http://arxiv.org/abs/1408.3538
The Doppler shift of de Broglie wave is obtained for fermions and massive bosons in a many body Fermi gas or in a Bose gas using the Lorentz transformations for momentum and energy of the particles. A formalism is developed to obtain the variation of de Broglie waves with temperature using the classic idea of Wien. It has been noticed that unlike the photon gas or electromagnetic waves in a black body chamber, where the variation is determined by the Wien’s displacement law, for Fermi gas the de Borglie wavelength increases with temperature and at a critical temperature it becomes infinity. This is the quantum to classical transition temperature for fermions. On the other hand for bosons, the de Broglie wavelength decreases with the increase in temperature. There is a minimum possible temperature at which condensation takes place. At the minimum of thr temperature the de Broglie wavelength of bosons become infinitely large. Unlike a transition from quantum to classical world this is indirectly related to the large value of coherence length for the bosons in the condensed phase.
S. De and S. Chakrabarty
Fri, 29 Aug 14
48/51
Comments: Five pages REVTEX file, no figures