Stability of driven systems with growing gaps, quantum rings, and Wannier ladders

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61389005%3A_____%2F98%3A00000727" target="_blank" >RIV/61389005:_____/98:00000727 - isvavai.cz</a>
Result on the web
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DOI - Digital Object Identifier
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Result language
angličtina
Original language name
Stability of driven systems with growing gaps, quantum rings, and Wannier ladders
Original language description
We consider a quantum particle in a periodic structure submitted to a constant external electromotive force. The periodic background is given by a smooth potential plus singular point interactions and has the property that the gaps between its bands aregrowing with the band index. We prove that the spectrum is pure point-i.e., trajectories of wave packets lie in compact sets in Hilbert space-if the Bloch frequency is nonresonant with the frequency of the system and satisfies a Diophantine-type estimate, or if it is resonant. Furthermore, we show that the KAM method employed in the nonresonant case produces uniform bounds on the growth of energy for driven systems.
Czech name
Stabilita buzených systémů s rostoucími lakunami, kvantové prstence a Wannierovy žebříky
Czech description
Uvažujeme kvantovou částici v periodické struktuře pod vlivem konstantní elektrické síly. Periodický podkled je dán hladkým potenciálem spolu se singulárními bodovými interakcemi.

Type
J<sub>x</sub> - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP classification
BE - Theoretical physics
OECD FORD branch
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Project
<a href="/en/project/IAA148409" target="_blank" >IAA148409: Schrödinger operators and quantum chaos</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year
1998
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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