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Magnetically Induced Rotating Rayleigh-Taylor Instability

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Published on: March 3, 2017

Ansatz for the Jahn-Teller triplet instability.

Arnout Ceulemans¹, P Bernát Szabó¹

¹Department of Chemistry, Katholieke Universiteit Leuven, Celestijnenlaan 200F, B-3001 Leuven, Belgium.

The Journal of Chemical Physics

|November 10, 2020

Summary

The Jahn-Teller instability in threefold degenerate electronic states is addressed by a new analytical method. This approach utilizes SO(5) to SO(3) symmetry breaking to solve vibronic equations.

Area of Science:

Quantum mechanics
Solid-state physics
Molecular spectroscopy

Background:

Jahn-Teller instability affects degenerate electronic states in molecules and solids.
Symmetry lowering distortions are crucial for understanding these instabilities.
Existing methods often rely on complex group-theoretical techniques.

Purpose of the Study:

To present an alternative analytical solution for the Jahn-Teller effect in threefold degenerate electronic states.
To explore symmetry breaking within the vibronic Hamiltonian.
To provide a new framework for analyzing vibronic coupling.

Main Methods:

Application of Bargmann's analytical method to the vibronic Hamiltonian.
Construction of an ansatz incorporating SO(5) to SO(3) symmetry breaking.

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Derivation and solution of Jahn-Teller equations using radial polynomials and Gegenbauer functions.

Main Results:

A novel analytical solution for the Jahn-Teller problem in threefold degenerate states is established.
The method successfully incorporates SO(5) to SO(3) symmetry breaking.
Jahn-Teller equations are solved explicitly in terms of special functions.

Conclusions:

The Bargmann analytical method offers an effective alternative to traditional group-theoretical approaches for Jahn-Teller systems.
The study provides a new mathematical framework for understanding vibronic interactions and symmetry breaking.
This work advances the theoretical understanding of degenerate electronic states and their distortions.