Bose-Einstein Condensation of a Gaussian Random Field in the Thermodynamic Limit

Physics – Condensed Matter – Statistical Mechanics

Scientific paper

Rate now

  [ 0.00 ] – not rated yet Voters 0   Comments 0

Details

REVTeX file, 32 pages, 2 figures, submitted to J. Phys. A: Math. Theor

Scientific paper

We derive the criterion for the Bose-Einstein condensation (BEC) of a Gaussian field $\phi$ (real or complex) in the thermodynamic limit. The field is characterized by its covariance function and the control parameter is the intensity $u=\|\phi\|_2^2/V$, where $V$ is the volume of the box containing the field. We show that for any dimension $d$ (including $d=1$), there is a class of covariance functions for which $\phi$ exhibits a BEC as $u$ is increased through a critical value $u_c$. In this case, we investigate the probability distribution of the part of $u$ contained in the condensate. We show that depending on the parameters characterizing the covariance function and the dimension $d$, there can be two distinct types of condensate: a Gaussian distributed "normal" condensate with fluctuations scaling as $1/\sqrt{V}$, and a non Gaussian distributed "anomalous" condensate. A detailed analysis of the anomalous condensate is performed for a one-dimensional system ($d=1$). Extending this one-dimensional analysis to exactly the point of transition between normal and anomalous condensations, we find that the condensate at the transition point is still Gaussian distributed but with anomalously large fluctuations scaling as $\sqrt{\ln(L)/L}$, where $L$ is the system length. The conditional spectral density of $\phi$, knowing $u$, is given for all the regimes (with and without BEC).

No associations

LandOfFree

Say what you really think

Search LandOfFree.com for scientists and scientific papers. Rate them and share your experience with other people.

Rating

Bose-Einstein Condensation of a Gaussian Random Field in the Thermodynamic Limit 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 Bose-Einstein Condensation of a Gaussian Random Field in the Thermodynamic Limit, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Bose-Einstein Condensation of a Gaussian Random Field in the Thermodynamic Limit will most certainly appreciate the feedback.

Rate now

     

Profile ID: LFWR-SCP-O-218389

  Search
All data on this website is collected from public sources. Our data reflects the most accurate information available at the time of publication.