Related Experiment Video
Updated: Jul 2, 2025
00:07
A Photonic System for Generating Unconditional Polarization-Entangled Photons Based on Multiple Quantum Interference
Published on: September 5, 2019
8.5K
Universal spectral correlations in interacting chaotic few-body quantum systems
Felix Fritzsch1,2, Maximilian F I Kieler3
1Physics Department, Faculty of Mathematics and Physics, University of Ljubljana, 1000 Ljubljana, Slovenia.
Physical Review. E
|February 17, 2024
Summary
We reveal a universal transition in quantum chaos spectral correlations, bridging noninteracting and strongly interacting systems. This behavior is governed by a single scaling parameter and confirmed in realistic models.
Area of Science:
- Quantum physics
- Chaos theory
- Statistical mechanics
Background:
- Quantum chaos is characterized by random matrix spectral correlations.
- Understanding these correlations in interacting systems is crucial for quantum physics.
- Previous studies focused on specific regimes, lacking a universal description.
Purpose of the Study:
- To investigate spectral correlations in interacting chaotic quantum systems.
- To develop a universal description of the transition between noninteracting and interacting regimes.
- To analyze the spectral form factor and its moments.
Main Methods:
- Modeling interacting chaotic systems using random-matrix ensembles.
- Exact calculation of the spectral form factor for large Hilbert space dimensions.
- Extrapolation to finite dimensions and analysis of scaling parameters.
- Perturbative approach for small-coupling regimes.
- Numerical studies on quantized kicked rotors.
Main Results:
- A universal transition in spectral correlations was identified.
- This transition combines noninteracting and strongly interacting limits, governed by a single scaling parameter.
- Results were validated for bipartite systems and extended to realistic models.
- The spectral form factor and its moments were analyzed.
Conclusions:
- The findings provide a unified understanding of spectral correlations across different interaction strengths.
- The single scaling parameter offers a powerful tool for characterizing quantum chaos.
- The results are applicable to a broad range of interacting quantum systems.
Related Concept Videos
01:02¹H NMR: Interpreting Distorted and Overlapping Signals
1.0K
Spin systems where the difference in chemical shifts of the coupled nuclei is greater than ten times J are called first-order spin systems. These nuclei are weakly coupled, and their chemical shifts and coupling constant can generally be estimated from the well-separated signals in the spectrum.
As Δν decreases and the signals move closer, the doublets appear increasingly distorted. The intensities of the inner lines increase at the cost of those of the outer lines as the signals are...
As Δν decreases and the signals move closer, the doublets appear increasingly distorted. The intensities of the inner lines increase at the cost of those of the outer lines as the signals are...
1.0K
01:182D NMR: Overview of Heteronuclear Correlation Techniques
179
Heteronuclear correlation spectroscopy is an analytical technique that investigates the coupling between different types of nuclei, often a proton and an X-nucleus, such as carbon-13 or nitrogen-15. This method is commonly used in nuclear magnetic resonance (NMR) spectroscopy to gain insights into complex chemical compounds' structural and compositional aspects. A typical heteronuclear correlation spectrum displays X-nucleus chemical shifts on one axis and a proton spectrum on the other...
179
03:06The Pauli Exclusion Principle
37.2K
The arrangement of electrons in the orbitals of an atom is called its electron configuration. We describe an electron configuration with a symbol that contains three pieces of information:
37.2K
01:192D NMR: Heteronuclear Single-Quantum Correlation Spectroscopy (HSQC)
715
Heteronuclear single-quantum correlation spectroscopy (HSQC) is a 2D NMR technique that reveals one-bond correlations between hydrogen and a heteronucleus. The HSQC experiment is similar to the heteronuclear correlation experiment (HETCOR) but is more sensitive. In the HSQC spectrum, the proton chemical shift is plotted on the horizontal F2 axis, while the 13C chemical shift is plotted on the vertical F1 axis. The corresponding proton and 13C spectra are also shown. The HSQC contour plot does...
715
02:45The Quantum-Mechanical Model of an Atom
42.3K
Shortly after de Broglie published his ideas that the electron in a hydrogen atom could be better thought of as being a circular standing wave instead of a particle moving in quantized circular orbits, Erwin Schrödinger extended de Broglie’s work by deriving what is now known as the Schrödinger equation. When Schrödinger applied his equation to hydrogen-like atoms, he was able to reproduce Bohr’s expression for the energy and, thus, the Rydberg formula governing hydrogen spectra.
42.3K
01:162D NMR: Overview of Homonuclear Correlation Techniques
198
Homonuclear correlation spectroscopy (COSY) is a powerful technique used in Nuclear Magnetic Resonance (NMR) spectroscopy to study the correlations between nuclei of the same type within a molecule. It provides information about scalar couplings between adjacent nuclei, which helps determine connectivity and structural information. There are several COSY variants, each with its unique strengths and experimental parameters.
COSY90 is the standard two-dimensional (2D) COSY experiment that...
COSY90 is the standard two-dimensional (2D) COSY experiment that...
198