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arXiv · 1801.04918

Time invariant $\mathcal{PT}$-product and phase locking in $\mathcal{PT}$-symmetric lattice models

Yogesh N. Joglekar·Franck Assogba Onanga·Andrew K. Harter
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Abstract

Over the past decade, non-Hermitian, $\mathcal{PT}$-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 $\mathcal{PT}$ (inner) product under time evolution, we discuss the dynamics of wave-function phases in a wide range of $\mathcal{PT}$-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 $\mathcal{PT}$-symmetry broken region. Our results pave the way towards understanding the physically observable implications of time-invariants in the non-unitary dynamics produced by $\mathcal{PT}$-symmetric Hamiltonians.

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Yogesh N. Joglekar, Franck Assogba Onanga, Andrew K. Harter. 2018-01-13. Time invariant $\mathcal{PT}$-product and phase locking in $\mathcal{PT}$-symmetric lattice models. https://doi.org/10.1103/physreva.97.012128

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