Zero BEC State Amplitude, and BEC Unnecessary to Define Phase \phi

TL;DR

The paper argues that in interacting many-body systems, the BEC state amplitude vanishes in the thermodynamic limit, yet the phase  can still be well-defined, supporting superfluidity without a traditional condensate.

Contribution

It introduces an argument that the BEC state amplitude tends to zero in large systems, but the phase  remains definable, challenging the necessity of a finite condensate for superfluidity.

Findings

BEC state amplitude vanishes in the thermodynamic limit

Superfluid phase  can be defined without a finite condensate

Superfluid velocity is determined by  regardless of BEC presence

Abstract

We define the "BEC state" to be the many-body wavefunction where all particles are in the same one-body state. Using an argument analogous to Anderson's Orthogonality Catastrophe, we argue that for interacting particles the amplitude of the BEC state within the many-body wavefunction goes to zero in the thermodynamic limit. This does not mean that there is no condensate. However, we argue that, if the excitations satisfy the Landau criterion, then the absence of a finite amplitude for the BEC state, or the absence of a condensate, do not prevent the definition of the phase function \phi, from which the superfluid velocity follows.