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

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.