%0 Journal Article
%T $\mathcal{PT}$-symmetric strings
%A Paolo Amore
%A Francisco M. Fern¨˘ndez
%A Javier Garcia
%A German Gutierrez
%J Physics
%D 2013
%I arXiv
%R 10.1016/j.aop.2014.01.013
%X 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.
%U http://arxiv.org/abs/1306.1419v1