Time-dependent mean field theory of nuclear dynamics.

P. Maedler

J. Uhlig, Jörg C. Lemm, A. Weiguny

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.

Pervez Amirali Hoodbhoy

Kazuhiro Yabana, Y. Kawashita, Tsunenori Inakura +5 more

The time‐dependent mean‐field theory has a long history in describing many‐nucleon dynamics in nuclear physics, and is now widely applied to many‐electron dynamics in atomic, molecular, and condensed matter physics. We present our recent studies in these fields, applying similar computational methods to both nuclear and electronic systems. In the linear response regime, we show calculations of the optical response of a medium mass nucleus and a fullerene molecule C60. The applications in nonlinear regime are also briefly mentioned.

Federico Carollo, Igor Lesanovsky

Understanding quantum many-body systems with long-range or infinite-range interactions is of relevance across a broad set of physical disciplines, including quantum optics, nuclear magnetic resonance, and nuclear physics. From a theoretical viewpoint, these systems are appealing since they can be efficiently studied with numerics, and in the thermodynamic limit are expected to be governed by mean-field equations of motion. Over the past years the capabilities to experimentally create long-range interacting systems have dramatically improved permitting their control in space and time. This allows us to induce and explore a plethora of nonequilibrium dynamical phases, including time crystals and even chaotic regimes. However, establishing the emergence of these phases from numerical simulations turns out to be surprisingly challenging. This difficulty led to the assertion that mean-field theory may not be applicable to time-dependent infinite-range interacting systems. Here, we rigorously prove that mean-field theory in fact exactly captures their dynamics, in the thermodynamic limit. We further provide bounds for finite-size effects and their dependence on the evolution time.