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Related Experiment Video

Updated: Jul 16, 2026

Scalable Quantum Integrated Circuits on Superconducting Two-Dimensional Electron Gas Platform

Scalable Quantum Integrated Circuits on Superconducting Two-Dimensional Electron Gas Platform

Published on: August 2, 2019

Quantum Systems at The Brink: Helium-Type Systems.

Dirk Hundertmark^1,2, Michal Jex^3,4, Markus Lange⁵

¹Department of Mathematics, Institute for Analysis, Karlsruhe Institute of Technology, 76128 Karlsruhe, Germany.

Archive for Rational Mechanics and Analysis

|July 15, 2026

Summary

This study introduces a new method to analyze critical helium-type systems, providing the first precise bounds for ground state behavior at the essential spectrum threshold.

Keywords:

35Q40 81Q05 81V45

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Area of Science:

Quantum mechanics
Quantum chemistry

Background:

Helium-type systems present challenges in eigenvalue analysis.
Standard methods fail when eigenvalues reach the essential spectrum.

Purpose of the Study:

To develop a method for analyzing eigenvalues at thresholds in helium-type systems.
To determine the asymptotic behavior of eigenfunctions in critical cases.

Main Methods:

A novel method is developed to overcome limitations of existing techniques.
Sharp upper and lower bounds are derived for asymptotic behavior.

Main Results:

The first proof of precise asymptotic behavior for the ground state of critical helium-type systems.
Demonstration of how asymptotic decay changes in critical systems.

Conclusions:

The developed method successfully addresses eigenvalue problems at thresholds.
New insights into the behavior of critical quantum systems are provided.