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Titlebook: Mathematical Challenges of Zero-Range Physics; Models, Methods, Rig Alessandro Michelangeli Conference proceedings 2021 The Editor(s) (if a

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Scattering Theory for Delta-Potentials Supported by Locally Deformed Planes,ness of the wave operators with respect to a suitable reference dynamics. Additionally, we provide an explicit expression for the related scattering matrix and show that it converges to the identity as the deformation goes to zero (giving a quantitative estimates on the rate of convergence).
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Ultraviolet Properties of a Polaron Model with Point Interactions and a Number Cutoff,ary conditions. The singularities occurring in this model are essentially the same as in the model with quadratic boson dispersion, with simplifications in the formulas highlighting their key features.
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Quantum Confinement in ,-Grushin Planes,gorously characterize the presence or absence of self-adjointness of these operators. We also compare our technique and result with the already studied problem of quantum confinement in the half-cylinder.
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Thermodynamic Properties of Ultracold Fermi Gases Across the BCS-BEC Crossover and the Bertsch ProbIn this chapter we review the thermodynamic properties of ultracold Fermi gases in which the strength of the interaction is continuously varied. The system features a crossover between a state described by the BCS theory of superconductivity and a Bose-Einstein condensate. A discussion of the Bertsch problem is presented.
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