Non-abelian thermal gauge potentials for high spin cold atom gases

TL;DR

This paper develops a theoretical framework using non-equilibrium Green functions to describe high-spin cold atom gases, revealing a non-abelian thermal gauge potential and analyzing spin coherence dynamics.

Contribution

It introduces a spinor Boltzmann equation for high-spin Bose gases and links thermal gauge potentials to non-abelian gauge structures, providing new insights into spin dynamics.

Findings

Derived a temperature-dependent spinor damping force.

Identified the thermal gauge potential as an SU(3) Lie algebra for spin-1 gases.

Numerically analyzed spin coherence oscillations and population dynamics.

Abstract

On the basis of the non-equilibrium Green function formalism, we derived a spinor Boltzmann equation for the Bose cold atom gases with high spin, which is achieved by a quantum Wigner transformation on the equation satisfied by the lesser Green function. After a Taylor series expansion on the scattering terms, a temperature-dependent spinor damping force can be obtained, which can be related to a non-abelian thermal gauge potential. For the spin-1 Bose gas, the thermal gauge potential constitutes a SU(3) Lie algebra. As an example, we calculate the spin coherence oscillation for the spin-1 Bose cold atom gas trapped in the optical lattice. The relative populations in the Zeeman states as well as the temperature-dependent damping force are illustrated numerically.