The hofstadter butterfly

Author: dsrn

August undefined, 2024

WebDec 2, 2024 · The Hofstadter butterfly is the emblem of a long-standing problem concerning the single-electron states in a periodic electric potential and a transverse, constant … WebApr 29, 2016 · The Hofstadter butterfly is a quantum fractal with a highly complex nested set of gaps, where each gap represents a quantum Hall state whose quantized conductivity is …

The Butterfly in the Quantum World - Google Books

WebJan 19, 2024 · The reconstructed energy spectra are reminiscent of the famous Hofstadter butterfly with a fractal structure, clearly showing that our Floquet photonic quantum walk can well reproduce the rich... WebApr 11, 2024 · Fractional disclination charge and discrete shift in the Hofstadter butterfly. In the presence of crystalline symmetries, topological phases of matter acquire a host of invariants leading to non-trivial quantized responses. Here we study a particular invariant, the discrete shift , for the square lattice Hofstadter model of free fermions. is ... encounter truth

Douglas Hofstadter - Wikipedia

WebThe Hofstadter butterﬂy, discovered some forty years ago, is destined to be immortal. In addition to its great visual appeal, it encodes one of the most exotic phenomena in physics, the quantum Hall effect. Webwhen the Hofstadter butterfly spectrum is undermined by electron's scattering. We expect that kagomé quantum oscillations are generic to rotationally-symmetric two-dimensional crystals close to Lifshitz transitions. We report the observation of coinciding features in the WebMay 30, 2003 · Creation of effective magnetic fields in optical lattices: the Hofstadter butterfly for cold neutral atoms. D Jaksch1,2 and P Zoller2. Published 30 May 2003 • … encounter topic

Multiple flat bands and topological Hofstadter butterfly in twisted ...

WebOct 19, 2024 · The Hofstadter model, well known for its fractal butterfly spectrum, describes two-dimensional electrons under a perpendicular magnetic field, which gives rise to the … WebMar 11, 2024 · We first briefly introduce the Hofstadter butterfly, including the theoretic toy model of Bloch electrons in the magnetic field, the resulting Harper's equation and its solution, and realizations... dr burgess congressWebIntricate interplay between the periodicity of the lattice structure and that of the cyclotron motion gives rise to a well-known self-similar fractal structure of the energy eigenvalue, known as the Hofstadter butterfl… encounter to go over test results icd 10

"WebHofstadter's butterfly is the resulting plot of as a function of the flux ratio , where is the set of all possible that are a solution to Harper's equation. … " - The hofstadter butterfly

The hofstadter butterfly

Physics - Looking for Hofstadter’s Butterfly in Cold Atoms

WebThe Hofstadter butterfly is the set, where f (x,y)=0. The picture to the right is colored according to the value of f (x,y). Mathematicians call the function f (x,y) a Lyapunov … WebMay 16, 2013 · The Hofstadter butterfly is a fractal pattern—meaning that it contains shapes that repeat on smaller and smaller size scales. Fractals are common in systems such as fluid mechanics, but rare in the quantum mechanical world. The Hofstadter butterfly is one of the first quantum fractals theoretically discovered in physics but, until now, there ...

Did you know?

WebNov 9, 2024 · Hofstadter Butterfly for graphene Ask Question Asked 3 years, 5 months ago Modified 3 years, 5 months ago Viewed 443 times 0 I am trying to extend the Harper equation from two dimensional square lattice to monolayer graphene by using mathematica. For square lattice the code is given here "Poor rendering of fractals". WebA kondenzált anyagok fizikája, Hofstadter pillangó egy grafikon a spektrális tulajdonságai nem kölcsönható kétdimenziós elektronok merőleges mágneses tér egy rács.A spektrum fraktál, önmagához hasonló jellegét az 1976-os Ph.D. Douglas Hofstadter munkája, és a modern tudományos adatok megjelenítésének egyik korai példája. A név azt a tényt …

WebApr 13, 2004 · The Hofstadter butterfly is the energy spectrum of an infinite square lattice, plotted as a function of the magnetic field. We illustrate a method of calculating similar spectra for finite lattices in a magnetic field, using methods that consider the appropriate molecular orbitals, and find that the spectra resemble the Hofstadter butterfly. WebMar 5, 2014 · The Hall conductivity for arbitrary Fermi energies is far more intricate, as illustrated in the coloured Hofstadter butterfly in figure 6 that covers the entire spectrum …

WebApr 8, 2003 · Hofstadter spectrum Hans Koch and Sa a Koci-Interacting fermions in two dimension in ... Hofstadter butterfly Zheng-Wei Zuo, Wladimir A Benalcazar, Yunzhe Liu et al.-This content was downloaded from IP address 207.46.13.43 on 22/12/2024 at 08:47. Creation of effective magnetic ﬁelds in optical lattices: the Hofstadter butterﬂy for cold ... WebThe Hofstadter butterfly is the set, where f(x,y)=0. The picture is colored according to the value of f(x,y). Mathematicians call the function f(x,y) a Lyapunov exponent. It is also …

WebMar 8, 2013 · The problem of two-dimensional, independent electrons subject to a periodic potential and a uniform perpendicular magnetic field unveils surprisingly rich physics, as epitomized by the fractal energy spectrum known as Hofstadter's Butterfly. It has hitherto been addressed using various approximations rooted in either the strong potential or the …

WebJul 23, 2024 · The connected Hofstadter butterfly strongly evidences the topologically nontrivial textures of the multiple moiré bands. Overall, our work provides a perspective for understanding the quantum phases in tBLG and the fractal Hofstadter spectra of multiple topological bands. encounter wadersWebApr 12, 2024 · Thanks to four of its stars, The Big Bang Theory made being a geek cool. Sheldon Cooper, Leonard Hofstadter, Raj Koothrappali and Howard Wolowitz all loved different aspects of science. dr burgess hinsdale orthoWebDec 23, 2008 · The fractalized Hofstadter butterfly energy spectrum predicted for magnetically confined fermions diffracted by a crystal lattice has remained beyond the reach of laboratory-accessible magnetic fields. We find the geometrically frustrated spin system SrCu 2 (BO 3) 2 to provide a sterling demonstration of a system in which bosons confined … dr burgess laurel bone and jointWebOne possible origin of the nontrivial unbound Hofstadter butterfly is the single-particle fragile topology hosted by the lowest two moiré bands of each spin and valley in tBLG … encounter tv dramaWebThe spectral flows in the Hofstadter gaps can be understood as edge states on a momentum space boundary, from which one can determine the two integers (tν,sν) of a gap ν satisfying the Diophantine equation. The spectral flows can also be removed to obtain a clear Hofstadter butterfly. encounter wesleyan churchWebOct 28, 2013 · In either case, observing the Hofstadter butterfly directly, or its associated topological state, will require temperatures that are small compared to the gaps between … dr burgess lake oswego plastic surgeryWebHofstadter is a surname. Notable people with the surname include: Albert Hofstadter (1910–1989), ... Hofstadter's butterfly, a fractal; Hofstadter Committee, a joint legislative … dr burgess murrieta ca