Duality and Anholonomy in Quantum Mechanics of 1D Contact Interactions

Abstract

We study systems with parity invariant contact interactions in one dimension. The model analyzed is the simplest nontrivial one --- a quantum wire with a point defect --- and yet is shown to exhibit exotic phenomena, such as strong vs weak coupling duality and spiral anholonomy in the spectral flow. The structure underlying these phenomena is SU(2), which arises as accidental symmetry for a particular class of interactions.

4 pages ReVTeX with 4 epsf figures. KEK preprint 2000-3. Correction in Eq.(14)

References in corpus (4)

• Kirchhoff's Rule for Quantum Wires
• Fermion-Boson Duality of One-dimensional Quantum Particles with Generalized Contact Interaction
• A Free Particle on a Circle with Point Interaction
• Double Spiral Energy Surface in One-dimensional Quantum Mechanics of Generalized Pointlike Potentials

Cited by in corpus (14)

• Symmetry, Duality and Anholonomy of Point Interactions in One Dimension
• Moebius Structure of the Spectral Space of Schroedinger Operators with Point Interaction
• Classical Aspects of Quantum Walls in One Dimension
• Self-adjoint extensions and SUSY breaking in Supersymmetric Quantum Mechanics
• Supersymmetry in quantum mechanics with point interactions
• Supersymmetry and discrete transformations on S^1 with point singularities
• Spectral properties on a circle with a singularity
• Extended supersymmetry and its reduction on a circle with point singularities
• Supersymmetric Quantum Mechanics with a Point Singularity
• Supersymmetric Quantum Mechanics under Point Singularities
• Effects of Two Successive Parity-Invariant Point Interactions on One-Dimensional Quantum Transmission: Resonance Conditions for the Parameter Space
• Resonant Transmission in One-Dimensional Quantum Mechanics with Two Independent Point Interactions: Full Parameter Analysis
• Hearing the shape of a quantum boundary condition
• Quantum contact interactions