Specific heat of a particle on the cone

Details Specific heat of a particle on the cone Specific heat of a particle on the cone

2006-04-05

arxiv.org/abs/gr-qc/0604019v1

Phys.Rev. A73 (2006) 052105

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

7 pages, 1 figure, REVTeX4 file. Version to appear in Physical Review A

Scientific paper

10.1103/PhysRevA.73.052105

This work investigates how a conical singularity can affect the specific heat of systems. A free nonrelativistic particle confined to the lateral surface of a cone -- conical box -- is taken as a toy model. Its specific heat is determined as a function of the deficit angle and the temperature. For a vanishing deficit angle, the specific heat is that of a particle in a flat disk where a characteristic temperature separates quantum and classical behaviors, as usual. By increasing the deficit angle the characteristic temperature increases also, and eventually another characteristic temperature (which does not depend on the deficit angle) arises. When the cone gets sufficiently sharp, at low and intermediate temperatures the azimuthal degree of freedom is suppressed. At low temperatures the specific heat varies discontinuously with the deficit angle. Connections between certain theorems regarding common zeros of the Bessel functions and this discontinuity are reported.

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