Spectra and transport of probability and energy densities in a $\mathcal{PT}$-symmetric square well with a delta-function potential
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866929633769816064 |
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| author | Arvizu, Francisco Ricardo Torres Ortega, Adrian Larralde, Hernán |
| author_facet | Arvizu, Francisco Ricardo Torres Ortega, Adrian Larralde, Hernán |
| contents | We study the spectrum, eigenstates and transport properties of a simple $\mathcal{P}\mathcal{T}$-symmetric model consisting in a finite, complex, square well potential with a delta potential at the origin. We show that as the strength of the delta potential increases, the system exhibits exceptional points accompanied by an accumulation of density associated with the break in the $\mathcal{P}\mathcal{T}$-symmetry. We also obtain the density and energy density fluxes and analyze their transport properties. We find that in the $\mathcal{P}\mathcal{T}-$ symmetric phase transport is efficient, in the sense that all the density that flows into the system at the source, flows out at the sink, which is sufficient to derive a generalized unitary relation for the transmission and reflection coefficients. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_00234 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Spectra and transport of probability and energy densities in a $\mathcal{PT}$-symmetric square well with a delta-function potential Arvizu, Francisco Ricardo Torres Ortega, Adrian Larralde, Hernán Quantum Physics We study the spectrum, eigenstates and transport properties of a simple $\mathcal{P}\mathcal{T}$-symmetric model consisting in a finite, complex, square well potential with a delta potential at the origin. We show that as the strength of the delta potential increases, the system exhibits exceptional points accompanied by an accumulation of density associated with the break in the $\mathcal{P}\mathcal{T}$-symmetry. We also obtain the density and energy density fluxes and analyze their transport properties. We find that in the $\mathcal{P}\mathcal{T}-$ symmetric phase transport is efficient, in the sense that all the density that flows into the system at the source, flows out at the sink, which is sufficient to derive a generalized unitary relation for the transmission and reflection coefficients. |
| title | Spectra and transport of probability and energy densities in a $\mathcal{PT}$-symmetric square well with a delta-function potential |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2410.00234 |