Fast conservative and entropic numerical methods for the Boson Boltzmann equation
For researchers simulating Bose-Einstein condensation, this provides faster, physically consistent numerical schemes.
The paper develops numerical methods for the quantum Boltzmann equation for bosons that preserve mass, energy, and entropy, and achieve O(N^2 log N) complexity instead of O(N^3).
In this paper we derive accurate numerical methods for the quantum Boltzmann equation for a gas of interacting bosons. The schemes preserve the main physical features of the continuous problem, namely conservation of mass and energy, the entropy inequality and generalized Bose-Einstein distributions as steady states. These properties are essential in order to develop schemes that are able to capture the energy concentration behavior of bosons. In addition we develop fast algorithms for the numerical evaluation of the resulting quadrature formulas which allow the final schemes to be computed only in O(N^2 log N) operations instead of O(N^3).