39 citations · 127 across the 28 of their papers we have counts for
19 papers · 1 filter
Random Schrödinger operators on manifolds and abstract bounds for multiplier-type operators
Jean-Claude Cuenin, Konstantin Merz, Eduard Stefanescu
We study random Schrödinger operators on closed Riemannian manifolds with Anderson-type potentials. We prove high-probability spectral inclusion bounds showing that eigenvalues rem…
Eigenvalue bounds for Schrödinger operators with complex potentials on compact manifolds
Jean-Claude Cuenin
We prove eigenvalue bounds for Schrödinger operator on compact manifolds with complex potentials . The bounds depend only on an -norm of the potential, and they ar…
Open problem: Violation of locality for Schrödinger operators with complex potentials
Jean-Claude Cuenin, Rupert L. Frank
We explain in which sense Schrödinger operators with complex potentials appear to violate locality (or Weyl's asymptotics), and we pose three open problems related to this phenomen…
Bounds for Eigenvalue Sums of Schrödinger Operators with Complex Radial Potentials
Jean-Claude Cuenin, Solomon Keedle-Isack
We consider eigenvalue sums of Schrödinger operators on with complex radial potentials , . We prove quantitative bounds on the distribution…
Lieb-Thirring-type inequalities for random Schrödinger operators with complex potentials
Jean-Claude Cuenin, Konstantin Merz
We review some results and proofs on eigenvalue bounds for random Schrödinger operators with complex-valued potentials. We also include new Schatten norm estimates for the resolven…
Effective upper bounds on the number of resonance in potential scattering
Jean-Claude Cuenin
We prove upper bounds on the number of resonances and eigenvalues of Schrödinger operators with complex-valued potentials, where is odd. The novel feature of our u…
Random Schrödinger operators with complex decaying potentials
Jean-Claude Cuenin, Konstantin Merz
We prove that the eigenvalues of a continuum random Schrödinger operator of Anderson type, with complex decaying potential, can be bounded (with high probability) in term…
Counterexample to the Laptev--Safronov conjecture
Sabine Bögli, Jean-Claude Cuenin
We prove that the Laptev--Safronov conjecture (Comm. Math. Phys., 2009) is false in the range that is not covered by Frank's positive result (Bull. Lond. Math. Soc., 2011). The sim…
Schrödinger operators with complex sparse potentials
Jean-Claude Cuenin
We establish quantitative upper and lower bounds for Schrödinger operators with complex potentials that satisfy some weak form of sparsity. Our first result is a quantitative versi…
Sharp spectral bounds for complex perturbations of the indefinite Laplacian
Jean-Claude Cuenin, Orif O. Ibrogimov
We derive quantitative bounds for eigenvalues of complex perturbations of the indefinite Laplacian on the real line. Our results substantially improve existing results even for rea…
Improved eigenvalue bounds for Schrödinger operators with slowly decaying potentials
Jean-Claude Cuenin
We extend a result of Davies and Nath on the location of eigenvalues of Schrödinger operators with slowly decaying complex-valued potentials to higher dimensions. In this context,…
Eigenvalue estimates for bilayer graphene
Jean-Claude Cuenin
Recently, Ferrulli-Laptev-Safronov (2016arXiv161205304F) obtained eigenvalue estimates for an operator associated to bilayer graphene in terms of norms of the (possibly non-s…
Eigenvalues of one-dimensional non-self-adjoint Dirac operators and applications
Jean-Claude Cuenin, Petr Siegl
We analyze eigenvalues emerging from thresholds of the essential spectrum of one-dimensional Dirac operators perturbed by complex and non-symmetric potentials. In the general non-s…
Sharp spectral estimates for the perturbed Landau Hamiltonian with potentials
Jean-Claude Cuenin
We establish a sharp estimate on the size of the spectral clusters of the Landau Hamiltonian with potentials in two dimensions as the cluster index tends to infinity. In thre…
Non-symmetric perturbations of self-adjoint operators
Jean-Claude Cuenin, Christiane Tretter
We investigate the effect of non-symmetric relatively bounded perturbations on the spectrum of self-adjoint operators. In particular, we establish stability theorems for one or inf…
Eigenvalue bounds for Dirac and fractional Schrödinger operators with complex potentials
Jean-Claude Cuenin
We prove Lieb-Thirring-type bounds for fractional Schrödinger operators and Dirac operators with complex-valued potentials. The main new ingredient is a resolvent bound in Schatten…
Estimates on complex eigenvalues for Dirac operators on the half-line
Jean-Claude Cuenin
We derive bounds on the location of non-embedded eigenvalues of Dirac operators on the half-line with non-Hermitian -potentials. The results are sharp in the non-relativistic…
Eigenvalue estimates for non-selfadjoint Dirac operators on the real line
Jean-Claude Cuenin, Ari Laptev, Christiane Tretter
We show that the non-embedded eigenvalues of the Dirac operator on the real line with non-Hermitian potential lie in the disjoint union of two disks in the right and left half…
Block-Diagonalization of Operators with Gaps, with Applications to Dirac Operators
Jean-Claude Cuenin
We present new results on the block-diagonalization of Dirac operators on three-dimensional Euclidean space with unbounded potentials. Classes of admissible potentials include elec…