Thermodynamic Properties of the Piecewise Uniform String
I. Brevik, A. A. Bytsenko, H. B. Nielsen
Abstract
The thermodynamic free energy F is calculated for a gas whose particles are the quantum excitations of a piecewise uniform bosonic string. The string consists of two parts of length LI and LII, endowed with different tensions and mass densities, adjusted in such a way that the velocity of sound always equals the velocity of light. The explicit calculation is done under the restrictive condition that the tension ratio x = TI/TII approaches zero. Also, the length ratio s = LII/LI is assumed to be an integer. The expression for F is given on an integral form, in which s is present as a parameter. For large values of s, the Hagedorn temperature becomes proportional to the square root of s.
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