# Relaxation Rates and Collision Integrals for Bose-Einstein Condensates

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## Abstract

Near equilibrium, the rate of relaxation to equilibrium and the transport properties of excitations (bogolons) in a dilute Bose-Einstein condensate (BEC) are determined by three collision integrals, Open image in new window , Open image in new window , and Open image in new window . All three collision integrals conserve momentum and energy during bogolon collisions, but only Open image in new window conserves bogolon number. Previous works have considered the contribution of only two collision integrals, Open image in new window and Open image in new window . In this work, we show that the third collision integral Open image in new window makes a significant contribution to the bogolon number relaxation rate and needs to be retained when computing relaxation properties of the BEC. We provide values of relaxation rates in a form that can be applied to a variety of dilute Bose-Einstein condensates.

## Keywords

Bose-Einstein condensate Kinetic equation Collision integral Relaxation## Notes

### Acknowledgements

The authors wish to thank the Robert A. Welch Foundation (Grant No. F-1051) for support of this work.

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