Effects of disorder on non-unitary $\mathcal{P}\mathcal{T}$ symmetric quantum walks

Abstract

$\mathcal{P}\mathcal{T}$ 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 $\mathcal{P}\mathcal{T}$ symmetry can be generalized and an arbitrary anti-unitary symmetry has a possibility to substitute $\mathcal{P}\mathcal{T}$ symmetry. The aim of the present work is to seek such non-unitary quantum walks with generalized $\mathcal{P}\mathcal{T}$ symmetry by focusing on effects of spatially random disorder which breaks $\mathcal{P}\mathcal{T}$ symmetry. We numerically find non-unitary quantum walks whose quasi-energy is entirely real despite $\mathcal{P}\mathcal{T}$ symmetry is broken.

9 pages, 4 figures

References in corpus (3)

• Exponentially Fragile PT-Symmetry in Lattices with Localized Eigenmodes
• Invisibility and PT-symmetry
• Explicit definition of $\mathcal{P}\mathcal{T}$ symmetry for non-unitary quantum walks with gain and loss

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