Thermodynamic properties of the 2N-piece relativistic string

Abstract

The thermodynamic free energy F(β) 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, J. Math. Phys. 38, 2774 (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, Class. Quantum Grav. 15, 3383 (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 space–time dimension D. If D=26, we find β=(2/N)2π/TII, TII being the tension in part II. Thermodynamic interactions of parts related to high genus g is also considered.