Bose-Condensed Gases at Finite Temperatures

Abstract

The discovery of Bose Einstein condensation (BEC) in trapped ultracold atomic gases in 1995 has led to an explosion of theoretical and experimental research on the properties of Bose-condensed dilute gases. The first treatment of BEC at finite temperatures, this book presents a thorough account of the theory of two-component dynamics and nonequilibrium behaviour in superfluid Bose gases. It uses a simplified microscopic model to give a clear, explicit account of collective modes in both the collisionless and collision-dominated regions. Major topics such as kinetic equations, local equilibrium and two-fluid hydrodynamics are introduced at an elementary level. Explicit predictions are worked out and linked to experiments. Providing a platform for future experimental and theoretical studies on the finite temperature dynamics of trapped Bose gases, this book is ideal for researchers and graduate students in ultracold atom physics, atomic, molecular and optical physics and condensed matter physics.

Cosmological evolution of finite temperature Bose-Einstein condensate dark matter

“…The equilibrium density of the thermal excitations is obtained by integrating the equilibrium Bose -Einstein distribution over the momentum. Thus we obtain [22][23][24][25] …”

“…For a detailed discussion of the considered issues and of the derivation of the main results we refer the reader to the papers and books in [22]- [27].…”

“…The Heisenberg equation of motion for the quantum field operatorΦ describing the dynamics of a BoseEinstein condensate at arbitrary temperatures is given by [22][23][24][25] i ∂Φ ( r, t) ∂t…”

“…By introducing the non-condensate field operator ψ ( r, t) so thatΦ ( r, t) = Ψ ( r, t) +ψ ( r, t), where the average value ofψ ( r, t) is zero, ψ ( r, t) = 0, we can separate out the condensate component of the quantum field operator to obtain the equation of motion for Ψ as follows [22][23][24][25] i ∂Ψ ( r, t) ∂t…”

“…Then by taking into account that in the present approach we neglect the effects of the mean field associated with the anomalous density and the three-field correlation function, it follows that Eq. (3) is equivalent to the following hydrodynamic type system [22][23][24] …”