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24 papers · 1 filter
Characterization of the critical magnetic field in the Dirac-Coulomb equation
Jean Dolbeault, Maria J. Esteban, Michael Loss
We consider a relativistic hydrogenic atom in a strong magnetic field. The ground state level depends on the strength of the magnetic field and reaches the lower end of the spectra…
Repeated Quantum Interactions and Unitary Random Walks
Stéphane Attal, Ameur Dhahri
Among the discrete evolution equations describing a quantum system $\rH_S$ undergoing repeated quantum interactions with a chain of exterior systems, we study and characterize thos…
Ground State and Charge Renormalization in a Nonlinear Model of Relativistic Atoms
Philippe Gravejat, Mathieu Lewin, Eric Sere
We study the reduced Bogoliubov-Dirac-Fock (BDF) energy which allows to describe relativistic electrons interacting with the Dirac sea, in an external electrostatic potential. The…
On the Bakry-Emery criterion for linear diffusions and weighted porous media equations
Jean Dolbeault, Bruno Nazaret, Giuseppe Savaré
The goal of this paper is to give a non-local sufficient condition for generalized Poincaré inequalities, which extends the well-known Bakry-Emery condition. Such generalized Poinc…
Super-linear elliptic equation for the Pucci operator without growth restrictions for the data
Maria J. Esteban, Patricio Felmer, Alexander Quaas
In this paper we deal with existence and uniqueness of solution to super-linear problems for the Pucci operator: $$ -\M^+(D^2u)+|u|^{s-1}u=f(x) \quad {in} \RR^n, $$ where and…
Stochastic Homogenization of Reflected Diffusion Processes
Remi Rhodes
We investigate a functional limit theorem (homogenization) for Reflected Stochastic Differential Equations on a half-plane with stationary coefficients when it is necessary to anal…