Thermodynamic Properties of the 2N-Piece Relativistic String

TL;DR

This paper calculates the thermodynamic free energy of a piecewise uniform relativistic bosonic string with 2N segments, revealing equal critical temperatures across parts and deriving asymptotic level density using Meinardus theorem.

Contribution

It extends previous work by analyzing thermodynamic properties of a 2N-piece relativistic string and deriving asymptotic level density and critical temperatures.

Findings

Critical temperatures in all parts are equal for any spacetime dimension.

Asymptotic density of states is calculated using Meinardus theorem.

For D=26, the inverse critical temperature is proportional to the square root of tension in part II.

Abstract

The thermodynamic free energy F(\beta) is calculated for a gas consisting of the transverse oscillations of a piecewise uniform bosonic string. The string consists of 2N parts of equal length, of alternating type I and type II material, and is relativistic in the sense that the velocity of sound everywhere equals the velocity of light. The present paper is a continuation of two earlier papers, one dealing with the Casimir energy of a 2N--piece string [I. Brevik and R. Sollie (1997)], and another dealing with the thermodynamic properties of a string divided into two (unequal) parts [I. Brevik, A. A. Bytsenko and H. B. Nielsen (1998)]. Making use of the Meinardus theorem we calculate the asymptotics of the level state density, and show that the critical temperatures in the individual parts are equal, for arbitrary spacetime dimension D. If D=26, we find \beta= (2/N)\sqrt{2\pi /T_{II}}, T_{II} being the tension in part II. Thermodynamic interactions of parts related to high genus g is also considered.