Time invariant -product and phase locking in -symmetric lattice models
arXiv:1801.04918 · doi:10.1103/PhysRevA.97.012128
Abstract
Over the past decade, non-Hermitian, -symmetric Hamiltonians have been investigated as candidates for both, a fundamental, unitary, quantum theory, and open systems with a non-unitary time evolution. In this paper, we investigate the implications of the former approach in the context of the latter. Motivated by the invariance of the (inner) product under time evolution, we discuss the dynamics of wave-function phases in a wide range of -symmetric lattice models. In particular, we numerically show that, starting with a random initial state, a universal, gain-site location dependent locking between wave function phases at adjacent sites occurs in the -symmetry broken region. Our results pave the way towards understanding the physically observable implications of time-invariants in the non-unitary dynamics produced by -symmetric Hamiltonians.
arXiv comment7 pages, 5 figures
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