Non-perturbative approach for the time-dependent symmetry breaking

TL;DR

This paper introduces a variational method using a quartic exponential trial wave-function and a new variable to analyze time-dependent quantum systems, effectively capturing symmetry breaking and long-term evolution.

Contribution

It proposes a novel variational approach with a new physical variable to describe wave-packet shape and system evolution in quantum symmetry breaking.

Findings

Effective potential captures transition from false to true vacuum.

Method accurately describes long-term wave-function evolution.

Comparison with numerical results validates the approach.

Abstract

We present a variational method which uses a quartic exponential function as a trial wave-function to describe time-dependent quantum mechanical systems. We introduce a new physical variable $y$ which is appropriate to describe the shape of wave-packet, and calculate the effective action as a function of both the dispersion $\sqrt{< \hat{q}^2>}$ and $y$. The effective potential successfully describes the transition of the system from the false vacuum to the true vacuum. The present method well describes the long time evolution of the wave-function of the system after the symmetry breaking, which is shown in comparison with the direct numerical computations of wave-function.