W. H. Hu, L. Jin, Y. Li, Z. Song
A PT-symmetric non-Hermitian system can have full real spectrum but does not ensure probability preserving, in contrast to that of a Hermitian system during the time evolution. 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 the PT symmetry breaking and the metal-insulator transition occur simultaneously. It is also found 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 the Gaussian wave packet, are also observed.
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http://arxiv.org/abs/1203.0168
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