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Open Quantum Systems Decoherence
Quantum Simulation
Comparison of two semiclassical expansions for a family of PT-symmetric oscillators
arXiv
Authors: Francisco M. Fernández, Javier Garcia
Year
2013
Paper ID
31353
Status
Preprint
Abstract Read
~2 min
Abstract Words
88
Citations
N/A
Abstract
We show that a recently developed semiclassical expansion for the eigenvalues of PT-symmetric oscillators of the form V(x)=(ix)2N+1+bix does not agree with an earlier WKB expression for V(x)=-(ix)2N+1 the case b=0. The reason is due to the choice of different paths in the complex plane for the calculation of the WKB integrals. We compare the Stokes and anti-Stokes lines that apply to each case for the quintic oscillator and derive a general WKB expression that contains the two earlier ones.
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- We show that a recently developed semiclassical expansion for the eigenvalues of PT-symmetric oscillators of the form V(x)=(ix)^2N+1+bix does not agree with an earlier WKB...
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