Spectral Theory

New submissions

Submissions received from Wed 15 May 24 to Thu 16 May 24, announced Fri, 17 May 24

[ total of 7 entries: 1-7 ]
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[1] arXiv:2405.10009 [pdf, ps, other]: Title: Dirac operators on the half-line: stability of spectrum and non-relativistic limit

Authors: David Kramar, David Krejcirik

Comments: 17 pages, 1 figure

Subjects: Spectral Theory (math.SP); Mathematical Physics (math-ph); Analysis of PDEs (math.AP); Quantum Physics (quant-ph)

We consider Dirac operators on the half-line, subject to generalised infinite-mass boundary conditions. We derive sufficient conditions which guarantee the stability of the spectrum against possibly non-self-adjoint potential perturbations and study the optimality of the obtained results. Finally, we establish a non-relativistic limit which makes a relationship of the present model to the Robin Laplacian on the half-line.

[2] arXiv:2405.09949 (cross-list from math.AP) [pdf, other]: Title: Homogenization of the Dirac operator with position-dependent mass

Authors: Andrii Khrabustovskyi, Vladimir Lotoreichik

Comments: 18 pages, 2 figures

Subjects: Analysis of PDEs (math.AP); Mathematical Physics (math-ph); Spectral Theory (math.SP)

We address the homogenization of the two-dimensional Dirac operator with position-dependent mass. The mass is piecewise constant and supported on small pairwise disjoint inclusions evenly distributed along an $\varepsilon$-periodic square lattice. Under rather general assumptions on geometry of these inclusions we prove that the corresponding family of Dirac operators converges as $\varepsilon\to 0$ in the norm resolvent sense to the Dirac operator with a constant effective mass provided the masses in the inclusions are adjusted to the scaling of the geometry. We also estimate the speed of this convergence in terms of the scaling rates.
[3] arXiv:2405.09957 (cross-list from math.AP) [pdf, ps, other]: Title: Resolvent estimates in Schatten spaces for Laplace-Beltrami operators on compact manifolds

Authors: Jean-Claude Cuenin

Comments: 5 pages

Subjects: Analysis of PDEs (math.AP); Spectral Theory (math.SP)

We prove resolvent estimates in Schatten spaces for Laplace-Beltrami operators on compact manifolds at the critical exponent. Our proof only uses known bounds for the Hadamard parametrix.

[4] arXiv:1210.8070 (replaced) [pdf, ps, other]: Title: The eta invariant on two-step nilmanifolds

Authors: Ruth Gornet, Ken Richardson

Comments: 55 pages in this new version; corrected sign error found by M. Stone in computation of 3-dimensional Heisenberg Dirac eigenvalues

Journal-ref: Comm. Anal. Geom. 26 (2018), no. 2, 271-346

Subjects: Differential Geometry (math.DG); K-Theory and Homology (math.KT); Spectral Theory (math.SP)
[5] arXiv:2011.10458 (replaced) [pdf, other]: Title: Spectra of Complex Unit Hypergraphs

Authors: Raffaella Mulas, Nathan Reff

Subjects: Combinatorics (math.CO); Spectral Theory (math.SP)
[6] arXiv:2211.06916 (replaced) [pdf, other]: Title: On spectral simplicity of the Hodge Laplacian and Curl Operator along paths of metrics

Authors: Willi Kepplinger

Comments: final version, to appear in TAMS. The most important changes include a change in title (shortened), a more detailed proof of Theorem 1.4 and Lemma 3.3 as well as the inclusion of two new Lemmas (3.5 and 3.6) in section 3.2. Furthermore the Beltrami operator has been renamed into Curl operator at the suggestion of an anonymous referee

Subjects: Differential Geometry (math.DG); Spectral Theory (math.SP)
[7] arXiv:2405.06091 (replaced) [pdf, ps, other]: Title: Limit points of (signless) Laplacian spectral radii of linear trees

Authors: Francesco Belardo, Elismar R. Oliveira, Vilmar Trevisan

Subjects: Combinatorics (math.CO); Spectral Theory (math.SP)

[ total of 7 entries: 1-7 ]
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