Marco Falconi

On the rate of convergence for the mean field approximation of bosonic many-body quantum dynamics

We consider the time evolution of quantum states by many-body Schrodinger dynamics and study the rate of convergence of their reduced density matrices in the mean field limit. If the prepared state at initial time is of coherent or factorized type and the number of particles

Wigner measures approach to the classical limit of the Nelson model: Convergence of dynamics and ground state energy

n

Bohr's correspondence principle in quantum field theory and classical renormalization scheme: the Nelson model

is large enough then it is known that

Classical limit of the Nelson model with cutoff

1/n

Mode regularization for N = 1, 2 SUSY Sigma model

is the correct rate of convergence at any time. We show in the simple case of bounded pair potentials that the previous rate of convergence holds in more general situations with possibly correlated prepared states. In particular, it turns out that the coherent structure at initial time is unessential and the important fact is rather the speed of convergence of all reduced density matrices of the prepared states. We illustrate our result with several numerical simulations and examples of multi-partite entangled quantum states borrowed from quantum information.

Self-Adjointness Criterion for Operators in Fock Spaces

We consider the classical limit of the Nelson model, a system of stable nucleons interacting with a meson field. We prove convergence of the quantum dynamics towards the evolution of the coupled Klein–Gordon–Schrödinger equation. Also, we show that the ground state energy level of

Concentration of cylindrical Wigner measures

N

Effective Potentials Generated by Field Interaction in the Quasi-Classical Limit

N nucleons, when