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arXiv · 1203.0168

Probability-preserving evolution in a non-Hermitian two-band model

W. H. Hu·L. Jin·Y. Li·Z. Song
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Abstract

A non-Hermitian PT-symmetric system can have full real spectrum but does not ensure probability preserving time evolution, in contrast to that of a Hermitian system. We present a non-Hermitian two-band model, which is comprised of dimerized hopping terms and staggered imaginary on-site potentials, and study the dynamics in the exact PT-symmetric phase based on the exact solution. It is shown that an initial state, which does not involve two equal-momentum-vector eigenstates in different bands, obeys perfectly probability-preserving time evolution in terms of the Dirac inner product. Beyond this constriction, the quasi-Hermitian dynamical behaviors, such as non-spreading propagation and fractional revival of a Gaussian wave packet, are also observed.

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W. H. Hu, L. Jin, Y. Li, Z. Song. 2012-03-01. Probability-preserving evolution in a non-Hermitian two-band model. https://doi.org/10.1103/physreva.86.042110

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