Theory of the weakly interacting Bose gas
By J. Andersen. 2003
361 citations recorded by the source corpus.
This article reviews 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 a system at $T=0.$ The perturbative expansion of these properties is essentially an expansion in the gas parameter $\sqrt{{\mathrm{na}}^{3}},$ where $a$ is the $s$-wave scattering length and $n$ 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 an efficient and economical manner. Nonuniversal effects are also discussed. These effects are higher-order corrections that depend on properties of the interatomic potential other than the scattering length, such as the effective range. The article critically examines 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 \ensuremath{\Phi}-derivable approach, optimized perturbation theory, and renormalization-group techniques. The article ends with a look at 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.
Subfields: Atomic and Molecular Physics, and Optics, Condensed Matter Physics
View Paper: https://www.semanticscholar.org/paper/5d014cc9bfd587ed01a65492756287ffccc69639
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In Atomic and Molecular Physics, and Optics
In Condensed Matter Physics
Citations in the corpus
- Dynamics and statistical mechanics of ultra-cold Bose gases using c-field techniques (2008, methodology): “onfirm 54 that the shift is in the positive direction with combined estimate of c ˇ1:31 0:02 [7,119]. A number of recent improved results broadly agree, and useful discussions are provided by Andersen [5] and Holzmann et al. [96]. Here, we briefly describe the procedure used by Davis et al. [50] to ca”
- Universality in few‐body systems with large scattering length (2004, background): “Examples include the Landau theory of Fermi liquids [139], phonons [140], spin waves [141], the weakly-interacting Fermi gas [142], and the weakly-interacting Bose gas [1].”
- Mathematical Models and Numerical Methods for Bose-Einstein Condensation (2012, background): “8)) – Thomas-Fermi (TF) approximation – [11,130], we obtain μ g φ TF g (x) = V (x)φ TF g (x) + β|φ g (x)|(2)φ g (x), x ∈ R.”