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

TL;DR

This paper explores the Klein-Gordon oscillator in a non-commutative complex phase space, revealing negative heat capacity effects and the role of non-commutativity as a magnetic-like interaction affecting thermal properties.

Contribution

It provides exact solutions for the energy levels of the Klein-Gordon oscillator in non-commutative space and analyzes the impact on thermal behavior, highlighting novel negative heat capacity phenomena.

Findings

Energy levels split into 2m levels due to non-commutativity

Non-commutativity acts like a magnetic field interacting with particle spin

Heat capacity can become negative, indicating self-gravitation effects

Abstract

We obtain exact solutions to the two-dimensional Klein-Gordon oscillator in a non-commutative complex phase space to first order in the non-commutativity parameter. We derive the exact non-commutative energy levels and show that the energy levels split to $2m$ 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 $C_V$ on the non-commutative 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.