Two-Dimensional Dirac Operators with Interactions on Unbounded Smooth Curves

2021 ◽  
Vol 28 (4) ◽  
pp. 524-542
Author(s):  
V. Rabinovich
Keyword(s):  
Dirac Operators ◽  
Two Dimensional ◽  
Smooth Curves

scholarly journals On the Gauss-Bonnet for the quasi-Dirac operators on the sphere

2017 ◽  
Vol 50 (1) ◽  
pp. 66-71
Author(s):  
Andrzej Sitarz
Keyword(s):  
Scalar Curvature ◽  
Dirac Operators ◽  
Two Dimensional ◽  
Spectral Triples ◽  
Bonnet Theorem

Abstract We investigate examples of Gauss-Bonnet theorem and the scalar curvature for the two-dimensional commutative sphere with quasi-spectral triples obtained by modifying the order-one condition.

Creeping modes in a shadow

1968 ◽  
Vol 64 (1) ◽  
pp. 171-192 ◽  
Author(s):  
F. Ursell
Keyword(s):  
Asymptotic Series ◽  
Shadow Region ◽  
Two Dimensional ◽  
Dimensional Theory ◽  
Smooth Curves ◽  
Original Series ◽  
Mode Expansion ◽  
In Series ◽  
Watson Transformation ◽  
Residue Series

AbstractIn the two-dimensional theory of diffraction by smooth curves there are certain canonical problems that can be solved explicitly in series form. The series converge slowly at short wavelengths but they can be transformed by Watson's transformation into another form (the residue series or creeping-mode expansion) which has been much used in shadow regions. It is found that throughout the shadow region the first few terms of the residue series are exponentially small and decrease rapidly, and these have often been used as an estimate of the wave potential without further justification. Leppington's recent work on the shadow of an ellipse has shown, however, that in part of the shadow some of the later terms of the residue series are exponentially large. In other words, the complete residue series in part of the shadow is even more slowly convergent than the original series.In the present paper the Watson transformation is re-examined in the light of this result. The original series is expressed as the sum of a finite number of terms of the residue series and of a remainder. It is shown that throughout the shadow the remainder is at short wavelengths asymptotically of smaller order than the last term retained in the finite residue series. It follows that the residue series (which is a convergent infinite series) is also an asymptotic series, and this fact is sufficient to justify most of the usual applications. The proof is given in detail for the circle and in outline for the ellipse; it makes use of the theory of conformal mapping.

scholarly journals Two-dimensional Dirac operators with singular interactions supported on closed curves

2020 ◽  
Vol 279 (8) ◽  
pp. 108700
Author(s):  
Jussi Behrndt ◽  
Markus Holzmann ◽  
Thomas Ourmières-Bonafos ◽  
Konstantin Pankrashkin
Keyword(s):  
Dirac Operators ◽  
Two Dimensional ◽  
Closed Curves ◽  
Singular Interactions

scholarly journals Self-Adjointness of Two-Dimensional Dirac Operators on Domains

2017 ◽  
Vol 18 (4) ◽  
pp. 1371-1383 ◽  
Author(s):  
Rafael D. Benguria ◽  
Søren Fournais ◽  
Edgardo Stockmeyer ◽  
Hanne Van Den Bosch
Keyword(s):  
Dirac Operators ◽  
Two Dimensional
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