Bose-Einstein condensation of interacting bosons: A two-step proof
Abstract
We prove two equilibrium properties of a system of interacting atoms in three or higher dimensional continuous space. (i) If the particles interact via pair potentials of a nonnegative Fourier transform, their self-organization into infinite permutation cycles is simultaneous with off-diagonal long-range order. If the cycle lengths tend to infinity not slower than the square of the linear extension of the system, there is also Bose-Einstein condensation. (ii) If the pair potential is also nonnegative, cycles composed of a nonzero fraction of the total number of particles do appear if the density exceeds a temperature-dependent threshold value. The two together constitute the proof that in such a system Bose-Einstein condensation takes place at high enough densities.
Cite
@article{arxiv.2305.18959,
title = {Bose-Einstein condensation of interacting bosons: A two-step proof},
author = {Andras Suto},
journal= {arXiv preprint arXiv:2305.18959},
year = {2023}
}
Comments
66 pages, combined from 2106.10032[math-ph], 2108.02659 [math-ph], 2208.08931[math-ph]. arXiv admin note: text overlap with arXiv:2208.08931, arXiv:2106.10032, arXiv:2108.02659