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Updated: Jun 5, 2026

Generation and Coherent Control of Pulsed Quantum Frequency Combs

Generation and Coherent Control of Pulsed Quantum Frequency Combs

Published on: June 8, 2018

Multifractal wave functions of simple quantum maps.

John Martin¹, Ignacio García-Mata, Olivier Giraud

¹Institut de Physique Nucléaire, Atomique et de Spectroscopie, Université de Liège, Bât B15, B-4000 Liège, Belgium.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics

|January 15, 2011

Summary

This summary is machine-generated.

This study numerically investigates multifractal properties of quantum maps. Results show distinct multifractal behaviors for Anderson and intermediate maps, offering new insights into quantum chaos and localization.

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Last Updated: Jun 5, 2026

Generation and Coherent Control of Pulsed Quantum Frequency Combs

Generation and Coherent Control of Pulsed Quantum Frequency Combs

Published on: June 8, 2018

Area of Science:

Quantum chaos
Condensed matter physics
Statistical mechanics

Background:

One-dimensional quantum maps exhibit complex dynamics.
Multifractality describes the scaling properties of wave functions.
Anderson localization is a key phenomenon in disordered systems.

Purpose of the Study:

To numerically investigate the multifractal properties of quantum wave functions in two distinct 1D quantum map models.
To compare the multifractal behavior of these maps with known results from the 3D Anderson transition.
To analyze the applicability of classical multifractal methods to quantum systems.

Main Methods:

Extensive numerical simulations were performed.
Multifractal exponents of quantum wave functions were computed.
Box-counting and wavelet methods were employed and compared.

Main Results:

The Anderson map's wave functions show weaker multifractality compared to 3D Anderson transitions.
The intermediate map exhibits unique multifractal properties, differing from Anderson transition characteristics.
Finite-size effects on multifractality were also discussed.

Conclusions:

The intermediate quantum map displays original multifractal properties not fully explained by the nonlinear sigma model.
The study highlights differences and similarities between quantum map multifractality and Anderson transitions.
Numerical methods for classical multifractal systems are applicable but require careful interpretation for quantum wave functions.