71 citations · 410 across the 46 of their papers we have counts for
8 papers · 1 filter
Cwikel-Lieb-Rozenblum type inequalities for Hardy-Schrödinger operator
Giao Ky Duong, Rupert L. Frank, Thi Minh Thao Le +2
We prove a Cwikel-Lieb-Rozenblum type inequality for the number of negative eigenvalues of the Hardy-Schrödinger operator on . The b…
Hardy-Sobolev interpolation inequalities
Charlotte Dietze, Phan Thành Nam
We derive a family of interpolation estimates which improve Hardy's inequality and cover the Sobolev critical exponent. We also determine all optimizers among radial functions in t…
Second Order Expansion of Gibbs State Reduced Density Matrices in the Gross-Pitaevskii Regime
Christian Brennecke, Jinyeop Lee, Phan Thành Nam
We consider a translation-invariant system of bosons in that interact through a repulsive two-body potential with scattering length of order in the li…
Positive-density ground states of the Gross-Pitaevskii equation
Mathieu Lewin, Phan Thành Nam
We consider the nonlinear Gross-Pitaevskii equation at positive density, that is, for a bounded solution not tending to 0 at infinity. We focus on infinite ground states, which are…
Focusing dynamics of 2D Bose gases in the instability regime
Lea Boßmann, Charlotte Dietze, Phan Thành Nam
We consider the dynamics of a 2D Bose gas with an interaction potential of the form for . The interaction may be chosen to be negative and large…
Exponential bounds of the condensation for dilute Bose gases
Phan Thành Nam, Simone Rademacher
We consider N bosons on the unit torus in the Gross-Pitaevski regime where the interaction potential scales as . We prove that the thermal equilibrium…