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Energy and vorticity in fast rotating Bose–Einstein condensates

We study a rapidly rotating Bose–Einstein condensate confined to a finite trap in the framework of two-dimensional Gross–Pitaevskii theory in the strong coupling (Thomas–Fermi) limit. Denoting the…
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Stability for a System of N Fermions Plus a Different Particle with Zero-Range Interactions

We study the stability problem for a non-relativistic quantum system in dimension three composed by N ≥ 2 identical fermions, with unit mass, interacting with a different particle, with mass m, via a…
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Rapidly rotating Bose-Einstein condensates in homogeneous traps

We extend the results of a previous paper on the Gross-Pitaevskii description of rotating Bose-Einstein condensates in two-dimensional traps to confining potentials of the form V(r)=rs, 2<s<∞.…
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Validity of the Spin-Wave Approximation for the Free Energy of the Heisenberg Ferromagnet

We consider the quantum ferromagnetic Heisenberg model in three dimensions, for all spins S ≥ 1/2. We rigorously prove the validity of the spin-wave approximation for the excitation spectrum, at the…
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Surface Superconductivity in Presence of Corners

We consider an extreme type-II superconducting wire with non-smooth cross section, i.e., with one or more corners at the boundary, in the framework of the Ginzburg-Landau theory. We prove the…
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Critical Rotational Speeds in the Gross-Pitaevskii Theory on a Disc with Dirichlet Boundary Conditions

We study the two-dimensional Gross-Pitaevskii theory of a rotating Bose gas in a disc-shaped trap with Dirichlet boundary conditions, generalizing and extending previous results that were obtained…
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Rapidly rotating Bose-Einstein condensates in strongly anharmonic traps

We study a rotating Bose-Einstein condensate in a strongly anharmonic trap (flat trap with a finite radius) in the framework of two-dimensional Gross-Pitaevskii theory. We write the coupling constant…
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Quantum Mechanics and Stochastic Mechanics for Compatible Observables at Different Times

Abstract Bohm mechanics and Nelson stochastic mechanics are confronted with quantum mechanics in the presence of noninteracting subsystems. In both cases, it is shown that correlations at different…
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On the Ginzburg–Landau Functional in the Surface Superconductivity Regime

We present new estimates on the two-dimensional Ginzburg–Landau energy of a type-II superconductor in an applied magnetic field varying between the second and third critical fields. In this regime,…
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The Transition to a Giant Vortex Phase in a Fast Rotating Bose-Einstein Condensate

We study the Gross-Pitaevskii (GP) energy functional for a fast rotating Bose-Einstein condensate on the unit disc in two dimensions. Writing the coupling parameter as 1/ε2 we consider the asymptotic…
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