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Resolving Water, Proteins, and Lipids from In Vivo Confocal Raman Spectra of Stratum Corneum through a Chemometric Approach

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Aharonov and Bohm versus Welsh eigenvalues.

P Exner^1,2, S Kondej³

¹1Doppler Institute for Mathematical Physics and Applied Mathematics, Czech Technical University in Prague, Břehová 7, 11519 Prague, Czechia.

Letters in Mathematical Physics

|August 14, 2018

Summary

This summary is machine-generated.

Investigating Schrödinger operators with singular interactions on concentric circles reveals a critical flux value. Below this threshold, discrete spectrums accumulate; above it, they become finite or empty.

Keywords:

Aharonov–Bohm flux Discrete spectrum Radial symmetry Singular Schrödinger operator

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Area of Science:

Mathematical Physics
Quantum Mechanics

Background:

Schrödinger operators model quantum systems.
Singular interactions and Aharonov-Bohm flux introduce complex behaviors.

Purpose of the Study:

Analyze the spectral properties of a 2D Schrödinger operator.
Investigate the impact of Aharonov-Bohm flux on singular interactions.

Main Methods:

Considered a 2D Schrödinger operator with type singular interaction.
Introduced an Aharonov-Bohm flux to the system.
Analyzed the behavior of the discrete spectrum below the essential spectrum.

Main Results:

Identified a critical flux value when .
Observed accumulation points in the discrete spectrum for .
Found a finite or empty discrete spectrum for and small .

Conclusions:

The Aharonov-Bohm flux significantly alters spectral properties.
A critical flux exists, distinguishing between accumulation and finiteness of eigenvalues.
The system exhibits rich spectral behavior dependent on flux strength and interaction parameters.