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A Lower Bound on the Critical Momentum of an Impurity in a Bose-Einstein Condensate

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arxiv 2311.05361 v2 pith:COJ3LV45 submitted 2023-11-09 math-ph math.MPmath.SPquant-ph

classification math-phmath.MPmath.SPquant-ph
keywords bose-einsteincondensateimpuritymodelmomentumquasi-particleassumebehavior
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In the Bogoliubov-Fr\"ohlich model, we prove that an impurity immersed in a Bose-Einstein condensate forms a stable quasi-particle when the total momentum is less than its mass times the speed of sound. The system thus exhibits superfluid behavior, as this quasi-particle does not experience friction. We do not assume any infrared or ultraviolet regularization of the model, which contains massless excitations and point-like interactions.

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Cited by 3 Pith papers

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    Infrared-divergent spin boson model loses its ground state above a finite critical coupling, proved via long range order in a dual continuum Ising model.

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  3. On the Ergodicity of Renormalized Translation-Invariant Nelson-Type Semigroups

    math-ph 2024-12 conditional novelty 7.0 of 10

    For negative coupling, the renormalized non-relativistic and semi-relativistic Nelson semigroups are positivity improving with respect to the Fröhlich cone at every total momentum, proven via Feynman-Kac functional in...

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