Resolvent estimates and spectrum of the Dirac operator with periodic potential

1995 ◽  
Vol 103 (1) ◽  
pp. 349-365 ◽  
Author(s):  
L. I. Danilov
Keyword(s):  
Dirac Operator ◽  
Periodic Potential ◽  
Resolvent Estimates

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.

scholarly journals RESOLVENT ESTIMATES OF THE DIRAC OPERATOR

Analysis ◽  
1995 ◽  
Vol 15 (2) ◽  
pp. 123-150 ◽  
Author(s):  
Chris Pladdy ◽  
Yoshimi Saitō ◽  
Tomio Umeda
Keyword(s):  
Dirac Operator ◽  
Resolvent Estimates

Spectrum of the dirac operator in ? n with periodic potential

1990 ◽  
Vol 85 (1) ◽  
pp. 1039-1048 ◽  
Author(s):  
L. I. Danilov
Keyword(s):  
Dirac Operator ◽  
Periodic Potential

Study of potential oscillations during reaction of an aluminium single crystal with an aqueous KOH solution

1990 ◽  
Vol 55 (2) ◽  
pp. 345-353 ◽  
Author(s):  
Ivan Halaša ◽  
Milica Miadoková
Keyword(s):  
Aqueous Solutions ◽  
Single Crystal ◽  
Single Crystals ◽  
Periodic Potential ◽  
Optimum Conditions ◽  
Potential Oscillations ◽  
Dilute Aqueous Solutions ◽  
Experimental Findings ◽  
Kinetics Of

The authors investigated periodic potential changes measured on oriented sections of Al single crystals during spontaneous dissolution in dilute aqueous solutions of KOH, with the aim to find optimum conditions for the formation of potential oscillations. It was found that this phenomenon is related with the kinetics of the reaction investigated, whose rate also changed periodically. The mechanism of the oscillations is discussed in view of the experimental findings.

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
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