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

Mathieu Beau (1) , Baptiste Savoie (2)

1 STP-DIAS - School of Theoretical Physics [Dublin]
2 Aarhus University [Aarhus]

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 W.J. Mullin in [38]. 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-BEC 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 (PIMC) method.

Mots clés: Cold atomic gases; Bose-Einstein condensation; harmonic traps; loop-gas approach; permutation cycles; Penrose-Onsager criterion; anisotropic traps; generalized Bose-Einstein condensation; mesoscopic-loops.; mesoscopic-loops

Domaines: Physique mathématique [math-ph]; Physique mathématique [math-ph]; Gaz Quantiques [cond-mat.quant-gas]; Mécanique statistique [cond-mat.stat-mech]

Mathieu Beau, Baptiste Savoie. Rigorous investigation of the reduced density matrix for the ideal Bose gas in harmonic traps by a loop-gas-like approach.. 2014. ⟨hal-00834501v3⟩