Dense point spectrum for the one-dimensional Dirac operator with an electrostatic potential

1996 ◽  
Vol 126 (5) ◽  
pp. 1087-1096 ◽  
Author(s):  
Karl Michael Schmidt
Keyword(s):  
Dirac Operator ◽  
Essential Spectrum ◽  
Electrostatic Potential ◽  
Simple Proof ◽  
Point Spectrum ◽  
Electrostatic Potentials ◽  
One Dimensional ◽  
Decay Behaviour ◽  
Dense Point ◽  
The One

For the one-dimensional Dirac operator, examples of electrostatic potentials with decay behaviour arbitrarily close to Coulomb decay are constructed for which the operator has a prescribed set of eigenvalues dense in the whole or part of its essential spectrum. A simple proof that the essential spectrum of one-dimensional Dirac operators with electrostatic potentials is never empty is given in the appendix.

Properties of root vector functions for the one-dimensional Dirac operator

2010 ◽  
Vol 82 (1) ◽  
pp. 617-620 ◽  
Author(s):  
V. M. Kurbanov ◽  
A. I. Ismailova
Keyword(s):  
Dirac Operator ◽  
Root Vector ◽  
One Dimensional ◽  
The One

scholarly journals AN O(3) GLOBAL ANOMALY IN 0+1 DIMENSION

1994 ◽  
Vol 09 (07) ◽  
pp. 623-630
Author(s):  
MINOS AXENIDES ◽  
HOLGER BECH NIELSEN ◽  
ANDREI JOHANSEN
Keyword(s):  
External Field ◽  
Dirac Operator ◽  
Degrees Of Freedom ◽  
Eigenvalue Spectrum ◽  
Level Crossing ◽  
One Dimensional ◽  
Exactly Solvable ◽  
Solvable Quantum ◽  
Global Anomaly ◽  
The One

We present a simple exactly solvable quantum mechanical example of the global anomaly in an O(3) model with an odd number of fermionic triplets coupled to a gauge field on a circle. Because the fundamental group is non-trivial, π1(O(3))=Z2, fermionic level crossing—circling occurs in the eigenvalue spectrum of the one-dimensional Dirac operator under continuous external field transformations. They are shown to be related to the presence of an odd number of normalizable zero modes in the spectrum of an appropriate two-dimensional Dirac operator. We argue that fermionic degrees of freedom in the presence of an infinitely large external field violate perturbative decoupling.

ON THE PHASE CONSTRAINT OF THE MAGNETOTELLURIC IMPEDANCE

Geophysics ◽  
1975 ◽  
Vol 40 (2) ◽  
pp. 325-330 ◽  
Author(s):  
D. Loewenthal
Keyword(s):  
Simple Proof ◽  
Phase Constraint ◽  
Adjoint Model ◽  
Polynomial Representation ◽  
Rational Representation ◽  
One Dimensional ◽  
Numerical Example ◽  
Rational Polynomial ◽  
The One

A simple proof that the phase of the one‐ dimensional magnetotelluric modified impedance lies between −π/4 and π/4 is given. The proof is based upon a rational polynomial representation of the impedance. The formalism from which the rational representation is obtained is outlined. An adjoint model is defined and it is shown to be pertinent for the proof. A numerical example is given.

On: “On the Phase Constraint of the Magnetotelluric Impedance,” by D. Loewenthal (GEOPHYSICS, April 1975, p. 325–330).

Geophysics ◽  
1975 ◽  
Vol 40 (6) ◽  
pp. 1076-1076
Author(s):  
Donald H. Eckhard
Keyword(s):  
Simple Proof ◽  
Phase Constraint ◽  
One Dimensional ◽  
The One

In his paper, Loewenthal presents what he calls a “simple proof” that the phase of the one‐dimensional magnetotelluric modified impedance lies between −π/4 and π/4. A much simpler proof exists (Eckhardt, 1968). My proof is buried as a rather minor feature of an obscure (alas) paper, and some of its sign conventions differ from standard, so I believe it appropriate to restate the proof here.

On the oscillation of eigenvector functions of the one-dimensional Dirac operator

2016 ◽  
Vol 94 (1) ◽  
pp. 401-405
Author(s):  
Z. S. Aliev ◽  
Kh. Sh. Rzaeva
Keyword(s):  
Dirac Operator ◽  
One Dimensional ◽  
The One

scholarly journals Spectral and localization properties for the one-dimensional Bernoulli discrete Dirac operator

2005 ◽  
Vol 46 (7) ◽  
pp. 072105 ◽  
Author(s):  
César R. de Oliveira ◽  
Roberto A. Prado
Keyword(s):  
Dirac Operator ◽  
One Dimensional ◽  
The One

scholarly journals The eigenvalue problem of one-dimensional Dirac operator

2020 ◽  
Vol 139 (12) ◽  
Author(s):  
Jacek Karwowski ◽  
Artur Ishkhanyan ◽  
Andrzej Poszwa
Keyword(s):  
Eigenvalue Problem ◽  
Dirac Operator ◽  
One Dimensional ◽  
Mutual Relations ◽  
The One ◽  
Pseudo Scalar

AbstractThe properties of the eigenvalue problem of the one-dimensional Dirac operator are discussed in terms of the mutual relations between vector, scalar and pseudo-scalar contributions to the potential. Relations to the exact solubility are analyzed.

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