Proper condensates and off-diagonal long range order

TL;DR

This paper establishes a model-independent criterion for the formation of proper condensates and off-diagonal long-range order in quantum states with high particle density, using a novel wave function characterization.

Contribution

It introduces a new, model-independent criterion for condensate formation based on wave function regularity and singularity, extending understanding of long-range order in quantum systems.

Findings

Proper condensates occur with high particle density in states with large particle number.

Condensates can be streaming with constant velocity, described by eigenstates of momentum.

A novel wave function approach characterizes the emergence of long-range order.

Abstract

Within the framework of the algebra of canonical commutation relations in Euclidean space, a long range order between particles in bounded regions is established in states with a sufficiently large particle number. It occurs whenever homogeneous proper (infinite) condensates form locally in the states in the limit of infinite densities. The condensates are described by eigenstates of the momentum operator, covering also those cases, where they are streaming with a constant velocity. The arguments given are model independent and lead to a new criterion for the occurrence of condensates. It makes use of a novel approach to the identification of condensates, based on a characterization of regular and singular wave functions.