Negative heat capacity for a Klein–Gordon oscillator in non-commutative complex phase space

Abstract

We obtain exact solutions to the two-dimensional (2D) Klein–Gordon oscillator in a non-commutative (NC) complex phase space to first order in the non-commutativity parameter. We derive the exact NC energy levels and show that the energy levels split to [Formula: see text] levels. We find that the non-commutativity plays the role of a magnetic field interacting automatically with the spin of a particle induced by the non-commutativity of complex phase space. The effect of the non-commutativity parameter on the thermal properties is discussed. It is found that the dependence of the heat capacity [Formula: see text] on the NC parameter gives rise to a negative quantity. Phenomenologically, this effectively confirms the presence of the effects of self-gravitation induced by the non-commutativity of complex phase space.