Nonlinear Classical Dynamics described by a Density Matrix in the Classical Limit

TL;DR

This paper explores the classical limit of nonlinear semiclassical hybrid systems using a MaxEnt framework, showing that the classical limit is represented by a pure density matrix that reproduces classical dynamics.

Contribution

It introduces a general approach to derive classical dynamics from nonlinear hybrid quantum-classical systems within a MaxEnt framework, highlighting algebraic and smoothness constraints.

Findings

Classical limit characterized by a pure density matrix.

Reproduces classical dynamics from quantum operators.

Synthesizes previous examples to illustrate methodology.

Abstract

We examine the classical limit of a fairly general nonlinear semiclassical hybrid system within a MaxEnt framework. The consistency of the hybrid dynamics requires algebraic constraints on quantum operators and smoothness conditions for the classical variables. Analytically, we demonstrate that the classical limit is characterized by a pure density matrix representing a single state, which reproduces the dynamics of its classical analogue. To illustrate the methodology, we revisit and synthesize two previously studied examples.