Dynamic localization of a charged particle moving under the influence of an electric field
Abstract
The motion of a charged particle on a discrete lattice under the action of an electric field is studied with the help of explicit calculations of probability propagators and mean-square displacements. Exact results are presented for arbitrary time dependence of the electric field on a one-dimensional lattice. Existing results for the limiting cases of zero frequency and zero field are recovered. A new phenomenon involving the dynamic localization of the moving particle is shown to result in the case of a sinusoidally varying field: The particle is generally delocalized except for the cases when the ratio of the field magnitude and the field frequency is a root of the ordinary Bessel function of order 0. For these special cases it is found to be localized. This localization could be used, in principle, for inducing anisotropy in the transport properties of an ordinarily isotropic material.
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It was predicted in 1986 that a time-periodic transverse electric field causes periodic collapse of the evolving wavefunction, known as dynamic localization.
“it was predicted in 1986 that a transverse electric field, which is periodic in time (ac field), yields periodic collapse of the evolving wavefunction, which is well known as dynamic localization (DL) [43].”
From Discrete optics in femtosecond-laser-written photonic structures (2010) · cites this paper as [43]
Control over the sign can be acquired by dynamical modulation of the lattice, Raman-assisted tunneling or embedding defects in infinite arrays.
“Control over this sign can be acquired by dynamical modulation of the lattice [16-21], Raman-assisted tunneling [22, 23] or embedding defects in infinite arrays [24].”
From Universal Sign Control of Coupling in Tight-Binding Lattices (2016) · cites this paper as [16]
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- Authors
- Dunlap, D. H., & Kenkre, V. M.
- Affiliations
- University of New Mexico (US)
- Venue
- Physical Review B
- Publisher
- American Physical Society (APS)
- Published
- 1986-09-15
- Volume
- 34
- Issue
- 6
- Pages
- 3625-3633
- ISSN
- 0163-1829 (ISSN-L)
- OpenAlex
- W2085247228
- Cited by
- 896
- References
- 0
- Citations by year
- 2026: 21 · 2025: 37 · 2024: 31 · 2023: 29 · 2022: 40 · 2021: 42 · 2020: 30 · 2019: 25 · 2018: 45 · 2017: 51 · 2016: 35 · 2015: 30 · 2014: 28 · 2013: 20 · 2012: 35
- FWCI
- 0.70
- Type
- journal article
- Language
- en
- Open access
- closed
- Locations
- Physical review. B, Condensed matter (publishedVersion)
- PubMed (publishedVersion)
- Funders
- National Science Foundation
- Topics
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum and electron transport phenomena
- Physical Sciences › Physics and Astronomy › Statistical and Nonlinear Physics › Quantum chaos and dynamical systems
- Physical Sciences › Mathematics › Mathematical Physics › Spectral Theory in Mathematical Physics
- Keywords
- dynamical localization, charged particle motion, electric field, discrete lattices, mean square displacement, zeros of Bessel functions, time-dependent fields
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