The Functional Integration and the Two-Point Correlation Function of the One-Dimensional Bose Gas in the Harmonic Potential

Details The Functional Integration and the Two-Point Correlation Function of the One-Dimensional Bose Gas in the Harmonic Potential The Functional Integration and the Two-Point Correlation Function of the One-Dimensional Bose Gas in the Harmonic Potential

2006-04-18

arxiv.org/abs/cond-mat/0604413v1

St.-Petersburg Mathematical Journal, Vol. 17, No. 1 (2006), 63-84

Physics

Condensed Matter

Statistical Mechanics

26 pages, no figures

Scientific paper

A quantum field-theoretical model which describes spatially non-homogeneous one-dimensional non-relativistic repulsive Bose gas in an external harmonic potential is considered. We calculate the two-point thermal correlation function of the Bose gas in the framework of the functional integration approach. The calculations are done in the coordinate representation. A method of 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 calculated in one loop approximation. The functional integral representation for the correlation function is obtained in terms of the low-energy variables, and is estimated by means of the stationary phase approximation. The asymptotics of the correlation function is studied in the limit when the temperature is going to zero while the volume occupied by non-homogeneous Bose gas infinitely increases. It is demonstrated that the behaviour of the thermal correlation function in the limit described is power-like, and it is governed by the critical exponent which depends on the spatial and thermal arguments.

Affiliated with

Also associated with

No associations

Rating

The Functional Integration and the Two-Point Correlation Function of the One-Dimensional Bose Gas in the Harmonic Potential does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with The Functional Integration and the Two-Point Correlation Function of the One-Dimensional Bose Gas in the Harmonic Potential, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and The Functional Integration and the Two-Point Correlation Function of the One-Dimensional Bose Gas in the Harmonic Potential will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-196080