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Related Experiment Video

Updated: Nov 20, 2025

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

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Published on: May 27, 2020

Random matrix spectral form factor in kicked interacting fermionic chains.

Dibyendu Roy¹, Tomaž Prosen²

¹Raman Research Institute, Bangalore 560080, India.

Physical Review. E

|January 20, 2021

Summary

This summary is machine-generated.

We investigate quantum chaos in driven fermionic chains. The spectral form factor matches random matrix theory predictions, with Thouless time scaling dependent on particle-number conservation symmetry.

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Area of Science:

Quantum physics
Condensed matter theory
Quantum chaos

Background:

Periodically driven (Floquet) fermionic chains exhibit complex dynamics.
Long-range two-particle interactions significantly influence spectral properties.
Particle-number conservation (U(1) symmetry) plays a crucial role in quantum systems.

Purpose of the Study:

To analyze quantum chaos and spectral correlations in Floquet fermionic chains.
To investigate the impact of long-range interactions and U(1) symmetry on spectral properties.
To determine the scaling of Thouless time in these systems.

Main Methods:

Analytical derivation of the spectral form factor.
Application of random matrix theory predictions.
Analysis of Thouless time scaling under different symmetry conditions.
Utilizing a random phase assumption for long-range interactions.

Main Results:

The spectral form factor precisely follows random matrix theory predictions for long chains.
Thouless time scales as O(L^2) with U(1) symmetry and O(L^0) without it.
The Thouless time scaling is shown to be equivalent to the spectral gap behavior of classical Markov chains.

Conclusions:

Floquet fermionic chains with long-range interactions exhibit universal spectral correlations governed by random matrix theory.
The presence or absence of U(1) symmetry dictates the Thouless time scaling, impacting the onset of quantum chaos.
The connection to classical Markov chains provides a novel perspective on the dynamics of these quantum systems.