Bifurcations of Essential Spectra Generated by a Small Non-Hermitian Hole. I. Meromorphic Continuations

2021 ◽  
Vol 28 (4) ◽  
pp. 416-433
Author(s):  
D. I. Borisov ◽  
D. A. Zezyulin
Keyword(s):  
Essential Spectra

A characterization of some subsets of S-essential spectra of a multivalued linear operator

2014 ◽  
Vol 135 (2) ◽  
pp. 171-186 ◽  
Author(s):  
Teresa Álvarez ◽  
Aymen Ammar ◽  
Aref Jeribi
Keyword(s):  
Linear Operator ◽  
Essential Spectra ◽  
Multivalued Linear Operator

scholarly journals Dirichlet and Neumann eigenvalues for half-plane magnetic Hamiltonians

2014 ◽  
Vol 26 (02) ◽  
pp. 1450003 ◽  
Author(s):  
Vincent Bruneau ◽  
Pablo Miranda ◽  
Georgi Raikov
Keyword(s):  
Magnetic Field ◽  
Asymptotic Behavior ◽  
Half Plane ◽  
Compact Support ◽  
Constant Magnetic Field ◽  
Scalar Potential ◽  
Neumann Boundary ◽  
Essential Spectra ◽  
Neumann Eigenvalues ◽  
Effective Hamiltonians

Let H0,D (respectively, H0,N) be the Schrödinger operator in constant magnetic field on the half-plane with Dirichlet (respectively, Neumann) boundary conditions, and let Hℓ := H0,ℓ - V, ℓ = D, N, where the scalar potential V is non-negative, bounded, does not vanish identically, and decays at infinity. We compare the distribution of the eigenvalues of HD and HN below the respective infima of the essential spectra. To this end, we construct effective Hamiltonians which govern the asymptotic behavior of the discrete spectrum of Hℓ near inf σ ess (Hℓ) = inf σ(H0,ℓ), ℓ = D, N. Applying these Hamiltonians, we show that σ disc (HD) is infinite even if V has a compact support, while σ disc (HN) could be finite or infinite depending on the decay rate of V.

Numerical estimates of the essential spectra of quantum graphs with delta-interactions at vertices

2017 ◽  
Vol 98 (1-2) ◽  
pp. 458-482 ◽  
Author(s):  
Víctor Barrera-Figueroa ◽  
Vladimir S. Rabinovich ◽  
Miguel Maldonado Rosas
Keyword(s):  
Quantum Graphs ◽  
Essential Spectra
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