skip to main content

Title: Rigorous investigation of the reduced density matrix for the ideal Bose gas in harmonic traps by a loop-gas-like approach

In this paper, we rigorously investigate the reduced density matrix (RDM) associated to the ideal Bose gas in harmonic traps. We present a method based on a sum-decomposition of the RDM allowing to treat not only the isotropic trap, but also general anisotropic traps. When focusing on the isotropic trap, the method is analogous to the loop-gas approach developed by Mullin [“The loop-gas approach to Bose-Einstein condensation for trapped particles,” Am. J. Phys. 68(2), 120 (2000)]. Turning to the case of anisotropic traps, we examine the RDM for some anisotropic trap models corresponding to some quasi-1D and quasi-2D regimes. For such models, we bring out an additional contribution in the local density of particles which arises from the mesoscopic loops. The close connection with the occurrence of generalized-Bose-Einstein condensation is discussed. Our loop-gas-like approach provides relevant information which can help guide numerical investigations on highly anisotropic systems based on the Path Integral Monte Carlo method.
Authors:
 [1] ;  [2]
  1. Dublin Institute for Advanced Studies School of Theoretical Physics, 10 Burlington Road, Dublin 4 (Ireland)
  2. Department of Mathematical Sciences, University of Aarhus, Ny Munkegade, Building 1530, DK-8000 Aarhus C (Denmark)
Publication Date:
OSTI Identifier:
22250600
Resource Type:
Journal Article
Resource Relation:
Journal Name: Journal of Mathematical Physics; Journal Volume: 55; Journal Issue: 5; Other Information: (c) 2014 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; ANISOTROPY; BOSE-EINSTEIN CONDENSATION; BOSE-EINSTEIN GAS; DENSITY MATRIX; MONTE CARLO METHOD; PATH INTEGRALS; TRAPS