We study the time evolution of Fröhlich Hamiltonian in a mean-field limit which many particles weakly couple to quantized phonon field. Assuming that are initially Bose-Einstein condensate and excitations field coherent state we provide an effective dynamics approximates evolved many-body norm, provided number is large. The approximation given by product evolves according Landau–Pekar equations...

<p style='text-indent:20px;'>We study a particle approximation for one-dimensional first-order Mean-Field-Games (MFGs) with local interactions planning conditions. Our problem comprises system of Hamilton-Jacobi equation coupled transport equation. As we deal the problem, prescribe initial and terminal distributions The builds on semi-discrete variational problem. First, address existence...

Mean field approximation is a powerful technique to study the performance of large stochastic systems represented as interacting objects. Applications include load balancing models, epidemic spreading, cache replacement policies, or large-scale data centers, for which mean gives very accurate estimates transient steady-state behaviors. In series recent papers [9, 7], new and more approximation,...