# On pairs of interacting electrons in a quantum wire

@article{Kerner2018OnPO, title={On pairs of interacting electrons in a quantum wire}, author={Joachim Kerner}, journal={Journal of Mathematical Physics}, year={2018} }

In this paper we consider pairs of interacting electrons moving in a simple quantum wire, namely the half-line. In particular, we extend the results obtained in [arXiv:1708.03753] by allowing for contact interactions of the Lieb-Liniger type between the two electrons constituting the pair. We construct the associated Hamiltonian rigorously and study its spectral properties. We then investigate Bose-Einstein condensation of pairs and prove, as a main result, the existence of condensation…

## 8 Citations

### On the number of isolated eigenvalues of a pair of particles on the half-line

- Mathematics, Physics
- 2018

In this note we consider a pair of particles moving on the positive half-line with the pairing generated by a hard-wall potential. This model was first introduced in [arXiv:1604.06693] and later…

### Impact of surface defects on a condensate of electron pairs in a quantum wire

- PhysicsTheoretical and Mathematical Physics
- 2020

We study the impact of surface defects on a condensate of electron pairs in a quantum wire. Based on previous results, we formulate a simple mathematical model accounting for such surface effects.…

### Impact of surface defects on a condensate of electron pairs in a quantum wire

- Physics
- 2020

We study the impact of surface defects on a condensate of electron pairs in a quantum wire. Based on previous results, we formulate a simple mathematical model accounting for such surface effects.…

### On surface defects and their impact on the superconducting phase in quantum wires

- Physics
- 2017

In this paper we are interested in understanding the impact of surface defects on the superconducting phase in quantum wires. Based on previous results [arXiv:1708.03753], we establish a simple…

### Bound states of a pair of particles on the half-line with a general interaction potential

- MathematicsJournal of Spectral Theory
- 2020

In this paper we study an interacting two-particle system on the positive half-line. We focus on spectral properties of the Hamiltonian for a large class of two-particle potentials. We characterize…

### Measurement of Junction Depth in Sub-Micron Device Using SIMS Technique for Performance Estimation in RF Range

- Physics
- 2020

This chapter shows the measurement procedure of junction depth using SIMS method with detailed experimental procedure, and the result is verified by theoretical computation. SIMS profile is…

### Many-Particle Quantum Graphs: A Review

- PhysicsDiscrete and Continuous Models in the Theory of Networks
- 2020

In this paper we review recent work that has been done on quantum many-particle systems on metric graphs. Topics include the implementation of singular interactions, Bose-Einstein condensation,…

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