  In this work, we study different quantum thermodynamic functions (QTFs) of a
cold atom subjected to an artificial non-Abelian uniform magnetic field and
linearly coupled to a quantum heat bath through either usual
coordinate-coordinate coupling or through momentum variables. The bath is
modelled as a collection of independent quantum harmonic oscillators. In each
of the coupling scheme, the effect of the non-Abelian magnetic field on
different QTFs are explicitly demonstrated for a U(2) gauge transformation. In
each case, we show that the free energy has a different expression than that
for the Abelian case. We consider two illustrative heat bath spectrum (Ohmic
bath and Drude model) to evaluate explicit closed form expressions of free
energy (F), specific heat (C), and entropy (S) in the low temperature limit for
each of the above mentioned coupling scheme. The dependence of different QTFs
on the non-Abelian magnetic field are pointed out even if the gauge potential
is uniform in space.
