Bose-Einstein condensation distribution

Fig. 1-1. Probability density functions of partiele energy distribution (a) Fermi function, (b) Bose-Einstein function, e = particle energy f(i) - probability density function cp = Fermi level sb - Bose-Einstein condensation level.

This difference between fermions and bosons is reflected in how they occupy a set of states, especially as a function of temperature. Consider the system shown in Figure E.10. At zero temperature (T = 0), the bosons will try to occupy the lowest energy state (a Bose-Einstein condensate) while for the fermions the occupancy will be one per quantum state. At high temperatures the distributions are similar and approach the Maxwell Boltzman distribution. 

In order to study the decoherence of quasi-particles within BEC, we use Bragg spectroscopy and Monte Carlo hydrodynamic simulations of the system [Castin 1996], and confirm recent theoretical predictions of the identical particle collision cross-section within a Bose-Einstein condensate. We use computerized tomography [Ozeri 2002] of the experimental images in determining the exact distributions. We then conduct both quantum mechanical and hydrodynamic simulation of the expansion dynamics, to model the distribution of the atoms, and compare theory and experiment [Katz 2002] (see Fig. 2). 

An interesting phenomenon predicted for boson systems where the number of particles is fixed is that of Bose-Einstein condensation. This implies that, as the temperature is gradually reduced, there is a sudden occupation of the zero momentum state by a macroscopic number of particles. The number of particles per increment range of energy is sketched in Fig. 3 for temperatures above and just below the Bose-Einstein condensation temperature Tb. The distribution retains, at least approximately, the classical Maxwellian form until Tb is reached. Below Tj, there are two classes of particles those in the condensate (represented by the spike at = 0) and those in excited states. The criterion for a high or low temperature in a boson system is simply that of whether T >T or T < 7b, where 7b is given by ... 

FIGURE 3 Sketch of the energy distribution function n E) of an ideal Bose-Einstein gas above, and very slightly below, the Bose-Einstein condensation temperature 7b. 

To understand the possibility of this type of coherent excitation, the strong interaction with the heat bath must be emphasized. It endeavors to impose its temperature on the distribution which is demonstrated by the form (12), which represents a Bose distribution at temperature T, But while in a Bose gas the number of particles is fixed so that the Einstein condensation arises only when the temperature is sufficiently lowered, in our case the temperature is fixed, but the number of particles (quanta) increases with increasing rate of energy supply. 

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