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arXiv · 1306.1419

$\mathcal{PT}$-symmetric strings

Paolo Amore·Francisco M. Fernández·Javier Garcia·German Gutierrez
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Abstract

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.

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Paolo Amore, Francisco M. Fernández, Javier Garcia, German Gutierrez. 2013-06-06. $\mathcal{PT}$-symmetric strings. https://doi.org/10.1016/j.aop.2014.01.013

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