Large amplitude collective dynamic beyond the independent particle/quasiparticle picture

TL;DR

This paper reviews time-dependent mean-field theory and explores advanced methods beyond it to better describe collective dynamics and quantum fluctuations in finite fermionic systems, especially at low excitation energies.

Contribution

It provides a comparative overview of theories beyond mean-field, highlighting their advantages, limitations, and relevance for describing complex collective phenomena.

Findings

Discusses the impact of correlations on predictive power.

Highlights the importance of quantum fluctuations in low-energy systems.

Compares approaches like Balian-Vénéroni, TDRPA, and Stochastic Mean-Field.

Abstract

In the present note, a summary of selected aspects of time-dependent mean-field theory is first recalled. This approach is optimized to describe one-body degrees of freedom. A special focus is made on how this microscopic theory can be reduced to a macroscopic dynamic for a selected set of collective variables. Important physical phenomena like adiabaticity/diabaticity, one-body dissipation or memory effect are discussed. Special aspects related to the use of a time-dependent density functional instead of a time-dependent Hartree-Fock theory based on a bare hamiltonian are underlined. The absence of proper description of complex internal correlations however strongly impacts the predictive power of mean-field. A brief overview of theories going beyond the independent particles/quasi-particles theory is given. Then, a special attention is paid for finite fermionic systems at low internal excitation. In that case, quantum fluctuations in collective space that are poorly treated at the mean-field level, are important. Several approaches going beyond mean-field, that are anticipated to improve the description of quantum fluctuations, are discussed: the Balian-V\'en\'eroni variational principle, the Time-Dependent Random Phase Approximation and the recently proposed Stochastic Mean-Field theory. Relations between these theories are underlined as well as their advantages and shortcomings.