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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2023
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2310.10263 |
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| _version_ | 1866916664166055936 |
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| author | Bhasin, Priyanshi Das, Tanmoy |
| author_facet | Bhasin, Priyanshi Das, Tanmoy |
| contents | Describing systems with non-Hermitian (NH) operators remains a challenge in quantum theory due to instabilities (e.g., exceptional points and decoherence) arising from interactions with the environment. We propose a framework to express the energy states of NH Hamiltonians using a well-defined basis (dub computational basis) derived from a related Hermitian operator. This suitably shifts the singularities from the basis states to the expansion coefficients, allowing for their easier mathematical treatment and parametric control. Furthermore, we introduce a `space-time' transformation on the computational basis that defines a generic dual space map for the energy states. Interestingly, this transformation leads to a symmetry for real/imaginary energy values, revealing the existence of weaker condition than hermiticity or the $\mathcal{PT}$ symmetry. This leads to clearer understanding and novel interpretations of key features like exceptional points, dual space, and weaker symmetry-enforced real eigenvalues. The applicability of our framework extends to various branches of physics where NH operators manifest as ladder operators, order parameters, self-energies, projectors, and other entities. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2310_10263 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | A Hermitian bypass to the non-Hermitian quantum theory Bhasin, Priyanshi Das, Tanmoy Quantum Physics Disordered Systems and Neural Networks Strongly Correlated Electrons Mathematical Physics Optics Describing systems with non-Hermitian (NH) operators remains a challenge in quantum theory due to instabilities (e.g., exceptional points and decoherence) arising from interactions with the environment. We propose a framework to express the energy states of NH Hamiltonians using a well-defined basis (dub computational basis) derived from a related Hermitian operator. This suitably shifts the singularities from the basis states to the expansion coefficients, allowing for their easier mathematical treatment and parametric control. Furthermore, we introduce a `space-time' transformation on the computational basis that defines a generic dual space map for the energy states. Interestingly, this transformation leads to a symmetry for real/imaginary energy values, revealing the existence of weaker condition than hermiticity or the $\mathcal{PT}$ symmetry. This leads to clearer understanding and novel interpretations of key features like exceptional points, dual space, and weaker symmetry-enforced real eigenvalues. The applicability of our framework extends to various branches of physics where NH operators manifest as ladder operators, order parameters, self-energies, projectors, and other entities. |
| title | A Hermitian bypass to the non-Hermitian quantum theory |
| topic | Quantum Physics Disordered Systems and Neural Networks Strongly Correlated Electrons Mathematical Physics Optics |
| url | https://arxiv.org/abs/2310.10263 |