Geometric characteristics of quantum evolution: curvature and torsion

TL;DR

This paper introduces the concepts of curvature and torsion in quantum evolution, analyzing how quantum states deviate from geodesic paths and planes, providing new geometric insights into quantum dynamics.

Contribution

It defines and explores the geometric characteristics of quantum evolution, specifically curvature and torsion, which are novel measures of state deviation in quantum dynamics.

Findings

Curvature quantifies deviation from geodesic in quantum evolution.

Torsion measures deviation from the two-dimensional evolution plane.

Provides a geometric framework for understanding quantum state trajectories.

Abstract

We study characteristics of quantum evolution which can be called curvature and torsion. The curvature shows a deviation of the state vector in quantum evolution from the geodesic line. The torsion shows a deviation of state vector from the plane of evolution (a two-dimensional subspace) at a given time.