerge from local equilibrium states.

Explicit calculations in oscillator chains support the theoretical framework.

Abstract

Macroscopic systems are described most completely by local densities (particle number, momentum and energy) yet the superposition states of such physical variables, indicated by the Everett interpretation, are not observed. In order to explain this, it is argued that histories of local number, momentum and energy density are approximately decoherent when coarse-grained over sufficiently large volumes. Decoherence arises directly from the proximity of these variables to exactly conserved quantities (which are exactly decoherent), and not from environmentally-induced decoherence. We discuss the approach to local equilibrium and the subsequent emergence of hydrodynamic equations for the local densities. The results are general but we focus on a chain of oscillators as a specific example in which explicit calculations may be carried out. We discuss the relationships between environmentally-induced and conservation-induced decoherence and present a unified view of these two mechanisms.