Hartree-Fock Mean-Field Theory for Trapped Dirty Bosons

Abstract

Here we work out in detail a non-perturbative approach to the dirty boson problem, which relies on the Hartree-Fock theory and the replica method. For a weakly interacting Bose gas within a trapped confinement and a delta-correlated disorder potential at finite temperature, we determine the underlying free energy. From it we determine via extremization self-consistency equations for the three components of the particle density, namely the condensate density, the thermal density, and the density of fragmented local Bose-Einstein condensates within the respective minima of the random potential landscape. Solving these self-consistency equations in one and three dimensions in two other publications has revealed how these three densities change for increasing disorder strength.

References in corpus (12)

• Direct observation of Anderson localization of matter-waves in a controlled disorder
• Bose-Einstein condensation of photons in an optical microcavity
• Bose-Einstein-condensed systems in random potentials
• Bogoliubov Excitations of Disordered Bose-Einstein Condensates
• Bose-Einstein-condensed gases in arbitrarily strong random potentials
• Bose-Einstein Condensates in Strongly Disordered Traps
• Bogoliubov Theory of Dipolar Bose Gas in Weak Random Potential
• Dipolar Bose gas in a weak isotropic speckle disorder
• Quantum Critical Scaling of Dirty Bosons in Two Dimensions
• Analytical and numerical study of dirty bosons in a quasi-one-dimensional harmonic trap
• Disorder-Induced Shift of Condensation Temperature for Dilute Trapped Bose Gases
• Variational approach for Bose-Einstein condensates in strongly disordered traps

Cited by in corpus (12)

• Excitation spectra of a Bose-Einstein condensate with an angular spin-orbit coupling
• Enhancement of the Bose glass phase in the presence of an artificial gauge field
• Cloud shape of a molecular Bose-Einstein condensate in a disordered trap: a case study of the dirty boson problem
• Measuring the Edwards-Anderson order parameter of the Bose glass: a quantum gas microscope approach
• Analytical and numerical study of dirty bosons in a quasi-one-dimensional harmonic trap
• Superfluids, Fluctuations and Disorder
• Faraday and resonant waves in binary collisionally-inhomogeneous Bose-Einstein condensates
• Green's function approach to the Bose-Hubbard model with disorder
• Multifractality and Hyperuniformity in Quasicrystalline Bose-Hubbard Models with and without Disorder
• Disordered Bose-Einstein condensate in hard walls trap
• Localization landscape for interacting Bose gases in one-dimensional speckle potentials
• Phase Diagram and Spectral Function of the Two-Dimensional Disordered Bose-Hubbard Model: A Real-Space Dynamical Mean-Field Theory Analysis