Disentangling theorem and scattering functions for long-range coherent tunneling
| Autor: | Peter S. M. Townsend, Alex W. Chin |
|---|---|
| Přispěvatelé: | Institut des Nanosciences de Paris (INSP), Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS), Photonique et cohérence de spin (INSP-E12), Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS) |
| Jazyk: | angličtina |
| Rok vydání: | 2019 |
| Předmět: |
Physics
Quasielastic scattering Antisymmetric relation Scattering media_common.quotation_subject Diagonal 01 natural sciences Asymmetry 010305 fluids & plasmas symbols.namesake [PHYS.QPHY]Physics [physics]/Quantum Physics [quant-ph] Quantum mechanics 0103 physical sciences symbols [PHYS.COND]Physics [physics]/Condensed Matter [cond-mat] 010306 general physics Quantum Bessel function Quantum tunnelling media_common |
| Zdroj: | Physical Review A Physical Review A, American Physical Society 2019, 99 (1), ⟨10.1103/PhysRevA.99.012112⟩ |
| ISSN: | 2469-9926 2469-9934 |
| DOI: | 10.1103/PhysRevA.99.012112⟩ |
| Popis: | International audience; A closed form of the disentangling theorem is used to derive an exact expression for the quantum mechanical intermediate scattering function describing long-range coherent quantum tunneling. The result applies to a single particle in a large periodic nearest-neighbor tight-binding system in one spatial dimension, with one localized site per unit cell. The result is exact up to the assumption of orthogonal localized states and the substitution of the coordinate operator with a discrete representation diagonal in the on-site basis. The intermediate scattering function is expressed in terms of modified Bessel functions, and consists of a symmetric real part and antisymmetric imaginary part. The real and imaginary parts both exhibit decaying oscillations reflecting the oscillatory dynamics among neighboring sites combined with the long-term spreading of the wave function from any initial site. The imaginary part is significant only when the thermal energy is comparable to or smaller than the width of the tight-binding energy band, and represents quantum recoil or the asymmetry of energy exchange probability in quasielastic scattering from the coherent system. The one-dimensional result is extended, in the form of k-space integrals, to describe the coherent tunneling dynamics in hexagonal and honeycomb systems. The prospects for observing the phenomenology of the analytical line shapes are discussed with respect to the practical implementation of helium-3 surface spin echo spectroscopy. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|