22 citations · 58 across the 17 of their papers we have counts for
9 papers · 1 filter
Dispersion for the Schr{ö}dinger equation on the line with short-range array of delta potentials
Romain Duboscq, Élio Durand-Simonnet, Stefan Le Coz
We study dispersive properties of the one-dimensional Schr{ö}dinger equation with a short-range array of delta interactions. More precisely, we consider the self-adjoint operator o…
Ground States of the Nonlinear Schr{ö}dinger Equation on the Tadpole Graph with a Repulsive Delta Vertex Condition
Romain Duboscq, Élio Durand-Simonnet, Stefan Le Coz
We consider the stationary nonlinear Schr{ö}dinger equation set on a tadpole graph with a repulsive delta vertex condition between the loop and the tail of the tadpole. We establis…
An asymptotic preserving scheme for the quantum Liouville-BGK equation
Romain Duboscq, Olivier Pinaud
We are interested in this work in the numerical resolution of the Quantum Liouville-BGK equation, which arises in the derivation of quantum hydrodynamical models from first princip…
Computation of excited states for the nonlinear Schr{ö}dinger equation: numerical and theoretical analysis
Christophe Besse, Romain Duboscq, Stefan Le Coz
Our goal is to compute excited states for the nonlinear Schr{ö}dinger equation in the radial setting. We introduce a new technique based on the Nehari manifold approach and give a…
Numerical Simulations on Nonlinear Quantum Graphs with the GraFiDi Library
Christophe Besse, Romain Duboscq, Stefan Le Coz
Nonlinear quantum graphs are metric graphs equipped with a nonlinear Schr{ö}dinger equation. Whereas in the last ten years they have known considerable developments on the theoreti…
Entropy minimization for many-body quantum systems
Romain Duboscq, Olivier Pinaud
The problem considered here is motivated by a work by B. Nachtergaele and H.T. Yau where the Euler equations of fluid dynamics are derived from manybody quantum mechanics, see [10]…
Gradient Flow Approach to the Calculation of Stationary States on Nonlinear Quantum Graphs
Christophe Besse, Romain Duboscq, Stefan Le Coz
We introduce and implement a method to compute stationary states of nonlinear Schr\''odinger equations on metric graphs. Stationary states are obtained as local minimizers of the n…
On Strichartz estimates for a dispersion modulated by a time-dependent deterministic noise
Romain Duboscq
We address the Cauchy problem for a nonlinear Schr{ö}dinger equation where the dispersion is modulated by a deterministic noise. The noise is understood as the derivative of a self…
On a stochastic Hardy-Littlewood-Sobolev inequality with application to Strichartz estimates for the white noise dispersion
Romain Duboscq, Anthony Réveillac
In this paper, we investigate a stochastic Hardy-Littlewood-Sobolev inequality. Due to the stochastic nature of the inequality, the relation between the exponents of intgrability i…