Spectral properties on a circle with a singularity

Abstract

We investigate the spectral and symmetry properties of a quantum particle moving on a circle with a pointlike singularity (or point interaction). We find that, within the U(2) family of the quantum mechanically allowed distinct singularities, a U(1) equivalence (of duality-type) exists, and accordingly the space of distinct spectra is U(1) x [SU(2)/U(1)], topologically a filled torus. We explore the relationship of special subfamilies of the U(2) family to corresponding symmetries, and identify the singularities that admit an N = 2 supersymmetry. Subfamilies that are distinguished in the spectral properties or the WKB exactness are also pointed out. The spectral and symmetry properties are also studied in the context of the circle with two singularities, which provides a useful scheme to discuss the symmetry properties on a general basis.

TeX, 26 pages. v2: one reference added and two updated

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Cited by in corpus (13)

• Supersymmetry and discrete transformations on S^1 with point singularities
• Effects of Two Successive Parity-Invariant Point Interactions on One-Dimensional Quantum Transmission: Resonance Conditions for the Parameter Space
• Non-Abelian Monopole in the Parameter Space of Point-like Interactions
• Inequivalent Quantizations of the N = 3 Calogero model with Scale and Mirror-S_3 Symmetry
• Boundary effect of a partition in a quantum well
• Path Integral on Star Graph
• Parasupersymmetry in Quantum Graphs
• Supersymmetry Transformations for Delta Potentials
• Exact energy spectrum for models with equally spaced point potentials
• Particle Propagation on a Circle with a Point Interaction
• Mathematical methods of factorization and a feedback approach for biological systems
• Supersymmetry and non-Abelian geometric phase for a free particle on a circle with point-like interactions
• Locational Qubit Realization with One-dimensional Contact Interactions