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¹H NMR Signal Integration: Overview

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Excitonic Hamiltonians for Calculating Optical Absorption Spectra and Optoelectronic Properties of Molecular Aggregates and Solids

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Published on: May 27, 2020

Spectrum statistics in the integrable Lieb-Liniger model.

Samy Mailoud¹, Fausto Borgonovi^2,3, Felix M Izrailev^1,4

¹Instituto de Física, Benemérita Universidad Autónoma de Puebla, Apartado Postal J-48, Puebla 72570, Mexico.

Physical Review. E

|October 16, 2021

Summary

This summary is machine-generated.

Quantum system energy spectra depend on momentum and interaction strength. We analyzed the Lieb-Liniger model, finding Poisson distributions for specific energy subsets, not the full spectrum.

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Area of Science:

Quantum Many-Body Physics
Statistical Mechanics
Condensed Matter Theory

Background:

Integrable quantum systems exhibit complex energy spectra.
Understanding spectrum statistics is crucial for characterizing quantum behavior.
The Lieb-Liniger model is a fundamental system for studying 1D interacting bosons.

Purpose of the Study:

To investigate the spectrum statistics of the Lieb-Liniger model.
To determine how energy level distributions depend on model parameters and momentum.
To explore deviations from random matrix theory predictions.

Main Methods:

Analytical and numerical studies of the Lieb-Liniger model.
Utilizing the Bethe ansatz for exact energy spectra determination.
Analyzing nearest-neighbor and long-range energy level correlations.

Main Results:

Spectrum statistics are sensitive to whether the full spectrum or a fixed momentum subset is analyzed.
Poisson distribution of energy spacings occurs for fixed momentum subsets under specific conditions (intermediate interaction, high energy).
Significant deviations from pseudorandom predictions were observed in long-range correlations.

Conclusions:

The spectral properties of integrable systems are more nuanced than often assumed.
Fixed momentum sectors reveal distinct statistical behaviors compared to the full spectrum.
The Lieb-Liniger model provides a key testbed for theories of quantum chaos and integrability.