Related Experiment Video
Updated: Feb 6, 2026

Gradient Echo Quantum Memory in Warm Atomic Vapor
Published on: November 11, 2013
Spectral Statistics in Spatially Extended Chaotic Quantum Many-Body Systems
Amos Chan1, Andrea De Luca1, J T Chalker1
1Theoretical Physics, Oxford University, 1 Keble Road, Oxford OX1 3NP, United Kingdom.
Abstract:
We study spectral statistics in spatially extended chaotic quantum many-body systems, using simple lattice Floquet models without time-reversal symmetry. Computing the spectral form factor K(t) analytically and numerically, we show that it follows random matrix theory (RMT) at times longer than a many-body Thouless time, t_{Th}. We obtain a striking dependence of t_{Th} on the spatial dimension d and size of the system. For d>1, t_{Th} is finite in the thermodynamic limit and set by the intersite coupling strength. By contrast, in one dimension t_{Th} diverges with system size, and for large systems there is a wide window in which spectral correlations are not of RMT form. Lastly, our Floquet model exhibits a many-body localization transition, and we discuss the behavior of the spectral form factor in the localized phase.
Related Concept Videos
Quantum Numbers
Buffer Systems in the Body
A typical buffer system in bodily fluids includes a weak acid and its corresponding...
Statistical Significance
The Quantum-Mechanical Model of an Atom
Probability in Statistics
An example of a simple event is a coin toss. The result of a coin toss is either a head or a tail. Here, head and tail are two simple events. These two simple events make up the sample space. Further, the probability of an event occurring falls within the range of 0 to 1. The probability of an...
Introduction to Statistics
In statistics, the collection of individuals or objects under study is called population. The idea of sampling is to select a portion of the larger population...

