Nonlinear Description of Quantum Dynamics. Generalized Coherent States

TL;DR

This paper demonstrates that generalized coherent states exhibit inherent nonlinear quantum dynamics by embedding classical manifolds into quantum Hilbert space, enabling classical-quantum analogy for analyzing wave function evolution.

Contribution

It introduces a method to describe quantum dynamics of generalized coherent states using classical manifold immersion, highlighting the nonlinear nature of their evolution.

Findings

Reveals nonlinear evolution in generalized coherent states.

Uses classical manifold immersion to analyze quantum dynamics.

Establishes classical-quantum analogy in state evolution.

Abstract

In this work it is shown that there is an inherent nonlinear evolution in the dynamics of the so-called generalized coherent states. To show this, the immersion of a classical manifold into the Hilbert space of quantum mechanics is employed. Then one may parametrize the time-dependence of the wave function through the variation of parameters in the classical manifold. Therefore, the immersion allows to consider the so-called principle of analogy, i.e. using the procedures and structures available from the classical setting to employ them in the quantum framework.