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Spectral Methods in Surface Superconductivity
Preface.- Notation.- Part I Linear Analysis.- 1 Spectral Analysis of Schr..odinger Operators.- 2 Diamagnetism.- 3 Models in One Dimension.- 4 Constant Field Models in Dimension 2: Noncompact Case.- 5…
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SUPERCONDUCTIVITY IN DOMAINS WITH CORNERS
We study the two-dimensional Ginzburg-Landau functional in a domain with corners for exterior magnetic field strengths near the critical field where the transition from the superconducting to the…
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Analytic Structure of Many-Body Coulombic Wave Functions
We investigate the analytic structure of solutions of non-relativistic Schrödinger equations describing Coulombic many-particle systems. We prove the following: Let ψ(x) with $${{\bf x} =…
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Self-Adjointness of Two-Dimensional Dirac Operators on Domains
We consider Dirac operators defined on planar domains. For a large class of boundary conditions, we give a direct proof of their self-adjointness in the Sobolev space $$H^1$$H1.
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The semi-classical limit of large fermionic systems
We study a system of N fermions in the regime where the intensity of the interaction scales as 1 / N and with an effective semi-classical parameter $$\hbar =N^{-1/d}$$ħ=N-1/d where d is the space…
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The ground state energy of the three dimensional Ginzburg-Landau functional. Part~II: Surface regime
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Energy asymptotics for Type II superconductors
We study the Ginzburg–Landau functional in the parameter regime describing ‘Type II superconductors’. In the exact regime considered minimizers are localized to the boundary — i.e. the sample is only…
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A uniqueness theorem for higher order anharmonic oscillators
We study for $\alpha\in\R$, $k \in {\mathbb N} \setminus \{0\}$ the family of self-adjoint operators \[ -\frac{d^2}{dt^2}+\Bigl(\frac{t^{k+1}}{k+1}-\alpha\Bigr)^2 \] in $L^2(\R)$ and show that if $k$…
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Analyticity of the density of electronic wavefunctions
We prove that the electronic densities of atomic and molecular eigenfunctions are real analytic inR3 away from the nuclei.
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The energy of dilute Bose gases
For a dilute system of non-relativistic bosons interacting through a positive $L^1$ potential $v$ with scattering length $a$ we prove that the ground state energy density satisfies the bound $e(\rho)…
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