相关论文: Mean-Field Approximation of Quantum Systems and Cl…

The nonlinear Schrodinger equation on the half line with mixed boundary condition is investigated. After a brief introduction to the corresponding classical boundary value problem, the exact second quantized solution of the system is…

We consider systems of $N$ particles in dimension one, driven by pair Coulombian or gravitational interactions. When the number of particles goes to infinity in the so called mean field scaling, we formally expect convergence towards the…

Mean-field models approximate large stochastic systems by simpler differential equations that are supposed to approximate the mean of the larger system. It is generally assumed that as the stochastic systems get larger (i.e., more people or…

Using Chetaev's theorem on stable trajectories in dynamics in the presence of perturbation forces we obtain a generalized stability condition for Hamiltonian systems that has the form of the Schrodinger equation. We show that the energy of…

Motivated by the initial value problem in semiclassical gravity, we study the initial value problem of a system consisting of a quantum scalar field weakly interacting with a classical one. The quantum field obeys a Klein-Gordon equation…

We consider the Vlasov-HMF (Hamiltonian Mean-Field) model. We consider solutions starting in a small Sobolev neighborhood of a spatially homogeneous state satisfying a linearized stability criterion (Penrose criterion). We prove that these…

The Hamiltonian Mean-Field model (HMF), an inertial XY ferromagnet with infinite-range interactions, has been extensively studied in the last few years, especially due to its long-lived meta-equilibrium states, which exhibit a series of…

In this article we consider a large system of fermions in a combined mean-field and semiclassical limit, in three dimensions. We investigate the convergence of the Wigner function of the ground state, towards the classical Thomas-Fermi…

In this paper, we rewrite the time-dependent Bogoliubov$\unicode{x2013}$de Gennes equation in an appropriate semiclassical form and establish its semiclassical limit to a two-particle kinetic transport equation with an effective mean-field…

We prove the global existence and uniqueness of classical solutions with small initial data and with wake-like decaying null infinity for the spherically symmetric Einstein-scalar-field equations with potential, where the scalar potential V…

We derive the relativistic Vlasov equation from quantum Hartree dynamics for fermions with relativistic dispersion in the mean-field scaling, which is naturally linked with an effective semiclassic limit. Similar results in the…

We formulate a kinetic theory of self-interacting meson fields with an aim to describe the freezeout stage of the space-time evolution of matter in ultrarelativistic nuclear collisions. Kinetic equations are obtained from the Heisenberg…

In this paper we elaborate a hybrid classical-quantum framework which allows one to model and solve heat and mass transfer problems occurring in electric contacts. We utilize special functions and Harrow-Hassidim-Lloyd (HHL) quantum…

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.

The Schrodinger equation for non-relativistic quantum systems is derived from some classical physics axioms within an ensemble hamiltonian framework. Such an approach enables one to understand the structure of the equation, in particular…

In this paper we discuss a Schwinger-Dyson [SD] approach for determining the time evolution of the unequal time correlation functions of a non-equilibrium classical field theory, where the classical system is described by an initial density…

We present a two-dimensional classical stochastic differential equation for a displacement field of a point particle in two dimensions and show that its components define real and imaginary parts of a complex field satisfying the…

We propose a system of equations to describe the interaction of a quasiclassical variable $X$ with a set of quantum variables $x$ that goes beyond the usual mean field approximation. The idea is to regard the quantum system as continuously…

Mean-field approaches where a complex fermionic many-body problem is replaced by an ensemble of independent particles in a self-consistent mean-field can describe many static and dynamical aspects. It generally provides a rather good…

We present a probabilistic proof of the mean field limit and propagation of chaos $N$-particle systems in three dimensions with positive (Coulomb) or negative (Newton) $1/r$ potentials scaling like $1/N$ and an $N$-dependent cut-off which…