Collective quantum tunneling with time-dependent generator coordinate method

TL;DR

This paper demonstrates that the time-dependent generator coordinate method (TDGCM) accurately models collective quantum tunneling of interacting particles, overcoming mean-field limitations and aligning well with exact solutions.

Contribution

It applies TDGCM to a two-particle tunneling system, showing its effectiveness in capturing dynamics and providing insights into collective versus single-particle behaviors.

Findings

TDGCM reproduces exact quantum tunneling results

It overcomes the self-trapping effect in mean-field dynamics

Discrepancies in expectation value calculations reveal complex behaviors

Abstract

Inspired by the work of McGlynn and Simenel [Phys. Rev. C {\bf 102}, 064614 (2020)], this study investigates the quantum tunneling of two interacting distinguishable particles in two potential wells. We first benchmark the system by reproducing key established results: the exact quantum solution and the spurious self-trapping effect that arises in the real-time mean-field dynamics for strong interactions. To exactly capture the tunneling dynamics, we apply the time-dependent generator coordinate method (TDGCM) to the model. Numerical simulations demonstrate that the TDGCM, by utilizing the real-time mean-field states as generator states, successfully overcomes the self-trapping effect, yielding tunneling dynamics in excellent agreement with the exact solution. Furthermore, we explore the expectation values of the generator coordinates from the correlated TDGCM many-body wave function. While different methods for calculating expectation values show consistent results in some cases, significant discrepancies are observed in others, providing critical insights into the emergence of collective and single-particle behaviors in interacting systems. This work also verifies the TDGCM as a robust framework for describing collective quantum tunneling and opens avenues for its application to more complex and realistic systems.