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| Format: | Preprint |
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2024
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| Online Access: | https://arxiv.org/abs/2401.01126 |
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| _version_ | 1866909059664314368 |
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| author | Ghosh, Pijush K. |
| author_facet | Ghosh, Pijush K. |
| contents | We present a general construction of pseudo-hermitian matrices in an arbitrary large, but finite dimensional vector space. The positive-definite metric which ensures reality of the entire spectra of a pseudo-hermitian operator, and is used for defining a modified inner-product in the associated vector space is also presented. The construction for an N dimensional vector space is based on the generators of SU (N ) in the fundamental representation and the identity operator. We apply the results to construct a generic pseudo-hermitian lattice model of size N with balanced loss-gain. The system is amenable to periodic as well as open boundary conditions and by construction, admits entirely real spectra along with unitary time-evolution. The tight binding and Su-Schrieffer-Heeger(SSH) models with nearest neighbour(NN) and next-nearest neighbour(NNN) interaction with balanced loss-gain appear as limiting cases. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_01126 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Construction of Pseudo-hermitian matrices describing systems with balanced loss-gain Ghosh, Pijush K. Quantum Physics Other Condensed Matter High Energy Physics - Theory Mathematical Physics We present a general construction of pseudo-hermitian matrices in an arbitrary large, but finite dimensional vector space. The positive-definite metric which ensures reality of the entire spectra of a pseudo-hermitian operator, and is used for defining a modified inner-product in the associated vector space is also presented. The construction for an N dimensional vector space is based on the generators of SU (N ) in the fundamental representation and the identity operator. We apply the results to construct a generic pseudo-hermitian lattice model of size N with balanced loss-gain. The system is amenable to periodic as well as open boundary conditions and by construction, admits entirely real spectra along with unitary time-evolution. The tight binding and Su-Schrieffer-Heeger(SSH) models with nearest neighbour(NN) and next-nearest neighbour(NNN) interaction with balanced loss-gain appear as limiting cases. |
| title | Construction of Pseudo-hermitian matrices describing systems with balanced loss-gain |
| topic | Quantum Physics Other Condensed Matter High Energy Physics - Theory Mathematical Physics |
| url | https://arxiv.org/abs/2401.01126 |