Extension of Bogoliubov theory to quasicondensates
By Christophe Mora, Y. Castin. 2002
284 citations recorded by the source corpus.
We present an extension of the well-known Bogoliubov theory to treat low-dimensional degenerate Bose gases in the limit of weak interactions and low density fluctuations. We use a density-phase representation and show that a precise definition of the phase operator requires a space discretization in cells of size l. We perform a systematic expansion of the Hamiltonian in terms of two small parameters, the relative density fluctuations inside a cell and the phase change over a cell. The resulting macroscopic observables can be computed in one, two, and three dimensions with no ultraviolet or infrared divergence. Furthermore, this approach exactly matches Bogoliubov's approach when there is a true condensate. We give the resulting expressions for the equation of state of the gas, the ground state energy, and the first order and second order correlation functions of the field. Explicit calculations are done for homogeneous systems.
Subfields: Atomic and Molecular Physics, and Optics, Condensed Matter Physics
View Paper: https://www.semanticscholar.org/paper/8829cab2f0a1a892c8b7d2ed69046a7bf77a14f9
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In Atomic and Molecular Physics, and Optics
In Condensed Matter Physics
Citations in the corpus
- One-dimensional quantum liquids: Beyond the Luttinger liquid paradigm (2011, background): “In the limit of weak interactions (γ 1) 1D bosons form a quasicondensate characterized by slow algebraic decay of real-space correlation functions at long distances (Mora and Castin, 2003; Petrov et al., 2000; Popov, 1980).”
- Physics with coherent matter waves (2004, background): “In corresponding investigations it was indeed found that the phase coherence length in this case can be much smaller than the axial size of the sample [119, 120, 121, 122, 123, 124, 125, 126, 127, 128] Theoretical predictions result in a temperature dependend phase coherence length, lφc̃itePetrov200”