Atomic hydrogen in an inhomogeneous magnetic field: Density profile and Bose-Einstein condensation

Thermodynamics of a trapped Bose-condensed gas

“…At high T it approaches the finite-temperature Hartree-Fock theory [9] with which it exactly coincides above the critical temperature. These two important features (collective and single-particle effects) are the main ingredients of the Popov approximation, which is then expected to be a good approximation in the whole range of temperature except near T c where mean-field theories are known to fail.…”

“…Finally it is worth noting that when the energy ǫ(p, r) is much larger than the chemical potential µ one obtains the Hartree-Fock type spectrum [9] …”

“…The self-consistent HF method has been already employed to study the thermodynamic properties of inhomogeneous dilute Bose systems [9,15].…”

“…In fact although the gas parameter na 3 is always very small, its 1/6-th power can be easily of the order of unity and in actual experiments it turns out that µ 0 is 0.3-0.4 k B T 0 c . Furthermore the ratio (9) depends on the number N of atoms in the trap in an extremely smooth way (η ∼ N 1/15 ).…”

“…The thermodynamic behaviour of trapped Bose gases has been already the object of several theoretical works, starting from the investigation of the ideal Bose gas [8], the development of the Hartree-Fock formalism [9], the inclusion of interaction effects using the local density approximation [10,11], up to the most recent approaches based on self-consistent mean-field theory [12][13][14][15] and numerical simulations [16].…”