The DOI matches its Crossref record; 1 of the 1 references it cites were found in a registry or an index.
One-Dimensional Schrödinger Equation with an Almost Periodic Potential
Abstract
Recent theories of scaling in quasiperiodic dynamical systems are applied to the behavior of a particle in an almost periodic potential. A special tight-binding model is solved exactly by a renormalization group whose fixed points determine the scaling properties of both the energy spectrum and certain features of the eigenstates. Similar results are found empirically for Harper's equation. In addition to ordinary extended and localized states, "critical" states are found which are neither extended nor localized according to conventional criteria.
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Citations
Cites
Energy levels and wave functions of Bloch electrons in rational and irrational magnetic fields
Hofstadter, D. R. (1976) · Physical Review B · doi:10.1103/physrevb.14.2239 · Cited by 3,495
Cited by
Localization of optics: Quasiperiodic media
Kohmoto, M., Sutherland, B., & Iguchi, K. (1987) · Physical Review Letters · doi:10.1103/physrevlett.58.2436 · Cited by 561
Observation of Topological Phase Transitions in Photonic Quasicrystals
Verbin, M., Zilberberg, O., Kraus, Y. E., Lahini, Y., & Silberberg, Y. (2013) · Physical Review Letters · doi:10.1103/physrevlett.110.076403 · Cited by 365
Topological Equivalence between the Fibonacci Quasicrystal and the Harper Model
Kraus, Y. E., & Zilberberg, O. (2012) · Physical Review Letters · doi:10.1103/physrevlett.109.116404 · Cited by 298
Deep learning for early warning signals of tipping points
Bury, T. M., Sujith, R. I., Pavithran, I., Scheffer, M., Lenton, T. M., Anand, M., & Bauch, C. T. (2021) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.2106140118 · Cited by 284
“Thus, dynamical systems are extremely diverse, ranging in spatial scale from the expanding universe (4) to quantum systems (5) and everything in between (6–8).”
BackgroundTopological pumping over a photonic Fibonacci quasicrystal
Verbin, M., Zilberberg, O., Lahini, Y., Kraus, Y. E., & Silberberg, Y. (2015) · Physical Review B · doi:10.1103/physrevb.91.064201 · Cited by 252
Metadata
- Authors
- Ostlund, S., Pandit, R., Rand, D., Schellnhuber, H. J., & Siggia, E. D.
- Venue
- Physical Review Letters
- Publisher
- American Physical Society (APS)
- Published
- 1983-06-06
- Volume
- 50
- Issue
- 23
- Pages
- 1873-1876
- ISSN
- 0031-9007 (ISSN-L)
- OpenAlex
- W1982527861
- Cited by
- 731
- References
- 1
- FWCI
- 20.15
- Type
- journal article
- Language
- en
- Open access
- closed
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- The paper
- Ostlund, S., Pandit, R., Rand, D., Schellnhuber, H. J., & Siggia, E. D. (1983). One-Dimensional Schrödinger Equation with an Almost Periodic Potential. Physical Review Letters. https://doi.org/10.1103/physrevlett.50.1873
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Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
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