2006/06/08 by C. Malyshev, Malyshev, C., N. M. Bogoliubov +1
Mathematics · Physics and Astronomy · #42C10 #81S40 #Cold Atom Physics and Bose-Einstein Condensates #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Physical sciences #Mathematical Physics (math-ph) #Quantum and Classical Electrodynamics #Quantum, superfluid, helium dynamics #Statistical Mechanics (cond-mat.stat-mech) #cond-mat.stat-mech #math-ph #math.MP #msc:42C10 #msc:81S40 #nlin.SI
paper · pdf · doi:10.48550/arxiv.math-ph/0606026
Extended version of the talk at The 8th International Conference ``Path Integrals from Quantum Information to Cosmology'' (Prague, June 6-10, 2005)
arxiv created 2006/06/08 · openalex publication_date 2006/06/08 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A quantum field-theoretical model, which describes spatially non-homogeneous repulsive Bose gas in an external harmonic potential is considered. Two-point thermal correlation functions of the Bose gas are calculated in the framework of the functional integration approach. Successive integration over the ``high-energy'' functional variables first and then over the ``low-energy'' ones is used. The effective action functional for the low-energy variables is obtained in one loop approximation. The functional integral representations for the correlation functions are estimated by means of the stationary phase approximation. A power-law asymptotical behaviour of the correlators of the one-dimensional Bose gas is demonstrated in the limit, when the temperature is going to zero, while the volume occupied by the non-homogeneous Bose gas infinitely increases. The power-law behaviour is governed by the critical exponent dependent on the spatial arguments.