Magnetic interpretation of the nodal defect on graphs
نویسنده
چکیده
In this note, we present a natural proof of a recent and surprising result of Gregory Berkolaiko interpreting the Courant nodal defect as a Morse index. This proof is inspired by a nice paper of Miroslav Fiedler published in 1975.
منابع مشابه
اثر چرخش گشتاور مغناطیسی نقص ها روی رسانش وابسته به اسپین یک نانو سیم فرومغناطیس
In this paper, we calculate the spin-dependent conductance of ferromagnetic quantum wire in the presence of one or two defects by using Green's function method at the tight-binding approach. We study the effect of rotation of defect magnetic moment on the system conductance. The results show that in the magnetic wire, independent of existence or absence of defect, the allowed energy region shi...
متن کاملStability of eigenvalues of quantum graphs with respect to magnetic perturbation and the nodal count of the eigenfunctions.
We prove an analogue of the magnetic nodal theorem on quantum graphs: the number of zeros of the nth eigenfunction of the Schrödinger operator on a quantum graph is related to the stability of the nth eigenvalue of the perturbation of the operator by magnetic potential. More precisely, we consider the nth eigenvalue as a function of the magnetic perturbation and show that its Morse index at zer...
متن کاملMafic Dykes of Moyar Shear Zone, North Kerala, India: Emplacement History and Petrogenetic interpretation based on Structure, Geochemistry and Magnetic Fabric
Cretaceous mafic dykes in the Moyar Shear Zone (MSZ) area, north Kerala, India, provide signatures to probe into the nature of their source and thereby the evolution of the Mesozoic lithospheric mantle beneath the South Indian Granulite Terrain (SIGT). Bulk of the dykes in northern parts of Kerala is broadly in spatial association with the shear system. Mafic dykes striking NE-SW, NWSE, NNW-SSE...
متن کاملThermal Convection in a (Kuvshiniski-type) Viscoelastic Rotating Fluid in the Presence of Magnetic Field through Porous Medium (TECHNICAL NOTE)
The effect of magnetic field on an incompressible (Kuvshiniski-Type) viscoelastic rotating fluid heated from below in porous medium is considered. For the case of stationary convection, magnetic field and medium permeability have both stabilizing and destabilizing effect on the thermal convection under some conditions whereas rotation has a stabilizing effect on the thermal convection. In the...
متن کاملEnhancement of the Magneto-Optical Kerr Effect in One- Dimensional Magnetophotonic Crystals with Adjustable Spatial Configuration
We studied magnetophotonic crystals (MPCs) with introduced magneticdefect layer sandwiched between magnetic and dielectric Bragg mirrors. Thesemagnetophotonic crystals have excellent capabilities to enhance reflection and Kerrrotation simultaneously. By adjusting spatial configuration such as repetition numbersof Bragg mirrors and thickness of magnetic defect layer, we a...
متن کامل