5 papers · 1 filter
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…
Ground state energy of the Bose--Hubbard model with large coordination number with a polaron-type quantum de Finetti theorem
Shahnaz Farhat, Denis Périce, Sören Petrat
We consider the ground state energy of the Bose--Hubbard model on a graph with large and homogeneous coordination number. In the limit of infinite coordination number, we prove con…
Mean-Field Dynamics of the Bose-Hubbard Model in High Dimension
Shahnaz Farhat, Denis Périce, Sören Petrat
The Bose-Hubbard model effectively describes bosons on a lattice with on-site interactions and nearest-neighbour hopping, serving as a foundational framework for understanding stro…
Quantum-classical motion of charged particles interacting with scalar fields
Shahnaz Farhat
The goal of this article is to investigate the dynamics of semi-relativistic or non-relativistic charged particles in interaction with a scalar meson field. Our main contribution i…
Expansion of the Many-body Quantum Gibbs State of the Bose-Hubbard Model on a Finite Graph
Zied Ammari, Shahnaz Farhat, Sören Petrat
We consider the many-body quantum Gibbs state for the Bose-Hubbard model on a finite graph at positive temperature. We scale the interaction with the inverse temperature, correspon…