相关论文: Norm approximation for many-body quantum dynamics …
We consider a system of $N$ bosons where the particles experience a short range two-body interaction given by $N^{-1}v_N(x)=N^{3\beta-1}v(N^\beta x)$ where $v \in C^\infty_c(\mathbb{R}^3)$, without a definite sign on $v$. We extend the…
We consider the focusing 3D quantum many-body dynamic which models a dilute bose gas strongly confined in two spatial directions. We assume that the microscopic pair interaction is attractive and given by $a^{3\beta-1}V(a^{\beta}\cdot)$…
We investigate Bose-Einstein condensation for interacting bosons at zero and nonzero temperature. Functional renormalization provides us with a consistent method to compute the effect of fluctuations beyond the Bogoliubov approximation. For…
We consider weakly interacting bosonic gases with local and non-local multi-body interactions. By using the Bogoliubov approximation, we first investigate contact interactions, studying the case in which the interparticle potential can be…
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…
The mean field approximation is numerically validated in the bosonic case by considering the time evolution of quantum states and their associated reduced density matrices by many-body Schr\"odinger dynamics. The model phase-space is…
A nonequilibrium master equation analysis for N interacting bosons, with Bogoliubov quasiparticles as the reservoir is presented. The analysis is based on a simplified Hamiltonian. The steady state solution yields the equilibrium density…
We consider the dynamics of $N$ bosons in three dimensions. We assume the pair interaction is given by $N^{3\beta -1}V(N^{\beta }\cdot )$ . By studying an associated many-body wave operator, we introduce a BBGKY hierarchy which takes into…
The derivation of mean-field limits for quantum systems at zero temperature has attracted many researchers in the last decades. Recent developments are the consideration of pair correlations in the effective description, which lead to a…
We consider a 2D quantum system of $N$ bosons in a trapping potential $|x|^s$, interacting via a pair potential of the form $N^{2\beta-1} w(N^\beta x)$. We show that for all $0 \textless{} \beta \textless{} (s+1)/(s+2)$, the leading order…
The mean-field approximations of many-boson dynamics are known to be effective in many physical relevant situations. The mathematical justifications of such approximations rely generally on specific considerations which depend too much on…
We consider a many-body Boson system with pairwise particle interaction given by $N^{3\beta-1}v(N^\beta x)$ for $0<\beta<1$ and $v$ a non-negative spherically-symmetric function. Our main result is the extension of the local-in-time Fock…
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 study the many-body dynamics of an initially factorized bosonic wave function in the mean-field regime. We prove large deviation estimates for the fluctuations around the condensate. We derive an upper bound extending a recent result to…
We consider N trapped bosons in R 3 interacting via a pair potential w which has a long range of dipolar type. We show the convergence of the energy and of the minimizers for the many-body problem towards those of the dipolar…
We study the mean-field and semiclassical limit of the quantum many-body dynamics with a repulsive $\delta$-type potential $N^{3\beta}V(N^{\beta}x)$ and a Coulomb potential, which leads to a macroscopic fluid equation, the Euler-Poisson…
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…
The formulation for zero mode of a Bose-Einstein condensate beyond the Bogoliubov approximation at zero temperature [Y.Nakamura et al., Phys. Rev. A 89, 013613 (2014)] is extended to finite temperature. Both thermal and quantum fluctuations…
We develop a quantum many-body theory of the Bose-Hubbard model based on the canonical quantization of the action derived from a Gutzwiller mean-field ansatz. Our theory is a systematic generalization of the Bogoliubov theory of…
We consider a trapped dilute gas of $N$ bosons in $\mathbb{R}^3$ interacting via a three-body interaction potential of the form $N\, V(N^{1/2}(x-y,x-z))$. In the limit $N\to \infty$, we prove that every approximate ground state of the…