scholarly journals Publisher’s Note: “Semiclassical WKB problem for the non-self-adjoint Dirac operator with analytic potential” [J. Math. Phys. 61, 011510 (2020)]

2021 ◽  
Vol 62 (1) ◽  
pp. 019901
Author(s):  
Setsuro Fujiié ◽  
Spyridon Kamvissis
Keyword(s):  
Dirac Operator ◽  
Analytic Potential ◽  
Math Phys

SCHRÖDINGER–LICHNEROWICZ LIKE FORMULA ON KÄHLER–NORDEN MANIFOLDS

2012 ◽  
Vol 09 (01) ◽  
pp. 1250010 ◽  
Author(s):  
NEDİM DEĞİRMENCI ◽  
ŞENAY KARAPAZAR
Keyword(s):  
Dirac Operator ◽  
Nonlinear Math ◽  
Math Phys

A new kind of spinors and Dirac operator are introduced on Kähler–Norden manifolds in [Spinors on Kähler–Norden manifolds, J. Nonlinear Math. Phys.17(1) (2010) 27–34]. In this work the square D2 of the Dirac operator D is computed and a kind of Schrödinger–Lichnerowicz formula is obtained.

scholarly journals Complex Eigenvalue Splitting for the Dirac Operator

2021 ◽  
Author(s):  
Koki Hirota ◽  
Jens Wittsten
Keyword(s):  
Eigenvalue Problem ◽  
Dirac Operator ◽  
Real Line ◽  
Imaginary Axis ◽  
Energy Levels ◽  
Reference Points ◽  
Complex Eigenvalue ◽  
Bump Function ◽  
The Real ◽  
Analytic Potential

AbstractWe analyze the eigenvalue problem for the semiclassical Dirac (or Zakharov–Shabat) operator on the real line with general analytic potential. We provide Bohr–Sommerfeld quantization conditions near energy levels where the potential exhibits the characteristics of a single or double bump function. From these conditions we infer that near energy levels where the potential (or rather its square) looks like a single bump function, all eigenvalues are purely imaginary. For even or odd potentials we infer that near energy levels where the square of the potential looks like a double bump function, eigenvalues split in pairs exponentially close to reference points on the imaginary axis. For even potentials this splitting is vertical and for odd potentials it is horizontal, meaning that all such eigenvalues are purely imaginary when the potential is even, and no such eigenvalue is purely imaginary when the potential is odd.

scholarly journals The set of points with Markovian symbolic dynamics for non-uniformly hyperbolic diffeomorphisms

2020 ◽  
pp. 1-26
Author(s):  
SNIR BEN OVADIA
Keyword(s):  
Symbolic Dynamics ◽  
Full Measure ◽  
Probability Measures ◽  
Positive Entropy ◽  
Surface Diffeomorphisms ◽  
Srb Measures ◽  
Hyperbolic Diffeomorphisms ◽  
Set Of Points ◽  
Math Phys ◽  
Homoclinic Classes

Abstract The papers [O. M. Sarig. Symbolic dynamics for surface diffeomorphisms with positive entropy. J. Amer. Math. Soc.26(2) (2013), 341–426] and [S. Ben Ovadia. Symbolic dynamics for non-uniformly hyperbolic diffeomorphisms of compact smooth manifolds. J. Mod. Dyn.13 (2018), 43–113] constructed symbolic dynamics for the restriction of $C^r$ diffeomorphisms to a set $M'$ with full measure for all sufficiently hyperbolic ergodic invariant probability measures, but the set $M'$ was not identified there. We improve the construction in a way that enables $M'$ to be identified explicitly. One application is the coding of infinite conservative measures on the homoclinic classes of Rodriguez-Hertz et al. [Uniqueness of SRB measures for transitive diffeomorphisms on surfaces. Comm. Math. Phys.306(1) (2011), 35–49].

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 New type of degenerate Daehee polynomials of the second kind

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Sunil Kumar Sharma ◽  
Waseem A. Khan ◽  
Serkan Araci ◽  
Sameh S. Ahmed
Keyword(s):  
Generating Function ◽  
Special Class ◽  
Stirling Numbers ◽  
Bernoulli Numbers ◽  
Higher Order ◽  
Bernoulli Numbers And Polynomials ◽  
New Type ◽  
Order Degenerate ◽  
Math Phys

Abstract Recently, Kim and Kim (Russ. J. Math. Phys. 27(2):227–235, 2020) have studied new type degenerate Bernoulli numbers and polynomials by making use of degenerate logarithm. Motivated by (Kim and Kim in Russ. J. Math. Phys. 27(2):227–235, 2020), we consider a special class of polynomials, which we call a new type of degenerate Daehee numbers and polynomials of the second kind. By using their generating function, we derive some new relations including the degenerate Stirling numbers of the first and second kinds. Moreover, we introduce a new type of higher-order degenerate Daehee polynomials of the second kind. We also derive some new identities and properties of this type of polynomials.

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