2014/11/12 by A. D. Ribeiro, Alexandre Dias Ribeiro, Ribeiro, Alexandre Dias
Physics and Astronomy · #Cold Atom Physics and Bose-Einstein Condensates #FOS: Physical sciences #Physics of Superconductivity and Magnetism #Quantum Gases (cond-mat.quant-gas) #Quantum, superfluid, helium dynamics #Statistical Mechanics (cond-mat.stat-mech) #cond-mat.quant-gas #cond-mat.stat-mech
paper · pdf · doi:10.48550/arxiv.1411.3946
arxiv created 2014/11/12 · openalex publication_date 2014/11/12 · arxiv updated 2014/11/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The present article is concerned with the use of approximations in the calculation of the many-body density of states (MBDS) of a system with total energy E, composed by N bosons. In the mean-field framework, an integral expression for MBDS, which is proper to be performed by asymptotic expansions, can be derived. However, the standard second order steepest descent method cannot be applied to this integral when the ground-state is sufficiently populated. Alternatively, we derive a uniform formula for MBDS, which is potentially able to deal with this regime. In the case of the one-dimensional harmonic oscillator, using results found in the number theory literature, we show that the uniform formula improves the standard expression achieved by means of the second order method.