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}
}
  • J. Kerner
  • Published 2 January 2018
  • Physics, Mathematics
  • Journal of Mathematical Physics
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… 

On Bound Electron Pairs on the Half-Line

  • J. Kerner
  • Mathematics, Physics
    Reports on Mathematical Physics
  • 2019

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

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

  • J. Kerner
  • Physics
    Theoretical 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

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

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

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

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

  • J. BolteJ. Kerner
  • Physics
    Discrete 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,

References

SHOWING 1-10 OF 17 REFERENCES

Two interacting particles on the half-line

In the case of general compact quantum graphs, many-particle models with singular two-particle interactions were introduced by Bolte and Kerner [J. Phys. A: Math. Theor. 46, 045206 (2013); 46, 045207

Strongly interacting confined quantum systems in one dimension.

This work proves that 1D fermionic and bosonic systems with strong short-range interactions are solvable in arbitrary confining geometries by introducing a new energy-functional technique and obtaining the full spectrum of energies and eigenstates.

EXACT ANALYSIS OF AN INTERACTING BOSE GAS. I. THE GENERAL SOLUTION AND THE GROUND STATE

A gas of one-dimensional Bose particles interacting via a repulsive delta-function potential has been solved exactly. All the eigenfunctions can be found explicitly and the energies are given by the

Quantum graphs with two-particle contact interactions

We construct models of many-particle quantum graphs with singular two-particle contact interactions, which can be either hardcore- or δ-interactions. Self-adjoint realizations of the two-particle

Theory of superconductivity

A theory of superconductivity is presented, based on the fact that the interaction between electrons resulting from virtual exchange of phonons is attractive when the energy difference between the

Exactly solvable interacting two-particle quantum graphs

We construct models of exactly solvable two-particle quantum graphs with certain non-local two-particle interactions, establishing appropriate boundary conditions via suitable self-adjoint

One dimensional bosons: From condensed matter systems to ultracold gases

The physics of one-dimensional interacting bosonic systems is reviewed. Beginning with results from exactly solvable models and computational approaches, the concept of bosonic Tomonaga-Luttinger

Short-distance correlation properties of the Lieb-Liniger system and momentum distributions of trapped one-dimensional atomic gases.

The high-p asymptotics of the momentum distribution of both free and harmonically trapped atoms are obtained and it is shown that it obeys a universal 1/p(4) law for all values of the interaction strength.

Two particles on a star graph, II

We consider a two-particle system on a star graph with delta function interaction. A complete description of the eigensolutions with real momenta is given; specifically, it is shown that all