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7 papers · 2 filters
Gell-Mann and Low formula for degenerate unperturbed states
Christian Brouder, Gianluca Panati, Gabriel Stoltz
The Gell-Mann and Low switching allows to transform eigenstates of an unperturbed Hamiltonian into eigenstates of the modified Hamiltonian . This switching can be pe…
Diagonal hyperbolic systems with large and monotone data Part I: Global continuous solutions
Ahmad El Hajj, Régis Monneau
In this paper, we study diagonal hyperbolic systems in one space dimension. Based on a new gradient entropy estimate, we prove the global existence of a continuous solution, for la…
The Dielectric Permittivity of Crystals in the reduced Hartree-Fock approximation
Eric Cancès, Mathieu Lewin
In a recent article (Cancès, Deleurence and Lewin, Commun. Math. Phys., 281 (2008), pp. 129-177), we have rigorously derived, by means of bulk limit arguments, a new variational mo…
Short time existence and uniqueness in Hölder spaces for the 2D dynamics of dislocation densities
Ahmad El Hajj
In this paper, we study the model of Groma and Balogh describing the dynamics of dislocation densities. This is a two-dimensional model where the dislocation densities satisfy a sy…
Derivation and study of dynamical models of dislocation densities
Ahmad El Hajj, H. Ibrahim, Régis Monneau
In this paper, starting from the microscopic dynamics of isolated dislocations, we explain how to derive formally mean field models for the dynamics of dislocation densities. Essen…
Global existence for a system of non-linear and non-local transport equations describing the dynamics of dislocation densities
Marco Cannone, Ahmad El Hajj, Regis Monneau +1
In this paper, we study the global in time existence problem for the Groma-Balogh model describing the dynamics of dislocation densities. This model is a two-dimensional model wher…