Observation of log-periodic oscillations in the quantum dynamics of electrons on the one-dimensional Fibonacci quasicrystal

Ron Lifshitz; Shahar Even Dar Mandel

doi:10.1080/14786435.2010.543092

Observation of log-periodic oscillations in the quantum dynamics of electrons on the one-dimensional Fibonacci quasicrystal

Ron Lifshitz^*, Shahar Even Dar Mandel

^*Corresponding author for this work

School of Physics and Astronomy

Tel Aviv University

Research output: Contribution to journal › Article › peer-review

4 Scopus citations

Abstract

We revisit the question of quantum dynamics of electrons on the off-diagonal Fibonacci tight-binding model. We find that typical dynamical quantities, such as the probability of an electron to remain in its original position as a function of time, display log-periodic oscillations on top of the leading-order power-law decay. These periodic oscillations with the logarithm of time are similar to the oscillations that are known to exist with the logarithm of temperature in the specific heat of Fibonacci electrons, yet they offer new possibilities for the experimental observation of this unique phenomenon.

Original language	English
Pages (from-to)	2792-2800
Number of pages	9
Journal	Philosophical Magazine
Volume	91
Issue number	19-21
DOIs	https://doi.org/10.1080/14786435.2010.543092
State	Published - 1 Jul 2011

Funding

Funders	Funder number
Israel Science Foundation	684/06, 556/10

Keywords

Fibonacci quasicrystals
electronic transport
log-periodic oscillations
quantum dynamics
quasicrystals
tight-binding model

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10.1080/14786435.2010.543092

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title = "Observation of log-periodic oscillations in the quantum dynamics of electrons on the one-dimensional Fibonacci quasicrystal",

abstract = "We revisit the question of quantum dynamics of electrons on the off-diagonal Fibonacci tight-binding model. We find that typical dynamical quantities, such as the probability of an electron to remain in its original position as a function of time, display log-periodic oscillations on top of the leading-order power-law decay. These periodic oscillations with the logarithm of time are similar to the oscillations that are known to exist with the logarithm of temperature in the specific heat of Fibonacci electrons, yet they offer new possibilities for the experimental observation of this unique phenomenon.",

keywords = "Fibonacci quasicrystals, electronic transport, log-periodic oscillations, quantum dynamics, quasicrystals, tight-binding model",

author = "Ron Lifshitz and Mandel, {Shahar Even Dar}",

note = "Funding Information: We wish to thank Amnon Aharony for fruitful discussions and for suggesting that the {\textquoteleft}{\textquoteleft}wiggles{\textquoteright}{\textquoteright} in our numerical data might be real. We also thank Eric Akkermans and Eli Eisenberg for helpful discussions. This research is supported by the Israel Science Foundation through Grant Nos. 684/06 and 556/10.",

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N2 - We revisit the question of quantum dynamics of electrons on the off-diagonal Fibonacci tight-binding model. We find that typical dynamical quantities, such as the probability of an electron to remain in its original position as a function of time, display log-periodic oscillations on top of the leading-order power-law decay. These periodic oscillations with the logarithm of time are similar to the oscillations that are known to exist with the logarithm of temperature in the specific heat of Fibonacci electrons, yet they offer new possibilities for the experimental observation of this unique phenomenon.

AB - We revisit the question of quantum dynamics of electrons on the off-diagonal Fibonacci tight-binding model. We find that typical dynamical quantities, such as the probability of an electron to remain in its original position as a function of time, display log-periodic oscillations on top of the leading-order power-law decay. These periodic oscillations with the logarithm of time are similar to the oscillations that are known to exist with the logarithm of temperature in the specific heat of Fibonacci electrons, yet they offer new possibilities for the experimental observation of this unique phenomenon.

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KW - electronic transport

KW - log-periodic oscillations

KW - quantum dynamics

KW - quasicrystals

KW - tight-binding model

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Observation of log-periodic oscillations in the quantum dynamics of electrons on the one-dimensional Fibonacci quasicrystal

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