An ideal relativistic Bose-gas model with pair production is solved exactly in $d$ dimensions. The critical behavior is shown to be the same as the usual nonrelativistic Bose gas. Scaling functions (including nonuniversal parameters) for the equation of state and the correlation functions are obtained in a closed form. The scale-factor universality is verified by the formation of the expected universal ratios. Various limiting cases of the model depending on the relative magnitudes of the three basic length scales, i.e., Compton wave-length, thermal wavelength, and interparticle distance are discussed. In these limiting cases, previously known results are recovered, wherever these are available.An ideal relativistic Bose-gas model with pair production is solved exactly in $d$ dimensions. The critical behavior is shown to be the same as the usual nonrelativistic Bose gas. Scaling functions (including nonuniversal parameters) for the equation of state and the correlation functions are obtained in a closed form. The scale-factor universality is verified by the formation of the expected universal ratios. Various limiting cases of the model depending on the relative magnitudes of the three basic length scales, i.e., Compton wave-length, thermal wavelength, and interparticle distance are discussed. In these limiting cases, previously known results are recovered, wherever these are available.

Physical Review ASep 1, 198326 citations

Scaling behaviour in the Bose gas

M. Broidioi, André F. Verbeure

Communications in Mathematical PhysicsJan 1, 19965 citations

Mapping out the quasi-condensate transition through the 1D-3D dimensional crossover

Julien Armijo, T. Jacqmin, Karen V. Kheruntsyan +1 more

By measuring the density fluctuations in a highly elongated weakly interacting Bose gas, we observe and quantify the transition from the ideal gas to a quasi-condensate regime throughout the dimensional crossover from a purely 1D to an almost 3D gas. We show that that the entire transition region and the dimensional crossover are described surprisingly well by the modified Yang-Yang model. Furthermore, we find that at low temperatures the linear density at the quasi-condensate transition scales according to an interaction-driven scenario of a longitudinally uniform 1D Bose gas, whereas at high temperatures it scales according to the degeneracy-driven critical scenario of transverse condensation of a 3D ideal gas.By measuring the density fluctuations in a highly elongated weakly interacting Bose gas, we observe and quantify the transition from the ideal gas to a quasi-condensate regime throughout the dimensional crossover from a purely 1D to an almost 3D gas. We show that that the entire transition region and the dimensional crossover are described surprisingly well by the modified Yang-Yang model. Furthermore, we find that at low temperatures the linear density at the quasi-condensate transition scales according to an interaction-driven scenario of a longitudinally uniform 1D Bose gas, whereas at high temperatures it scales according to the degeneracy-driven critical scenario of transverse condensation of a 3D ideal gas.

arXiv:1011.3631Nov 16, 20100 citations

The ideal Bose-Einstein gas, revisited

Robert M. Ziff

Jan 1, 19760 citations

The ideal Bose-Einstein gas, revisited

Robert M. Ziff, G. E. Uhlenbeck, Mark Kac

Physics ReportsSep 1, 1977316 citations

An ideal relativistic Bose-gas model with pair production is solved exactly in

d

dimensions. The critical behavior is shown to be the same as the usual nonrelativistic Bose gas. Scaling functions (including nonuniversal parameters) for the equation of state and the correlation functions are obtained in a closed form. The scale-factor universality is verified by the formation of the expected universal ratios. Various limiting cases of the model depending on the relative magnitudes of the three basic length scales, i.e., Compton wave-length, thermal wavelength, and interparticle distance are discussed. In these limiting cases, previously known results are recovered, wherever these are available.