Related papers: Mean-field quantum dynamics with magnetic fields
In this paper we consider an interacting Bose gas at zero temperature, constrained to a finite box and in the mean field limiting regime. The N gas particles interact through a pair potential of positive type and with an ultraviolet…
We formulate a solvable model that describes generation and saturation of mean magnetic field in a dynamo with kinetic helicity, in the limit of large magnetic Prandtl number. This model is based on the assumption that the stochastic part…
We develop two theoretical approaches for dealing with the low-energy effects of the repulsive interaction in one-dimensional electron systems. Renormalization Group methods allow us to study the low-energy behavior of the unscreened…
We study the norm approximation to the Schr\"odinger dynamics of $N$ bosons in $\mathbb{R}^d$ ($d=1,2$) with an interaction potential of the form $N^{d\beta-1}w(N^{\beta}(x-y))$. Here we are interested in the focusing case $w\le 0$.…
Based on the Schrodinger equation, exact expressions for the non-relativistic particle energy in the local external field and the external field potential are derived as inhomogeneous density functionals. On this basis, it is shown that,…
The beyond mean-field dynamics of a bent dark soliton embedded in a two-dimensional repulsively interacting Bose-Einstein condensate is explored. We examine the case of a single bent dark soliton comparing the mean-field dynamics to a…
How does charge density constrain many-body wavefunctions in nature? The Hohenberg-Kohn theorem for non-relativistic, interacting many-body Schr\"odinger systems is well-known and was proved using \emph{reductio-ad-absurdum}; however, the…
Inspired by the works of Rodnianski and Schlein and Wu, we derive a new nonlinear Schr\"odinger equation that describes a second-order correction to the usual tensor product (mean-field) approximation for the Hamiltonian evolution of a…
The relationship between the mean-field approximations in various interacting models of statistical physics and measures of classical and quantum correlations is explored. We present a method that allows us to bound the total amount of…
The moving neutral system of two Coulomb charges on a plane subject to a constant magnetic field $B$ perpendicular to the plane is considered. It is shown that the composite system of finite total mass is bound for any center-of-mass…
We study two interacting particle systems, both modeled as a system of $N$ stochastic differential equations driven by Brownian motions with singular kernels and moderate interaction. We show a quantitative result where the convergence rate…
We consider the quantum mechanical many-body problem of a single impurity particle immersed in a weakly interacting Bose gas. The impurity interacts with the bosons via a two-body potential. We study the Hamiltonian of this system in the…
By using a variant of the quantum inverse scattering method, commutation relations between all elements of the quantum monodromy matrix of bosonic Massive Thirring (BMT) model are obtained. Using those relations, the quantum integrability…
We study the energy of quasi-particles in graphene within the Hartree-Fock approximation. The quasi-particles are confined via an inhomogeneous magnetic field and interact via the Coulomb potential. We show that the associated functional…
We introduce a N-particle system which approaches, in the mean-field limit, the solutions of the Landau equation with Coulomb singularity. This model plays the same role as the Kac's model for the homogeneous Boltzmann equation.
In this paper, we have analyzed the spectral and transport properties of a weakly correlated single-level quantum dot hybridized with one normal conducting and another Bardeen-Cooper-Schrieffer (BCS) superconducting lead (N-QD-S system) in…
The quantum dynamics of an electron in a uniform magnetic field is studied for geometries corresponding to integrable cases. We obtain the uniform asymptotic approximation of the WKB energies and wavefunctions for the semi-infinite plane…
The compressibility of a two-dimensional electron system with spin in a spatially correlated random potential and a quantizing magnetic field is investigated. Electron-electron interaction is treated with the Hartree-Fock method. Numerical…
Ferromagnetic thin films with magnetic single-ion anisotropies are studied within the framework of Schwinger bosonization of a quantum Heisenberg model. Two alternative bosonizations are discussed. We show that qualitatively correct results…
Mean-field evolution equations for the exciton and photon populations and polarizations (Bloch-Lamb equations) are written and numerically solved in order to describe the dynamics of electronic states in a quantum dot coupled to the photon…