ﻻ يوجد ملخص باللغة العربية
We propose a general analytic method to study the localization transition in one-dimensional quasicrystals with parity-time ($mathcal{PT}$) symmetry, described by complex quasiperiodic mosaic lattice models. By applying Avilas global theory of quasiperiodic Schrodinger operators, we obtain exact mobility edges and prove that the mobility edge is identical to the boundary of $mathcal{PT}$-symmetry breaking, which also proves the existence of correspondence between extended (localized) states and $mathcal{PT}$-symmetry ($mathcal{PT}$-symmetry-broken) states. Furthermore, we generalize the models to more general cases with non-reciprocal hopping, which breaks $mathcal{PT}$ symmetry and generally induces skin effect, and obtain a general and analytical expression of mobility edges. While the localized states are not sensitive to the boundary conditions, the extended states become skin states when the periodic boundary condition is changed to open boundary condition. This indicates that the skin states and localized states can coexist with their boundary determined by the mobility edges.
We investigate localization-delocalization transition in one-dimensional non-Hermitian quasiperiodic lattices with exponential short-range hopping, which possess parity-time ($mathcal{PT}$) symmetry. The localization transition induced by the non-Her
According to the topological band theory of a Hermitian system, the different electronic phases are classified in terms of topological invariants, wherein the transition between the two phases characterized by a different topological invariant is the
The emergence of the mobility edge (ME) has been recognized as an important characteristic of Anderson localization. The difficulty in understanding the physics of the MEs in three-dimensional (3D) systems from a microscopic picture promotes discover
The mobility edges (MEs) in energy which separate extended and localized states are a central concept in understanding the localization physics. In one-dimensional (1D) quasiperiodic systems, while MEs may exist for certain cases, the analytic result
Quantum localization in 1D non-Hermitian systems, especially the search for exact single-particle mobility edges, has attracted considerable interest recently. While much progress has been made, the available methods to determine the ME of such model