Bogoliubov theory on the disordered lattice
Christopher Gaul, Cord A. M\"uller
TL;DR
This paper uses inhomogeneous Bogoliubov theory to analyze quantum fluctuations in Bose-Einstein condensates within disordered lattices, providing analytical and numerical insights into scattering, sound speed, and depletion effects.
Contribution
It introduces a comprehensive analytical framework for studying quantum fluctuations in disordered lattices using Bogoliubov theory, extending to arbitrary dimensions.
Findings
Calculated elastic scattering rates in disordered lattices.
Derived renormalized speed of sound in the presence of disorder.
Provided analytical expressions for condensate depletion that match numerical data.
Abstract
Quantum fluctuations of Bose-Einstein condensates trapped in disordered lattices are studied by inhomogeneous Bogoliubov theory. Weak-disorder perturbation theory is applied to compute the elastic scattering rate as well as the renormalized speed of sound in lattices of arbitrary dimensionality. Furthermore, analytical results for the condensate depletion are presented, which are in good agreement with numerical data.
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