Related Experiment Video
Updated: May 1, 2026

Quantum State Engineering of Light with Continuous-wave Optical Parametric Oscillators
Published on: May 30, 2014
Multifractal eigenstates of quantum chaos and the Thue-Morse sequence
N Meenakshisundaram1, Arul Lakshminarayan
1Department of Physics, Indian Institute of Technology Madras, Chennai, 600036, India.
Abstract:
We analyze certain eigenstates of the quantum baker's map and demonstrate, using the Walsh-Hadamard transform, the emergence of the ubiquitous Thue-Morse sequence, a simple sequence that is at the border between quasiperiodicity and chaos, and hence is a good paradigm for quantum chaotic states. We show a family of states that are also simply related to the Thue-Morse sequence and are strongly scarred by short periodic orbits and their homoclinic excursions. We give approximate expressions for these states and provide evidence that these and other generic states are multifractal.
Related Concept Videos
The de Broglie Wavelength
Quantum Numbers
Entropy Change in Reversible Processes
The statement can be further generalized to prove that entropy is a state function. Take a cyclic process between any two points on a p-V diagram.
The Entropy as a State Function
Basic Discrete Time Signals
The unit impulse or sample sequence is mathematically expressed as zero for all n values except at n=0, where it is one. The unit impulse sequence, denoted by δ(n), is the first difference of the unit step sequence, while the unit step sequence u(n) is...
Exponential Fourier series
Euler's identity...

