Scattering Expansion for Localization in One Dimension
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arXiv
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| Format: | Preprint |
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2022
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| _version_ | 1866914697901506560 |
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| author | Culver, Adrian B. Sathe, Pratik Roy, Rahul |
| author_facet | Culver, Adrian B. Sathe, Pratik Roy, Rahul |
| contents | We present a perturbative approach to disordered systems in one spatial dimension that accesses the full range of phase disorder and clarifies the connection between localization and phase information. We consider a long chain of identically disordered scatterers and expand in the reflection strength of any individual scatterer. As an example application, we show analytically that in a discrete-time quantum walk, the localization length can depend non-monotonically on the strength of phase disorder (whereas expanding in weak disorder yields monotonic decrease). More generally, we obtain to all orders in the expansion a particular non-separable form for the joint probability distribution of the transmission coefficient logarithm and reflection phase. Furthermore, we show that for weak local reflection strength, a version of the scaling theory of localization holds: the joint distribution is determined by just three parameters. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2210_07999 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Scattering Expansion for Localization in One Dimension Culver, Adrian B. Sathe, Pratik Roy, Rahul Disordered Systems and Neural Networks Mesoscale and Nanoscale Physics We present a perturbative approach to disordered systems in one spatial dimension that accesses the full range of phase disorder and clarifies the connection between localization and phase information. We consider a long chain of identically disordered scatterers and expand in the reflection strength of any individual scatterer. As an example application, we show analytically that in a discrete-time quantum walk, the localization length can depend non-monotonically on the strength of phase disorder (whereas expanding in weak disorder yields monotonic decrease). More generally, we obtain to all orders in the expansion a particular non-separable form for the joint probability distribution of the transmission coefficient logarithm and reflection phase. Furthermore, we show that for weak local reflection strength, a version of the scaling theory of localization holds: the joint distribution is determined by just three parameters. |
| title | Scattering Expansion for Localization in One Dimension |
| topic | Disordered Systems and Neural Networks Mesoscale and Nanoscale Physics |
| url | https://arxiv.org/abs/2210.07999 |