On evolutionary processes in large N quantum mechanics

TL;DR

This paper analyzes large N quantum mechanics with unbroken O(N) symmetry, showing that the equations of motion simplify to classical mechanics with a modified potential, and finds no tunneling occurs.

Contribution

It demonstrates that in the large N limit, quantum dynamics reduce to classical mechanics with a potential correction, simplifying analysis of such systems.

Findings

Only potential is corrected at infinite N

System dynamics can be described by classical mechanics

Tunneling is absent in the large N limit

Abstract

Equations of motion of large N quantum mechanics are solved for infinite N in the case of unbroken global O(N) symmetry. It is shown that the only correction to the action is a change in the potential. All characteristics of the motion (frequencies of oscillations, times of rolling, a phase portrait etc.) can be computed by means of a classical mechanics for the corrected potential. In particular, a tunneling in the system is absent.