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- W4387323986 abstract "We consider transport through a non-Hermitian conductor connected to a pair of Hermitian leads and analyze the underlying non-Hermitian scattering problem. In a typical non-Hermitian system, such as a Hatano--Nelson-type asymmetric hopping model, the continuity of probability and probability current is broken at a local level. As a result, the notion of transmission and reflection probabilities becomes ill-defined. Instead of these probabilities, we introduce the injection rate $R_{rm I}=1-|{cal R}|^2$ and the transmission rate $R_{rm T}=|{cal T}|^2$ as relevant physical quantities, where ${cal T}$ and ${cal R}$ are the transmission and reflection amplitudes, respectively. In a generic non-Hermitian case, $R_{rm I}$ and $R_{rm T}$ have independent information. We provide a modified continuity equation in terms of incoming and outgoing currents, from which we derive a global probability conservation law that relates $R_{rm I}$ and $R_{rm T}$. We have tested the usefulness of our probability conservation law in the interpretation of numerical results for non-Hermitian localization and delocalization phenomena." @default.
- W4387323986 created "2023-10-04" @default.
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- W4387323986 date "2023-10-01" @default.
- W4387323986 modified "2023-10-06" @default.
- W4387323986 title "Probability Conservation and Localization in a One-Dimensional Non-Hermitian System" @default.
- W4387323986 doi "https://doi.org/10.48550/arxiv.2310.00830" @default.
- W4387323986 hasPublicationYear "2023" @default.
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