Equivalence of a compressible inviscid flow and the Bloch vector under the thermal Jaynes-Cummings model

TL;DR

This paper demonstrates that the evolution of the Bloch vector in the thermal Jaynes-Cummings model is mathematically equivalent to a compressible inviscid flow with zero vorticity, revealing a hidden-variable structure with infinite degrees of freedom.

Contribution

It establishes a novel equivalence between quantum Bloch vector dynamics and classical fluid flow, and explores the underlying deterministic and integrable properties.

Findings

Bloch vector dynamics are equivalent to a zero-vorticity compressible flow.

The system exhibits quasiperiodicity with infinite angular momenta as integrals of motion.

The dynamics can be described by a hidden-variable model with local determinism.

Abstract

In this paper, we show that the time evolution of the Bloch vector governed by the thermal Jaynes-Cummings model is equivalent to a compressible inviscid flow with zero vorticity. Because of its quasiperiodicity, the dynamics of the Bloch vector includes countably infinite angular momenta as integrals of motion. Moreover, to derive the Bloch vector, we trace out the Hilbert space of the cavity field and remove entanglement between the single atom and the cavity mode. These facts indicate that the dynamics of the Bloch vector can be described with a hidden-variable model that has local determinism and a countably infinite number of degrees of freedom. Our results fit these considerations.