Related papers: On the Hartree-Fock-Bogoliubov equations
The multiconfigurational time-dependent Hartree-Fock equations are discussed and solved for a one-dimensional model of the Helium atom. Results for the ground state energy and two-particle density as well as the absorption spectrum are…
The derivation of effective evolution equations is central to the study of non-stationary quantum many-body sytems, and widely used in contexts such as superconductivity, nuclear physics, Bose-Einstein condensation and quantum chemistry. We…
The properties of quasi-one-dimensional quantum droplets of Bose-Einstein condensates are investigated analytically and numerically, taking into account the contribution of quantum fluctuations. Through the development of a variational…
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 $w\le 0$.…
We study the condensate phase dynamics in a low-temperature equilibrium gas of weakly interacting bosons, harmonically trapped and isolated from the environment. We find that at long times, much longer than the collision time between…
We analyze the correspondence between two formalisms describing an interacting Bose gas, namely the standard Feynman diagrammatic expansion on the one hand, and the hierarchy equations for the imaginary-time Green functions on the other…
The dynamics of Josephson-like oscillations between two coupled Bose-Einstein condensates is studied using the time-dependent variational method. We suppose that the quantum state of the condensates is a gaussian wave-packet which can…
We discuss the mean-field approximation for a trapped weakly-interacting Bose-Einstein condensate (BEC) and its connection with the exact many-body problem by deriving the Gross-Pitaevskii action of the condensate. The mechanics of the BEC…
A rotating bosonic many-body system in a harmonic trap is studied with the 3D-Cranked Hartree-Fock-Bogoliubov method at zero temperature, which has been applied to nuclear many-body systems at high spin. This method is a variational method…
We study the T=0 crossover from the BCS superconductivity to Bose-Einstein condensation in the attractive Hubbard Model within dynamical mean field theory(DMFT) in order to examine the validity of Hartree-Fock-Bogoliubov (HFB) mean field…
The Hartree-Fock-Bogoliubov (HFB) equations in coordinate representation are solved exactly, i.e., with correct asymptotic boundary conditions for the continuous spectrum. The calculations are preformed with effective Skyrme interactions.…
Mathematical results on some models describing the motion of a tracer particle through a Bose-Einstein condensate are described. In the limit of a very dense, very weakly interacting Bose gas and for a very large particle mass, the dynamics…
The nonlinear Hartree equation describes the macroscopic dynamics of initially factorized N-boson states, in the limit of large N. In this paper we provide estimates on the rate of convergence of the microscopic quantum mechanical evolution…
The Hamiltonian of a moving atom in electromagnetic fields includes velocity- dependent terms. We show that the leading velocity dependence emerges systematically in the non-relativistic limit from a scheme firmly based on the relativistic…
The disordered Bose Hubbard model is studied numerically within the Bogoliubov approximation. First, the spatially varying condensate wavefunction in the presence of disorder is found by solving a nonlinear Schrodinger equation. Using the…
An approximate many-body theory incorporating two-body correlations has been employed to calculate low-lying collective multipole frequencies in a Bose-Einstein condensate containing $A$ bosons, for different values of the interaction…
We present a theoretical study of the quantum depletion of microcavity polaritons that are excited with a resonant laser pulse. The dynamics of the quantum fluctuations are interpreted in the context of quantum quenches in general and in…
In this article, we prove the global well-posedness of the time-dependent Hartree-Fock-Bogoliubov (TDHFB) equations in $\mathbb{R}^{1+1}$ with two-body interaction potentials of the form $N^{-1}v_N(x) = N^{\beta-1} v(N^\beta x)$ where $v$…
The time dependent Gross-Pitaevskii equation describes the dynamics of initially trapped Bose-Einstein condensates. We present a rigorous proof of this fact starting from a many-body bosonic Schroedinger equation with a short scale…
Adiabatic approximations are a powerful tool for simplifying nonlinear quantum dynamics, and are applicable whenever a system exhibits a hierarchy of time scales. Current interest in small nonlinear quantum systems, such as few-mode…