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Spectral Methods in Surface Superconductivity

- S. Fournais, B. Helffer
- Mathematics
- 15 June 2010

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… Expand

SUPERCONDUCTIVITY IN DOMAINS WITH CORNERS

- V. Bonnaillie-Noel, S. Fournais
- Physics
- 15 February 2007

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… Expand

Analytic Structure of Many-Body Coulombic Wave Functions

- S. Fournais, M. Hoffmann-Ostenhof, T. Hoffmann-Ostenhof, T. O. Sorensen
- Mathematics
- 5 June 2008

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} =… Expand

Self-Adjointness of Two-Dimensional Dirac Operators on Domains

- R. Benguria, S. Fournais, E. Stockmeyer, H. Van Den Bosch
- Mathematics
- 6 February 2017

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.

The semi-classical limit of large fermionic systems

- S. Fournais, Mathieu Lewin, J. P. Solovej
- Mathematics, PhysicsCalculus of Variations and Partial Differential…
- 5 October 2015

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… Expand

The ground state energy of the three dimensional Ginzburg-Landau functional. Part~II: Surface regime

- S. Fournais, Ayman Kachmar, M. Persson
- Physics
- 19 October 2011

Energy asymptotics for Type II superconductors

- S. Fournais, B. Helffer
- Physics, Mathematics
- 13 September 2005

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… Expand

A uniqueness theorem for higher order anharmonic oscillators

- S. Fournais, M. Sundqvist
- Mathematics
- 9 September 2013

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 $k$… Expand

Analyticity of the density of electronic wavefunctions

- S. Fournais, M. Hoffmann-Ostenhof, T. Hoffmann-Ostenhof, Thomas Østergaard Sørensen
- Physics, Chemistry
- 29 November 2002

We prove that the electronic densities of atomic and molecular eigenfunctions are real analytic inR3 away from the nuclei.

The energy of dilute Bose gases

- S. Fournais, J. P. Solovej
- PhysicsAnnals of Mathematics
- 12 April 2019

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)… Expand

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