Microscopic scattering theory for interacting bosons in weak random potentials

Abstract

We develop a diagrammatic scattering theory for interacting bosons in a three-dimensional, weakly disordered potential. Based on a microscopic N-body scattering theory, we identify the relevant diagrams including elastic and inelastic collision processes that are sufficient to describe diffusive quantum transport. By taking advantage of the statistical properties of the weak disorder potential, we demonstrate how the N-body dynamics can be reduced to a nonlinear integral equation of Boltzmann type for the single-particle diffusive flux. Our theory reduces to the Gross-Pitaevskii mean field description in the limit where only elastic collisions are taken into account. However, even at weak interaction strength, inelastic collisions lead to energy redistribution between the bosons - initially prepared all at the same single-particle energy - and thereby induce thermalization of the single-particle current. In addition, we include also weak localization effects and determine the coherent corrections to the incoherent transport in terms of the coherent backscattering signal. We find that inelastic collisions lead to an enhancement of the backscattered cone in a narrow spectral window for increasing interaction strength.

References in corpus (8)

• Zero-Transmission Law for Multiport Beam Splitters
• Coherent Backscattering of Ultracold Atoms
• Localization of Matter Waves in 2D-Disordered Optical Potentials
• Anderson localization of a Bose-Einstein condensate in a 3D random potential
• Bogoliubov Excitations of Disordered Bose-Einstein Condensates
• Coherent Forward Scattering Peak Induced by Anderson Localization
• Coherent backscattering of Bose-Einstein condensates in two-dimensional disorder potentials
• Inelastic Multiple Scattering of Interacting Bosons in Weak Random Potentials

Cited by in corpus (10)

• Effective dynamics of disordered quantum systems
• Quantum boomerang effect for interacting particles
• Quench dynamics of a weakly interacting disordered Bose gas in momentum space
• Breakdown of Anderson localization in the transport of Bose-Einstein condensates through one-dimensional disordered potentials
• Elastic and inelastic transmission in guided atom lasers: a truncated Wigner approach
• Localization of wave packets in one-dimensional random potentials
• Charge and spin diffusion on the metallic side of the metal-insulator transition: a self-consistent approach
• Localization landscape for interacting Bose gases in one-dimensional speckle potentials
• Al'tshuler-Aronov-Spivak oscillations of bosonic matter-wave beams in the presence of interaction
• Inversion of coherent backscattering with interacting Bose-Einstein condensates in two-dimensional disorder : a Truncated Wigner approach