Momentum representation for equilibrium reduced density matrices

TL;DR

This paper explores the momentum representation of equilibrium reduced density matrices in quantum systems, revealing unique momentum distributions in fluids, crystals, and superfluids, with implications for understanding macroscopic quantum phenomena.

Contribution

It introduces a momentum-based approach to analyze equilibrium quantum systems, uncovering non-Bose/Fermi distributions and structured condensate momentum patterns.

Findings

Momentum distribution in quantum fluids resembles Maxwellian but is not strictly Maxwellian.

In superfluids, the momentum distribution includes a delta function.

Condensate in superfluid crystals shows periodic delta peaks in momentum space.

Abstract

The hierarchy of equations for reduced density matrices that describes a thermodynamically equilibrium quantum system obtained earlier by the author is investigated in the momentum representation. In the paper it is shown that the use of the momentum representation opens up new opportunities in studies of macroscopic quantum systems both nonsuperfluid and superfluid. It is found that the distribution over momenta in a quantum fluid is not a Bose or Fermi distribution even in the limit of practically noninteracting particles. The distribution looks like a Maxwellian one although, strictly speaking, it is not Maxwellian. The momentum distribution in a quantum crystal depends upon the interaction potential and the crystalline structure. The momentum distribution in a superfluid contains a delta function. The momentum distribution for the condensate in a superfluid crystal consists of delta peaks that are arranged periodically in momentum space. The periodical structure remains if the condensate crystal is not superfluid.