## $$\mathcal{PT}$$-symmetric strings

Paolo Amore, Francisco M. Fernández, Javier Garcia, German Gutierrez

We study both analytically and numerically the spectrum of inhomogeneous strings with $$\mathcal{PT}$$-symmetric density. We discuss an exactly solvable model of $$\mathcal{PT}$$-symmetric string which is isospectral to the uniform string; for more general strings, we calculate exactly the sum rules $$Z(p) \equiv \sum_{n=1}^\infty 1/E_n^p$$, with $$p=1,2,\dots$$ 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.

http://arxiv.org/abs/1306.1419
Mathematical Physics (math-ph)