7 papers
A perturbative microscopic derivation of the focusing measure with rough cut-off
Shahnaz Farhat, Andrew Rout
We give a derivation of the Gibbs measure for the focusing nonlinear Schrödinger equation (NLS) on the circle with rough cut-off. This extends earlier work by Sohinger and the seco…
Applications of renormalisation to orthonormal Strichartz estimates and the NLS system on the circle
Sonae Hadama, Andrew Rout
In this paper, we introduce a renormalisation procedure for the density associated with the system of nonlinear Schrödinger equations (NLSS) on a circle. We show that this renormal…
Well-posedness of the periodic nonlinear Schrödinger equation with concentrated nonlinearity
Jinyeop Lee, Andrew Rout
We study the solution theory of the nonlinear Schrödinger equation with a concentrated nonlinearity on the torus. In particular, we establish existence and uniqueness of global ene…
The well-posedness and convergence of higher-order Hartree equations in critical Sobolev spaces on
Ryan L. Acosta Babb, Andrew Rout
In this article, we consider Hartree equations generalised to order nonlinearities. These equations arise in the study of the mean-field limits of Bose gases with -body i…
Gibbs measures as local equilibrium KMS states for focusing nonlinear Schrödinger equations
Zied Ammari, Andrew Rout, Vedran Sohinger
In this paper, we are concerned with the study of statistical equilibria for focusing nonlinear Schrödinger and Hartree equations on the d-dimensional torus when d=1,2,3. Due to th…
A microscopic derivation of Gibbs measures for the 1D focusing quintic nonlinear Schrödinger equation
Andrew Rout, Vedran Sohinger
In this work, we obtain a microscopic derivation of Gibbs measures for the focusing quintic nonlinear Schrödinger equation (NLS) on from many-body quantum Gibbs states…
A microscopic derivation of Gibbs measures for the 1D focusing cubic nonlinear Schrödinger equation
Andrew Rout, Vedran Sohinger
In this paper, we give a microscopic derivation of Gibbs measures for the focusing cubic nonlinear Schrödinger equation on the one-dimensional torus from many-body quantum Gibbs st…