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Effects of disorder on non-unitary $\mathcal{PT}$ symmetric quantum walks (1608.00719v2)
Published 2 Aug 2016 in quant-ph and cond-mat.mes-hall
Abstract: $\mathcal{PT}$ symmetry, namely, a combined parity and time-reversal symmetry can make non-unitary quantum walks exhibit entirely real eigenenergy. However, it is known that the concept of $\mathcal{PT}$ symmetry can be generalized and an arbitrary anti-unitary symmetry has a possibility to substitute $\mathcal{PT}$ symmetry. The aim of the present work is to seek such non-unitary quantum walks with generalized $\mathcal{PT}$ symmetry by focusing on effects of spatially random disorder which breaks $\mathcal{PT}$ symmetry. We numerically find non-unitary quantum walks whose quasi-energy is entirely real despite $\mathcal{PT}$ symmetry is broken.