Eur. Phys. J. Special Topics 217, 69-78 (2013)
https://doi.org/10.1140/epjst/e2013-01755-9

Regular Article

Bogoliubov theory on the disordered lattice

¹ GISC, Departamento de Física de Materiales, Universidad Complutense, 28040 Madrid, Spain
² CEI Campus Moncloa, UCM-UPM, Madrid, Spain
³ Centre for Quantum Technologies, National University of Singapore, 117543 Singapore, Singapore

^a e-mail: cgaul@fis.ucm.es

Received: 24 September 2012
Revised: 15 January 2013
Published online: 11 March 2013

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.