Experimental realities refuting existence of p=0 condensate in a system of interacting bosons : I. Electron bubble

TL;DR

This paper presents experimental evidence from electron bubbles in liquid helium that refutes the existence of a zero-momentum condensate in interacting bosonic systems, showing particles occupy finite-sized quantum states.

Contribution

It provides direct experimental refutation of p=0 condensate in interacting bosons using electron bubble observations in liquid helium.

Findings

Electron bubbles demonstrate particles occupy finite quantum states.

No particles in the ground state have zero momentum.

All particles are in a state with energy proportional to 1/d^2.

Abstract

Physical reality of the existence of electron bubble in liquid $^4He$ (or $^3He$) renders a {\it clear experimental evidence} for a quantum particle (in an interacting environment as seen by electron in liquid helium) to occupy exclusively a space of size $\lambda/2$ that, obviously, depends on its energy/momentum. This unequivocally proves that {\it no particle} in a system of interacting bosons such as liquid $^4He$ has momentum $p=0$; in stead, {\it all particles} in the ground state of such a system are in the single quantum state of energy $\varepsilon_o = h^2/8md^2$ or momentum $p = h/2d$.