Abstract
The thermodynamics of ideal gas on the noncommutative geometry in the coherent state formalism is investigated. We first evaluate the statistical interparticle potential and see that there are residual “attraction (repulsion) potential” between boson (fermion) in the high temperature limit. The characters could be traced to the fact that, the particle with mass m in noncommutative thermal geometry with noncommutativity θ and temperature T will correspond to that in the commutative background with temperature T(1+kTmθ)−1. Such a correspondence implies that the ideal gas energy will asymptotically approach to a finite limiting value as that on commutative geometry at Tθ=(kmθ)−1. We also investigate the squeezed coherent states and see that they could have arbitrary mean energy. The thermal properties of those systems are calculated and compared to each other. We find that the heat capacity of the squeezed coherent states of boson and fermion on the noncommutative geometry have different values, contrast to that on the commutative geometry.
Highlights
The noncommutativity of spacetime which first studied by Snyder [1] is naturally found in the string/M theories [2,3]
We will see in subsection that when consider the contribution of the arbitrary squeezed coherent state the system will asymptotically approach to infinite energy, contrast to that approaches to a limiting energy in the system with un-squeezed coherent state
In this paper we first see that the particle with mass m in noncommutative thermal geometry with noncommutativity θ and temperature T will correspond to that in the commutative background with temperature T (1 + kT mθ)−1
Summary
The noncommutativity of spacetime which first studied by Snyder [1] is naturally found in the string/M theories [2,3]. Besides the above approach to noncommutative quantum theory there is another method, the coordinate coherent state approach [6,7]. Some interesting results have found are : there exists a finite maximum temperature that the black hole can reach before cooling down to absolute zero; there is no curvature singularity at the origin while existence a regular De-Sitter core at short distance. In this short paper we will report our investigations about the thermal property of ideal gas on the noncommutative geometry in the coherent state formalism
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