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Related Experiment Video

Updated: Feb 4, 2026

Generation and Coherent Control of Pulsed Quantum Frequency Combs

Generation and Coherent Control of Pulsed Quantum Frequency Combs

Published on: June 8, 2018

Statistical properties of eigenstate amplitudes in complex quantum systems.

Wouter Beugeling^1,2,3, Arnd Bäcker^1,4, Roderich Moessner¹

¹Max-Planck-Institut für Physik komplexer Systeme, Nöthnitzer Straße 38, 01187 Dresden, Germany.

Physical Review. E

|September 27, 2018

Summary

This summary is machine-generated.

Quantum system wave functions in large systems tend toward power-law distributions, deviating from the Gaussian behavior seen in chaotic systems. This deviation is linked to the entanglement properties of many-body eigenstates.

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Area of Science:

Quantum mechanics
Statistical physics
Condensed matter theory

Background:

Single-particle quantum billiards exhibit Gaussian wave-function amplitude distributions in chaotic systems.
Understanding many-body quantum systems requires analyzing their eigenstates.

Purpose of the Study:

To investigate the distribution of wave-function amplitudes for many-body lattice quantum systems.
To explore deviations from Gaussian behavior in integrable many-body systems.

Main Methods:

Analysis of wave-function amplitude distributions in a real-space basis.
Examination of integrable many-body systems and their eigenstates.
Relating amplitude distribution deviations to entanglement content.

Main Results:

Integrable many-body systems show a tendency towards power-law distributions for large system sizes.
Deviation from Gaussianity is connected to the entanglement properties of many-body eigenstates.
Specific integrable billiards demonstrate power-law tails in their amplitude distributions.

Conclusions:

Many-body quantum systems exhibit distinct statistical properties compared to single-particle systems.
Entanglement plays a crucial role in shaping the wave-function amplitude distributions in integrable systems.
The findings suggest a universal trend towards power-law behavior in complex quantum systems.