Optimal fluctations and tail states of non-Hermitian operators. (Q2773123)
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scientific article; zbMATH DE number 1709267
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Optimal fluctations and tail states of non-Hermitian operators. |
scientific article; zbMATH DE number 1709267 |
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2001
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Optimal fluctations and tail states of non-Hermitian operators. (English)
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Whilst the eigenvalues of Hermitian operators are real, the spectrum of non-Hermitian operators is generally complex, therefore new problems related to the localization of the eigenfunctions. The purpose of the present paper is to develop a supersymmetric field theory to explore the spatial profile of the states in the tail region which persists at the edge of the spectral support of the non- Hermitian system, and to determine the complex density of states in the vicinity of the band edge. A statistical field theory describing the spectral properties of the random imaginary scalar potenial Hamiltonian is formulated, and then the model is generalized to deal with random imaginary vector potential.
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