dorsal/arxiv
View SchemaDetecting Broken PT-Symmetry
| Authors | Stefan Weigert |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0602141 |
| URL | https://arxiv.org/abs/quant-ph/0602141 |
| DOI | 10.1088/0305-4470/39/32/S22 |
| Journal | J. Phys. A 39 (2006) 10239 |
Abstract
A fundamental problem in the theory of PT-invariant quantum systems is to determine whether a given system `respects' this symmetry or not. If not, the system usually develops non-real eigenvalues. It is shown in this contribution how to algorithmically detect the existence of complex eigenvalues for a given PT-symmetric matrix. The procedure uses classical results from stability theory which qualitatively locate the zeros of real polynomials in the complex plane. The interest and value of the present approach lies in the fact that it avoids diagonalization of the Hamiltonian at hand.
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"abstract": "A fundamental problem in the theory of PT-invariant quantum systems is to\ndetermine whether a given system `respects\u0027 this symmetry or not. If not, the\nsystem usually develops non-real eigenvalues. It is shown in this contribution\nhow to algorithmically detect the existence of complex eigenvalues for a given\nPT-symmetric matrix. The procedure uses classical results from stability theory\nwhich qualitatively locate the zeros of real polynomials in the complex plane.\nThe interest and value of the present approach lies in the fact that it avoids\ndiagonalization of the Hamiltonian at hand.",
"arxiv_id": "quant-ph/0602141",
"authors": [
"Stefan Weigert"
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"doi": "10.1088/0305-4470/39/32/S22",
"journal_ref": "J. Phys. A 39 (2006) 10239",
"title": "Detecting Broken PT-Symmetry",
"url": "https://arxiv.org/abs/quant-ph/0602141"
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