相关论文: Rate of Convergence in Nonlinear Hartree Dynamics …
In this paper the Hartree equation is derived from the $N$-body Schr\''odinger equation in the mean-field limit, with convergence rate estimates that are uniform in the Planck constant $\hbar$. Specifically, we consider the two following…
We develop and apply the multi-layer multi-configuration time-dependent Hartree method for bosons, which represents an ab initio method for investigating the non-equilibrium quantum dynamics of multi-species bosonic systems. Its multi-layer…
We study the time evolution in system of $N$ bosons with a relativistic dispersion law interacting through an attractive Coulomb potential with coupling constant $G$. We consider the mean field scaling where $N$ tends to infinity, $G$ tends…
We discuss the Hartree equation arising in the mean-field limit of large systems of bosons and explain its importance within the class of nonlinear Schroedinger equations. Of special interest to us is the Hartree equation with focusing…
In this paper we discuss in detail the nonlinear equations of the mean--field approximation and their connection to the exact many--body Schr\"odinger equation. Then we analyze the mean--field approach and the nonlinear dynamics of a…
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…
In the mean-field limit the dynamics of a quantum Bose gas is described by a Hartree equation. We present a simple method for proving the convergence of the microscopic quantum dynamics to the Hartree dynamics when the number of particles…
Mean-field Hartree theory is a central tool for reducing interacting many-body dynamics to an effective nonlinear one-particle evolution. This approximation has been employed also when the Hamiltonian that governs the many-body dynamics is…
We consider the dynamics of a large quantum system of $N$ identical bosons in 3D interacting via a two-body potential of the form $N^{3\beta-1} w(N^\beta(x-y))$. For fixed $0\leq \beta <1/3$ and large $N$, we obtain a norm approximation to…
We consider the dynamics of N bosons in one dimension. We assume that the pair interaction is attractive and given by N^{\beta -1}V(N^{\beta}\cdot) where \int V\leqslant 0. We develop new techniques in treating the N-body Hamiltonian so…
The occupation of more than one single-particle state and hence the emergence of fragmentation is a many-body phenomenon universal to systems of spatially confined interacting bosons. In the present study, we investigate the effect of the…
The derivation of the Hartree equation from many-body systems of Bosons in the mean field limit has been very intensively studied in the last couple of years. However, very few results exist showing convergence of the k-th marginal of the…
We consider the many-body dynamics of fermions with Coulomb interaction in a mean-field scaling limit where the kinetic and potential energy are of the same order for large particle numbers. In the considered limit the spatial variation of…
We consider a system of $N$ bosons interacting through a singular two-body potential scaling with $N$ and having the form $N^{3\beta-1} V (N^\beta x)$, for an arbitrary parameter $\beta \in (0,1)$. We provide a norm-approximation for the…
We solve the Schr\"odinger equation from first principles to investigate the many-body effects in the expansion dynamics of one-dimensional repulsively interacting bosons released from a harmonic trap. We utilize the multiconfigurational…
We study the quantum dynamics of a large number of interacting fermionic particles in a constant magnetic field. In a coupled mean-field and semiclassical scaling limit, we show that solutions of the many-body Schr\"odinger equation…
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 study the evolution of a many-particle system whose wave function obeys the N-body Schroedinger equation under Bose symmetry. The system Hamiltonian describes pairwise particle interactions in the absence of an external potential. We…
We review recent results concerning the evolution of fermionic systems. We are interested in the mean field regime, where particles experience many weak collisions. For fermions, the mean field regime is naturally linked with a…
In the mean-field regime, we prove convergence (with explicit bounds) of the many-body von Neumann dynamics with bounded interactions to the Hartree-von Neumann dynamics.