Related papers: Mean Field Limits in Strongly Confined Systems
The universal three-body dynamics in ultra-cold binary gases confined to one-dimensional motion are studied. The three-body binding energies and the (2 + 1)-scattering lengths are calculated for two identical particles of mass $m$ and a…
The Schr\"odinger equation with a harmonic potential coupled to the Poisson equation, called the Schr\"odinger-Newton-Hooke (SNH) system, has been considered in a variety of physical contexts, ranging from quantum mechanics to general…
We consider a system of interacting bosons in one dimension at a two-body resonance. This system, which is weakly interacting, is known to give rise to effective three-particle interactions, whose dynamics is similar to that of a…
We consider three-body systems in two dimensions with zero-range interactions for general masses and interaction strengths. The momentum-space Schr\"odinger equation is solved numerically and in the Born-Oppenheimer (BO) approximation. The…
We study the time evolution of an initially trapped weakly interacting Bose gas at positive temperature, after the trapping potential has been switched off. It has been recently shown in arXiv:2009.00992 that the one-particle density matrix…
The thesis is devoted to the problem of colour confinement in the non-Abelian Yang-Mills theory (gluon part of Quantum Chromodynamics). A generalisation of the 3-dimensional Fock-Schwinger gauge is proposed where the Gauss law constraint is…
The present work establishes the mean-field limit of a N-particle system towards a regularized variant of the relativistic Vlasov-Maxwell system, following the work of Braun-Hepp [Comm. in Math. Phys. 56 (1977), 101-113] and Dobrushin…
This work focuses on the mean field stochastic partial differential equations with nonlinear kernels. We first prove the existence and uniqueness of strong and weak solutions for mean field stochastic partial differential equations in the…
A solvable model of a generic trapped bosonic mixture, $N_1$ bosons of mass $m_1$ and $N_2$ bosons of mass $m_2$ trapped in an harmonic potential of frequency $\omega$ and interacting by harmonic inter-particle interactions of strengths…
We study the dynamics of a Fermi gas with a Coulomb interaction potential, and show that, in a mean-field limiting regime, the dynamics is described by the Hartree-Fock equation. This extends previous work of Bardos et al. to the case of…
We investigate the many-particle and mean-field correspondence for a non-Hermitian N-particle Bose-Hubbard dimer where a complex onsite energy describes an effective decay from one of the modes. Recently a generalized mean-field…
In the limit of large particle numbers and low densities systems of cold atoms can be effectively described as macroscopic single particle systems in a mean-field approximation. In the case of a Bose-Hubbard system, modelling bosons on a…
We study the non-equilibrium steady states in a closed system consisting of interacting particles obeying exclusion principle with quenched hopping rate. Cluster mean field approach is utilized to theoretically analyze the system dynamics…
$N$-body non efimovian bound or quasi-bound states for particles with short range interactions are considered in arbitrary dimensions. The different resonance regimes near the threshold are depicted by using a generalization of the…
Exploring the impact of dimensionality on the quantum dynamics of interacting bosons in traps including particle correlations is an interesting but challenging task. Due to the different participating length scales the modelling of the…
In this work, we describe the dynamics of a Bose-Einstein condensate interacting with a degenerate Fermi gas, at zero temperature. First, we analyze the mean-field approximation of the many-body Schr\"odinger dynamics and prove emergence of…
We use nematic Multi-particle Collision Dynamics (N-MPCD) simulations to study confined nematic liquid crystals in square domains, with three distinct mean-field potentials: the classical Maier-Saupe and Marrucci-Greco models, and a more…
For a system of $N$ bosons in one space dimension with two-body $\delta$-interactions the Hamiltonian can be defined in terms of the usual closed semi-bounded quadratic form. We approximate this Hamiltonian in norm resolvent sense by…
We study abelian anyons at the mean-field/almost-bosonic level, whose dynamics are governed by the Chern-Simons-Schr\"odinger system. We consider the dimensional reduction of this 2D model by introducing an anisotropic trapping potential,…
We consider the long-time dynamics of focusing energy-critical Schr\"odinger equation perturbed by the $\dot{H}^\frac{1}{2}$-critical nonlinearity and with inverse-square potential(CNLS$_a$) in dimensions $d\in\{3,4,5\}$…