Bogoliubov excitation spectrum of trapped Bose gases in the Gross–Pitaevskii regime
We consider an inhomogeneous system of N bosons in R 3 confined by an external
potential and interacting via a repulsive potential of the form N 2 V (N (x− y)). We prove that …
potential and interacting via a repulsive potential of the form N 2 V (N (x− y)). We prove that …
Scaling limits of bosonic ground states, from many-body to non-linear Schrödinger
N Rougerie - EMS Surveys in Mathematical Sciences, 2021 - ems.press
How and why could an interacting system of many particles be described as if all particles
were independent and identically distributed? This question is at least as old as statistical …
were independent and identically distributed? This question is at least as old as statistical …
Ground state energy of mixture of Bose gases
We consider the asymptotic behavior of a system of multi-component trapped bosons, when
the total particle number N becomes large. In the dilute regime, when the interaction …
the total particle number N becomes large. In the dilute regime, when the interaction …
Two-term expansion of the ground state one-body density matrix of a mean-field Bose gas
We consider the homogeneous Bose gas on a unit torus in the mean-field regime when the
interaction strength is proportional to the inverse of the particle number. In the limit when the …
interaction strength is proportional to the inverse of the particle number. In the limit when the …
Interacting many-particle systems in the random Kac–Luttinger model and proof of Bose–Einstein condensation
Following a model originally considered by Kac and Luttinger, we study interacting many-
particle systems in a random background. The background consists of hard spherical …
particle systems in a random background. The background consists of hard spherical …
On the characterisation of fragmented Bose–Einstein condensation and its emergent effective evolution
J Lee, A Michelangeli - Nonlinearity, 2023 - iopscience.iop.org
Abstract Fragmented Bose–Einstein condensates are large systems of identical bosons
displaying multiple macroscopic occupations of one-body states, in a suitable sense. The …
displaying multiple macroscopic occupations of one-body states, in a suitable sense. The …
Bosons in a double well: two-mode approximation and fluctuations
We study the ground state for many interacting bosons in a double-well potential, in a joint
limit where the particle number and the distance between the potential wells both go to …
limit where the particle number and the distance between the potential wells both go to …
The Hartree functional in a double well
We consider a non-linear Hartree energy for bosonic particles in a symmetric double-well
potential. In the limit where the wells are far apart and the potential barrier is high, we prove …
potential. In the limit where the wells are far apart and the potential barrier is high, we prove …
On some rigorous aspects of fragmented condensation
In this paper we discuss some aspects of fragmented condensation from a mathematical
perspective. We first propose a simple way of characterizing finite fragmentation. Then …
perspective. We first propose a simple way of characterizing finite fragmentation. Then …
Binding energy of homogeneous Bose gases
PT Nam - Letters in Mathematical Physics, 2018 - Springer
We compute the energy needed to add or remove one particle from a homogeneous system
of N bosons on a torus. We focus on the mean-field limit when N becomes large and the …
of N bosons on a torus. We focus on the mean-field limit when N becomes large and the …