Spectral edge regularity of magnetic Hamiltonians

Bounds for the Regularity of Edge Ideal of Vertex Decomposable and Shellable Graphs

An upper bound for the regularity of powers of edge ideals

‎A recent result due to Ha and Van Tuyl proved that the Castelnuovo-Mumford regularity of the quotient ring $R/I(G)$ is at most matching number of $G$‎, ‎denoted by match$(G)$‎. ‎In this paper‎, ‎we provide a generalization of this result for powers of edge ideals‎. ‎More precisely‎, ‎we show that for every graph $G$ and every $sgeq 1$‎, ‎$${rm reg}( R‎/ ‎I(G)^{s})leq (2s-1) |E(G)|^{s-1} {rm ma...

Regularity of second power of edge ideals

Let G be a graph with edge ideal I(G). Benerjee and Nevo proved that for every graph G, the inequality reg(I(G)2)≤reg(I(G))+2 holds. We provide an alternative proof for this result.

Spectral Flow and Level Spacing of Edge States for Quantum Hall Hamiltonians

We consider a non relativistic particle on the surface of a semi-infinite cylinder of circumference L submitted to a perpendicular magnetic field of strength B and to the potential of impurities of maximal amplitude w. This model is of importance in the context of the integer quantum Hall effect. In the regime of strong magnetic field or weak disorder B >> w it is known that there are chiral ed...

Discrete Spectrum of Quantum Hall Effect Hamiltonians I. Monotone Edge Potentials

We consider the unperturbed operator H0 := (−i∇ − A)2 + W , self-adjoint in L2(R2). Here A is a magnetic potential which generates a constant magnetic field b > 0, and the edge potential W is a non-decreasing non constant bounded function depending only on the first coordinate x ∈ R of (x, y) ∈ R2. Then the spectrum of H0 has a band structure and is absolutely continuous; moreover, the assumpti...