Dissipation Effects Induced by Internal Relative Motion Between Two Nonlinear σ-Models

Abstract

We studied the dissipation effect induced by the internal relative motion between two nonlinear [Formula: see text]-models (NLSMs). The internal degrees of freedom (DOF) of the two NLSMs coupled to each other via an interface potential. We performed the path integral of the vacuum persistence amplitude (VPA) and got the quantum action. Then we introduced the relative motion via a boost transformation with velocity parameter [Formula: see text]. Furthermore, we calculated the imaginary part of the boosted quantum action which was proportional to the vacuum decay probability. At last, we calculated the frictional force. The numerical results gave the velocity [Formula: see text] dependency of the vacuum decay probability, and the velocity [Formula: see text] dependency of the frictional force. There was a threshold of relative velocity [Formula: see text] for the vacuum decay probability and the frictional force. We gave a classical argument of the existence of the threshold, and the argument matched the mathematical results.