scholarly journals Distributions of Dirac operator eigenvalues

2004 ◽  
Vol 583 (1-2) ◽  
pp. 199-206 ◽  
Author(s):  
G. Akemann ◽  
P.H. Damgaard
Keyword(s):  
Dirac Operator ◽  
Operator Eigenvalues

scholarly journals Density profiles of small Dirac operator eigenvalues for two color QCD at nonzero chemical potential compared to matrix models

2005 ◽  
Vol 140 ◽  
pp. 568-570 ◽  
Author(s):  
Gernot Akemann ◽  
Elmar Bittner ◽  
Maria-Paola Lombardo ◽  
Harald Markum ◽  
Rainer Pullirsch
Keyword(s):  
Dirac Operator ◽  
Matrix Models ◽  
Chemical Potential ◽  
Density Profiles ◽  
Operator Eigenvalues

scholarly journals Overlap Dirac operator, eigenvalues and random matrix theory

2000 ◽  
Vol 83-84 ◽  
pp. 446-448
Author(s):  
Robert G. Edwards ◽  
Urs M. Heller ◽  
Joe Kiskis ◽  
Rajamani Narayanan
Keyword(s):  
Dirac Operator ◽  
Random Matrix Theory ◽  
Random Matrix ◽  
Matrix Theory ◽  
Operator Eigenvalues

scholarly journals Extended supersymmetries and the Dirac operator

2005 ◽  
Vol 315 (2) ◽  
pp. 467-487 ◽  
Author(s):  
A. Kirchberg ◽  
J.D. Länge ◽  
A. Wipf
Keyword(s):  
Dirac Operator

scholarly journals Eigenvalue bounds for non-selfadjoint Dirac operators

2021 ◽  
Author(s):  
Piero D’Ancona ◽  
Luca Fanelli ◽  
Nico Michele Schiavone
Keyword(s):  
Dirac Operator ◽  
Discrete Spectrum ◽  
Complex Plane ◽  
Dirac Operators ◽  
Resolvent Estimates ◽  
Eigenvalue Bounds ◽  
Mixed Norms ◽  
Massless Case ◽  
Abstract Version ◽  
Embedded Eigenvalues

AbstractWe prove that the eigenvalues of the n-dimensional massive Dirac operator $${\mathscr {D}}_0 + V$$ D 0 + V , $$n\ge 2$$ n ≥ 2 , perturbed by a potential V, possibly non-Hermitian, are contained in the union of two disjoint disks of the complex plane, provided V is sufficiently small with respect to the mixed norms $$L^1_{x_j} L^\infty _{{\widehat{x}}_j}$$ L x j 1 L x ^ j ∞ , for $$j\in \{1,\dots ,n\}$$ j ∈ { 1 , ⋯ , n } . In the massless case, we prove instead that the discrete spectrum is empty under the same smallness assumption on V, and in particular the spectrum coincides with the spectrum of the unperturbed operator: $$\sigma ({\mathscr {D}}_0+V)=\sigma ({\mathscr {D}}_0)={\mathbb {R}}$$ σ ( D 0 + V ) = σ ( D 0 ) = R . The main tools used are an abstract version of the Birman–Schwinger principle, which allows in particular to control embedded eigenvalues, and suitable resolvent estimates for the Schrödinger operator.

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