Boltzmann-type collision operators for Bogoliubov excitations of Bose-Einstein condensates: A unified framework

Abstract

Starting from the Bogoliubov diagonalization for the Hamiltonian of a weakly interacting Bose gas under the presence of a Bose-Enstein Condensate, we derive the kinetic equation for the Bogoliubov excitations. Without dropping any of the commutators, we find three collisional processes. One of them describes the $1\leftrightarrow 2$ interactions between the condensate and the excited atoms. The other two describe the $2\leftrightarrow 2$ and $1\leftrightarrow 3$ interactions between the excited atoms themselves.

References in corpus (5)

• Quantum Kinetic Theory I: A Quantum Kinetic Master Equation for Condensation of a weakly interacting Bose gas without a trapping potential
• Quantum Kinetic Theory III: Simulation of the Quantum Boltzmann Master Equation
• Quantum Kinetic Theory III: Quantum kinetic master equation for strongly condensed trapped systems
• Dynamics of trapped Bose gases at finite temperatures
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Cited by in corpus (4)

• Wave turbulence and collective behavior models for wave equations with short- and long-range interactions
• General collisionless kinetic approach to studying excitations in arbitrary-spin quantum atomic gases
• On the emergence of quantum Boltzmann fluctuation dynamics near a Bose-Einstein Condensate
• Method of numerical simulation of interacting quantum gas kinetics on finite momentum lattice