Publication: The mean-field limit of quantum Bose gases at positive temperature
The mean-field limit of quantum Bose gases at positive temperature
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Fröhlich, J., Knowles, A., Schlein, B., & Sohinger, V. (2021). The mean-field limit of quantum Bose gases at positive temperature. Journal of the American Mathematical Society, 35, 955–1030. https://doi.org/10.1090/jams/987
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We prove that the grand canonical Gibbs state of an interacting quantum Bose gas converges to the Gibbs measure of a nonlinear Schrödinger equation in the mean-field limit, where the density of the gas becomes large and the interaction strength is proportional to the inverse density. Our results hold in dimensions d ≤ 3. For d > 1 the Gibbs measure is supported on distributions of negative regularity and we have to renormalize the interaction. More precisely, we prove the convergence of the relative partition function and of the re
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- Fröhlich, Jürg
- Knowles, Antti
- Schlein, Benjamin
- Sohinger, Vedran
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Fröhlich, J., Knowles, A., Schlein, B., & Sohinger, V. (2021). The mean-field limit of quantum Bose gases at positive temperature. Journal of the American Mathematical Society, 35, 955–1030. https://doi.org/10.1090/jams/987