PT-symmetric strings

We study both analytically and numerically the spectrum of inhomogeneous strings with PT-symmetric density. We discuss an exactly solvable model of PT-symmetric string which is isospectral to the uniform string; for more general strings, we calculate exactly the sum rules Z(p)≡∑n=1∞1/Enp, with p=1,2,… and find explicit expressions which can be used to obtain bounds on the lowest eigenvalue. A detailed numerical calculation is carried out for two non-solvable models depending on a parameter, obtaining precise estimates of the critical values where pair of real eigenvalues become complex.