Instantons and Berry's connections on quantum graph
arXiv:2104.02311 · doi:10.1088/1751-8121/ac17a3
Abstract
In this paper, we study non-Abelian Berry's connections in the parameter space of boundary conditions for Dirac zero modes on quantum graphs. We apply the ADHM construction, which is the method for constructing Yang-Mills instanton solutions, to the Berry's connections. Then we find that the instanton configurations appear as the Berry's connections.
arXiv comment18 pages, 3figures
References in corpus (22)
- Kirchhoff's Rule for Quantum Wires
- Quantum Graphs II: Some spectral properties of quantum and combinatorial graphs
- Scattering theory on graphs
- Eigenfunction Statistics on Quantum Graphs
- Quark mass hierarchy and mixing via geometry of extra dimension with point interactions
- n-particle quantum statistics on graphs
- Non-abelian Quantum Statistics on Graphs
- Irregular Dynamics in a Solvable One-Dimensional Quantum Graph
- Supersymmetry and discrete transformations on S^1 with point singularities
- Realization of lepton masses and mixing angles from point interactions in an extra dimension
- Extended supersymmetry and its reduction on a circle with point singularities
- Topological Number of Edge States
- ADHM Construction of (Anti-)Self-dual Instantons in Eight Dimensions
- Non-Abelian Monopole in the Parameter Space of Point-like Interactions
- ADHM Construction of (Anti-)Self-dual Instantons in Dimensions
- Octonionic instantons in eight dimensions
- BPS Monopole in the Space of Boundary Conditions
- Parasupersymmetry in Quantum Graphs
- 5d Dirac fermion on quantum graph
- Quantum Reflection and Transmission in Ring Systems with Double Y-Junctions: Occurrence of Perfect Reflection
- Models for the BPS Berry Connection
- Berry's connection, Kähler geometry and the Nahm construction of monopoles