Related Experiment Video
Updated: Oct 14, 2025
07:11
ARL Spectral Fitting as an Application to Augment Spectral Data via Franck-Condon Lineshape Analysis and Color Analysis
Published on: August 19, 2021
2.7K
Spectral Properties of Schrödinger Operators Associated with Almost Minimal Substitution Systems.
Benjamin Eichinger1, Philipp Gohlke2
1Departments of Mathematics, Rice University MS-136, Box 1892, Houston, TX 77251-1892 USA.
Annales Henri Poincare
|November 1, 2021
Summary
This study explores spectral properties of ergodic Schrödinger operators linked to non-primitive substitutions. We found conditions for eigenvalue appearance and exclusion in complex dynamical systems.
Area of Science:
- Dynamical Systems and Ergodic Theory
- Mathematical Physics
- Spectral Theory
Background:
- Ergodic Schrödinger operators are fundamental in condensed matter physics and dynamical systems.
- Non-primitive substitutions generate complex sequences with properties beyond standard models.
- Understanding spectral properties is key to characterizing the behavior of such systems.
Purpose of the Study:
- To investigate the spectral properties of ergodic Schrödinger operators associated with non-primitive substitutions.
- To analyze dynamical systems that exhibit properties beyond minimality, unique ergodicity, and linear complexity.
- To determine conditions for the appearance and exclusion of eigenvalues in the spectrum.
Main Methods:
- Analysis of spectral properties using non-primitive substitutions on a binary alphabet.
- Exploration of dynamical systems, including those with infinite ergodic measures.
- Application of return word decompositions and induced systems (conjugate to an odometer).
Main Results:
- The almost sure spectrum is shown to be singular and contain an interval in certain parameter regions.
- Conditions for the appearance of eigenvalues are identified.
- Criteria for the exclusion of eigenvalues, including the role of strongly palindromic sequences, are fully characterized.
Conclusions:
- The study provides a comprehensive analysis of spectral properties for a complex class of dynamical systems.
- Insights into eigenvalue behavior are gained through structural analysis and return word decompositions.
- The findings contribute to the understanding of non-uniformly recurrent sequences and associated induced systems.
More Related Videos
Related Concept Videos
02:45The Quantum-Mechanical Model of an Atom
53.0K
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.
53.0K
01:02¹H NMR: Interpreting Distorted and Overlapping Signals
1.2K
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...
1.2K
01:16UV–Vis Spectroscopy: Molecular Electronic Transitions
2.0K
In Ultraviolet–Visible (UV–Vis) spectroscopy, the absorption of electromagnetic radiation is used to probe the electronic structure of molecules. This technique provides insights into molecular electronic transitions, particularly the movement of electrons between different molecular orbitals. Radiation is absorbed if the energy of the electromagnetic radiation passing through the molecule is precisely equal to the energy difference between the excited and ground states. During this...
2.0K
03:06The Pauli Exclusion Principle
55.1K
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:
55.1K
02:44Atomic Orbitals
39.2K
An atomic orbital represents the three-dimensional regions in an atom where an electron has the highest probability to reside. The radial distribution function indicates the total probability of finding an electron within the thin shell at a distance r from the nucleus. The atomic orbitals have distinct shapes which are determined by l, the angular momentum quantum number. The orbitals are often drawn with a boundary surface, enclosing densest regions of the cloud.
39.2K
03:51Molecular Orbital Theory II
20.7K
Molecular Orbital Energy Diagrams
20.7K