Exponential spreading and singular behavior of quantum dynamics near hyperbolic points

TL;DR

This paper investigates the quantum behavior near hyperbolic points, revealing exponential spreading of quantum states and analyzing the conditions under which this rapid evolution occurs.

Contribution

It introduces a detailed analysis of quantum dynamics near hyperbolic points, highlighting exponential spreading and the conditions for such behavior.

Findings

Quantum expectation values exhibit singular behavior near hyperbolic points.

Quantum states expand exponentially fast in this regime.

Conditions for exponential spreading are identified.

Abstract

Quantum dynamics of a particle in the vicinity of a hyperbolic point is considered. Expectation values of dynamical variables are calculated, and the singular behavior is analyzed. Exponentially fast extension of quantum dynamics is obtained, and conditions for this realization are analyzed.