17,942 research outputs found
Ground State Pressure and Energy Density of a Homogeneous Bose Gas in Two Dimensions
We consider an interacting homogeneous Bose gas at zero temperature in two
spatial dimensions. The properties of the system can be calculated as an
expansion in powers of g, where g is the coupling constant. We calculate the
ground state pressure and the ground state energy density to second order in
the quantum loop expansion. The renormalization group is used to sum up leading
and subleading logarithms from all orders in perturbation theory. In the dilute
limit, the renormalization group improved pressure and energy density are
essentially expansions in powers of the T-matrix.Comment: 1 figure, revte
Theory of the Weakly Interacting Bose Gas
We review recent advances in the theory of the three-dimensional dilute
homogeneous Bose gas at zero and finite temperature. Effective field theory
methods are used to formulate a systematic perturbative framework that can be
used to calculate the properties of the system at T=0. The perturbative
expansion of these properties is essentially an expansion in the gas parameter
, where is the s-wave scattering length and is the number
density. In particular, the leading quantum corrections to the ground state
energy density, the condensate depletion, and long-wavelength collective
excitations are rederived in and efficient and economical manner. We also
discuss nonuniversal effects. These effects are higher-order corrections that
depend on properties of the interatomic potential other than the scattering
length, such as the effective range. We critically examine various approaches
to the dilute Bose gas in equilibrium at finite temperature. These include the
Bogoliubov approximation, the Popov approximation, the Hartree-Fock-Bogoliubov
approximation, the -derivable approach, optimized perturbation theory,
and renormalization group techniques. Finally, we review recent calculations of
the critical temperature of the dilute Bose gas, which include 1/N-techniques,
lattice simulations, self-consistent calculations, and variational perturbation
theory.Comment: 44 pages, 20 Postscript figures. Revised version. Expanded by 7 pages
and 4 figs. Updated section on T_c and updated list of references. Discussion
on atomic potentials and effective field theory added. Revised version
accepted for publication in Review of Modern physic
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