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Questions tagged [quasi-periodic]

11 questions
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1 answer

Quasiperiodicity of the Fibonacci chain

I am interested in finding an intuitive way to show that the Fibonacci chain is quasiperiodic (and not simply random). Or put differently, how can I tell from just looking at a given chain whether or not it is quasiperiodic? Let us consider the…
Quasilattice
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Bloch potential with torsion: emerging pseudo-magnetic field

I have heard that applying uniform torsion to a system of Bloch electrons will induce Landau levels. Essentially, if I apply a uniform torsion about the $z$-direction, then a pseudo-magnetic field should emerge. My question is: how can I derive this…
user105620
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4
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1 answer

Symmetry of spectrum of tight binding model with quasiperiodic potential

In the Aubry-André model, a tight binding model with nearest neighor hopping and a cosine-like potential $\lambda_n = \lambda \cos(2\pi \beta n)$ (where $n$ is the lattice site, $\lambda$ is the potential strength and $\beta$ is typically…
Michael H.
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3 answers

Why the Lorenz system can't have quasi-periodic trajectories?

The nonlinear dynamics book by Hilborn gives the following argument about the famous Lorenz system: Let $\vec f$ represent the set of time evolution functions for the system. If we consider a set of initial points distributed through a volume of…
Peaceful
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3
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1 answer

What exactly is KAM stability and how can I determine if an orbit is KAM stable or not?

I have been working on the three-body problem lately and came across KAM stability. I read that KAM stability generally means that the solution is stable at different initial conditions (that of course must be close to the initial conditions of the…
Belal Bahaa
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3
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4 answers

What is quasi-periodic motion?

I'm currently 2nd year physics student (undergraduate). I have seminar which theme is double pendulum. I'm having trouble understanding quasi-periodic motion in general and more importantly in context of double pendulum. I was hoping you could give…
Šime Demo
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3
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Are quasicrystals always self-similar?

The diffraction patterns of quasicrystals very often display self-similarity ie. similarity under length scaling, thus relating them to fractals. My question is: Do they always display self-similarity? Standard literature (e.g. Janot,…
Quasilattice
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Solving Schrodinger Equation for scattering off a periodic potential

I am interesting in solving the time-independent Schrodinger equation (TISE) for the scenario where we have an electron plane wave of fixed energy incident upon a potential that is infinite and periodic only the transverse plane (i.e. a very thin or…
bdforbes
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Minimal dynamical system with quasiperiodic oscillations

What is a minimal, explicit dynamical system (as in, a series of coupled ordinary differential equations) that exhibits quasiperiodic oscillations for some region of parameter space? Two coupled Van der Pol oscillators have this property, for…
wil3
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Estimate of the period of noisy "event counting" data

I have a set of experimental data, which come from a periodical event. More specifically, these are detections from a single photon detector, so there is no intensity, I only have the timestamps of the detections. In the data there is some random…
Fabio
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Quasiperiodic dynamics of a System

i understand that, periodic behavior is defined as recurring at regular intervals. Does quasiperiodic mean, that the interval is shifted. If yes, is this shift well defined?
Kreisel
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