Imaginary Time Mean-Field Method for Collective Tunneling

TL;DR

This paper introduces an imaginary time mean-field method for accurately modeling collective quantum tunneling in strongly interacting many-body systems, outperforming real-time approaches and aligning well with exact solutions.

Contribution

The paper proposes a novel imaginary time mean-field approach for tunneling, offering an initial-value method that better captures tunneling rates in complex systems.

Findings

Imaginary-time mean-field method predicts tunneling rates matching exact solutions.

Real-time Hartree dynamics show spurious self-trapping effects.

Method is potentially more suitable for realistic systems like heavy-ion fusion.

Abstract

Background: Quantum tunneling in many-body systems is the subject of many experimental and theoretical studies in fields ranging from cold atoms to nuclear physics. However, theoretical description of quantum tunneling with strongly interacting particles, such as nucleons in atomic nuclei, remains a major challenge in quantum physics. Purpose: An initial-value approach to tunneling accounting for the degrees of freedom of each interacting particle is highly desirable. Methods: Inspired by existing methods to describe instantons with periodic solutions in imaginary time, we investigate the possibility to use an initial value approach to describe tunneling at the mean-field level. Real-time and imaginary-time Hartree dynamics are compared to the exact solution in the case of two particles in a two-well potential. Results: Whereas real-time evolutions exhibit a spurious self-trapping effect preventing tunneling in strongly interacting systems, the imaginary-time-dependent mean-field method predicts tunneling rates in excellent agreement with the exact solution. Conclusions: Being an initial-value method, it could be more suitable than approaches requiring periodic solutions to describe realistic systems such as heavy-ion fusion.