Project description
Thermodynamics and dynamics of dilute Bose gases at temperatures above zero
Bose-Einstein condensation is an exotic quantum phenomenon that was first observed in dilute alkali gases in 1995. Since then, it has triggered numerous mathematical investigations into dilute gas properties. In particular, substantial progress has been achieved in understanding their ground state properties in the Gross-Pitaevskii limit. Funded under the Marie Skłodowska-Curie programme, the DEBOGAS project aims to develop new mathematical tools to study the dilute Bose gases at positive temperatures on the Kelvin scale. The focus will be on proving refined estimates for the free energy in the Gross-Pitaevskii limit, which would increase understanding of how particle interactions affect the thermodynamic properties of dilute Bose gases. The project will also study the dynamics of approximate thermodynamic equilibrium states after external electric and/or magnetic fields have been changed.
Objective
The experimental realisation of Bose-Einstein condensation (BEC) in trapped alkali gases in 1995 triggered numerous mathematical investigations of the properties of dilute Bose gases. For the mathematical description of these experiments the Gross—Pitaevskii (GP) limit is relevant. In the past two decades there has been a substantial progress in the understanding of ground state properties of Bose gases in the GP limit, culminating in the recent rigorous justification of Bogoliubov’s theory for the ground state energy and for low lying excitations. Except for a recent contribution of me and my co-authors [1], the highly relevant GP limit at positive temperature has not been considered so far. The aim of the proposed project is to develop new mathematical tools to study dilute Bose gases at positive temperature. This will be done from two points of view: Thermodynamics and Dynamics. More precisely, in the first part of the project I plan to prove refined estimates (w.r.t. [1]) for the free energy in the GP limit which would yield a better understanding of how interactions affect the thermodynamic properties of such systems. In the second part I will investigate the dynamics of positive temperature states after the trapping potential will have been switched off and prove that a certain structure of the 1—pdm is stable under time evolution. Apart from asking two highly relevant questions in modern mathematical physics, the project is also interesting from a physics point of view since it would justify two frequently used approximations in the physics literature. [1] A. Deuchert, R. Seiringer, J. Yngvason, Bose-Einstein Condensation in a Dilute, Trapped Gas at Positive Temperaturre, Commun. Math. Phys. (2018). https://doi.org/10.1007/s00220-018-3239-0
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Funding Scheme
MSCA-IF - Marie Skłodowska-Curie Individual Fellowships (IF)Coordinator
8006 Zurich
Switzerland