Time-dependent mean-field theory: a classical approximation

M. C. Cambiaggio, G.G. Dussel, J. A. Ramirez

Jean-Paul Blaizot, Henri Orland

Pervez Amirali Hoodbhoy, John W. Negele

A general hierarchy of approximations to the many-body Schr\"odinger equation is presented which reduces to the time-dependent mean-field approximation in lowest order and provides systematic corrections in subsequent orders. The theory is applied to two interacting systems described by the Lipkin model Hamiltonian. Comparison of the results of the lowest two orders of approximation with the exact solution demonstrates the practicality of the method and its potential for generalizing nuclear dynamics beyond the mean field theory.NUCLEAR STRUCTURE Time-dependent approximation to nuclear dynamics. Corrections to time-dependent mean-field theory. Solution of Lipkin model for two interacting systems.

Roger Balian

Roger Balian, M. Vénéroni

Andrew Eberhardt, Michael Kopp, Alvaro Zamora +1 more

We introduce a numerical method and python package, chimes, that simulates quantum systems initially well approximated by mean field theory using a second order extension of the classical field approach. We call this the field moment expansion method. In this way, we can accurately approximate the evolution of first and second field moments beyond where the mean field theory breaks down. This allows us to estimate the quantum break time of a classical approximation without any calculations external to the theory. We investigate the accuracy of the field moment expansion using a number of well studied quantum test problems. Interacting bosonic systems similar to scalar field dark matter are chosen as test problems. We find that successful application of this method depends on two conditions: the quantum system must initially be well described by the classical theory, and the growth of the higher order moments must be hierarchical.