A new scaling property of the Casimir energy for a piecewise uniform string

An unexpected and very accurate scaling invariance of the Casimir energy of the piecewise uniform relativistic string is pointed out. The string consi sts of 2N pieces of equal length, of alternating type I/type II material, e ndowed with different tensions and mass densities but adjusted such that th e velocity of transverse sound equals c. If E-N(x) denotes the Casimir ener gy as a function of the tension ratio x = T-I/T-II, it turns out that the r atio f(N)(x)= E-N(x)/E-N(0), which lies between zero and one, will be pract ically independent of N for integers N greater than or equal to 2. Physical implications of this scaling invariance are discussed. Finite temperature theory is also considered. (C) 1999 American Institute of Physics. [S0022-2 488(99)02902-3].