The hofstadter butterfly
WebSep 6, 2016 · Butterfly in the Quantum World by Indu Satija, with contributions by Douglas Hofstadter, is the first book ever to tell the story of the "Hofstadter butterfly", a beautiful and fascinating graph lying at the heart of the quantum theory of matter. The butterfly came out of a simple-sounding question: What happens if you immerse a crystal in a magnetic field? 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.
The hofstadter butterfly
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WebDec 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 … WebJan 13, 2011 · The Hofstadter butterfly spectral patterns of lattice electrons in an external magnetic field yield some of the most beguiling images in physics. Here we explore the magneto-electronic spectra of systems with moire spatial patterns, concentrating on the case of twisted bilayer graphene. Because long-period spatial patterns are accurately …
WebNov 5, 2024 · The Hofstadter butterfly has long fascinated theorists, but it is only recently that the butterfly has been seen in moir\\'e systems. Its rich fractal structure can be understood fromsymmetry analysis of the magnetic translation group. Similar symmetry analysis reveals a new, equally rich, structure when Hofstadter systems become … WebIntricate 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…
WebApr 11, 2024 · Fractional disclination charge and discrete shift in the Hofstadter butterfly Yuxuan Zhang, Naren Manjunath, Gautam Nambiar, Maissam Barkeshli In the presence of … 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 …
WebThe 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.
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 … commercial agents newcastle upon tyneWebMay 15, 2013 · Hofstadter’s butterfly – a stunning fractal pattern that describes the behaviour of electrons in a magnetic field – has been measured experimentally for the … commercial air blowers for saledrywall repair sumter scWebButterfly in the Quantum World - Nov 12 2024 Butterfly in the Quantum World by Indu Satija, with contributions by Douglas Hofstadter, is the first book ever to tell the story of the "Hofstadter butterfly", a beautiful and fascinating graph lying at the heart of the quantum theory of matter. The butterfly came out of a simple-sounding question: What drywall repair texture matchingWebMay 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 ... commercial air cleaner machinesWebHofstadter is a surname. Notable people with the surname include: Albert Hofstadter (1910–1989), ... Hofstadter's butterfly, a fractal; Hofstadter Committee, a joint legislative … commercial air compressor for sale near meWebMay 16, 2013 · The Hofstadter butterfly is one of the first quantum fractals theoretically discovered in physics but, until now, there has been no direct experimental proof of this … commercial air cleaners for tobacco smoke