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Rigorous derivation of an effective model for periodic Schrödinger equations with linear band crossing of Dirac type
Elena Danesi
In this paper we consider a family of time-dependent 1-dimensional cubic Schrödinger equation (NLS) with periodic potential. Exploiting semiclassical scaling and multiscale analysi…
Dirac solitons in one-dimensional nonlinear Schrödinger equations
William Borrelli, Elena Danesi, Simone Dovetta +1
In this paper we study a family of one-dimensional stationary cubic nonlinear Schrödinger (NLS) equations with periodic potentials and linear part displaying Dirac points in the di…
Generalized Strichartz estimates for the massive Dirac equation with critical potentials
Federico Cacciafesta, Elena Danesi, Eric Séré
In this paper we prove generalized Strichartz estimates for the massive Dirac equation in the case of two critical potential perturbations, namely the Aharonov-Bohm magnetic p…
Stability of homogeneous equilibria of the Hartree-Fock equation, for its equivalent formulation for random fields
Charles Collot, Elena Danesi, Anne-Sophie de Suzzoni +1
The Hartree-Fock equation admits homogeneous states that model infinitely many particles at equilibrium. We prove their asymptotic stability in large dimensions, under assumptions…
Strichartz estimates for the 2D and 3D massless Dirac-Coulomb equations and applications
Elena Danesi
In this paper we continue the analysis of the dispersive properties of the 2D and 3D massless Dirac-Coulomb equations that has been started in arXiv:1503.00945 and arXiv:2101.07185…
Strichartz estimates for the half wave/Klein-Gordon and Dirac Equations on compact manifolds without boundary
Federico Cacciafesta, Elena Danesi, Long Meng
In this paper we study Strichartz estimates for the half wave, the half Klein-Gordon and the Dirac Equations on compact manifolds without boundary, proving in particular for each o…