scholarly journals ${\mathcal{CPT}}$-CONSERVING HAMILTONIANS AND THEIR NONLINEAR SUPERSYMMETRIZATION USING DIFFERENTIAL CHARGE-OPERATORS ${\mathcal C}$

2005 ◽  
Vol 20 (30) ◽  
pp. 7107-7128 ◽  
Author(s):  
BIJAN BAGCHI ◽  
A. BANERJEE ◽  
EMANUELA CALICETI ◽  
FRANCESCO CANNATA ◽  
HENDRIK B. GEYER ◽  
...  
Keyword(s):  
Quantum Mechanics ◽  
Differential Operator ◽  
Higher Order ◽  
Real Spectrum ◽  
New Class ◽  
Operator Form ◽  
Supersymmetric Version ◽  
Order Case ◽  
Recent Developments ◽  
Symmetric Quantum

A brief overview is given of recent developments and fresh ideas at the intersection of [Formula: see text]- and/or [Formula: see text]-symmetric quantum mechanics with supersymmetric quantum mechanics (SUSY QM). Within the framework of the resulting supersymmetric version of [Formula: see text]-symmetric quantum mechanics we study the consequences of the assumption that the "charge" operator [Formula: see text] is represented in a differential-operator form of the second or higher order. Besides the freedom allowed by the Hermiticity constraint for the operator [Formula: see text], encouraging results are obtained in the second-order case. In particular, the integrability of intertwining relations proves to match the closure of our nonlinear (viz., polynomial) SUSY algebra. In a particular illustration, our form of [Formula: see text]-symmetric SUSY QM leads to a new class of non-Hermitian polynomial oscillators with real spectrum which turn out to be [Formula: see text]-asymmetric.

scholarly journals EIGENVALUES AND EIGENFUNCTIONS OF WOODS–SAXON POTENTIAL IN PT-SYMMETRIC QUANTUM MECHANICS

2006 ◽  
Vol 21 (27) ◽  
pp. 2087-2097 ◽  
Author(s):  
AYŞE BERKDEMIR ◽  
CÜNEYT BERKDEMIR ◽  
RAMAZAN SEVER
Keyword(s):  
Quantum Mechanics ◽  
Real Spectrum ◽  
Saxon Potential ◽  
Eigenvalues And Eigenfunctions ◽  
Discrete Energy ◽  
Energy Eigenvalues ◽  
Symmetric Quantum ◽  
Symmetric Version ◽  
Uvarov Method ◽  
S States

Using the Nikiforov–Uvarov method which is based on solving the second-order differential equations, we firstly analyzed the energy spectra and eigenfunctions of the Woods–Saxon potential. In the framework of the PT-symmetric quantum mechanics, we secondly solved the time-independent Schrödinger equation for the PT and non-PT-symmetric version of the potential. It is shown that the discrete energy eigenvalues of the non-PT-symmetric potential consist of the real and imaginary parts, but the PT-symmetric one has a real spectrum. Results are obtained for s-states only.

scholarly journals RT-Symmetric Laplace Operators on Star Graphs: Real Spectrum and Self-Adjointness

2015 ◽  
Vol 2015 ◽  
pp. 1-9 ◽  
Author(s):  
Maria Astudillo ◽  
Pavel Kurasov ◽  
Muhammad Usman
Keyword(s):  
Quantum Mechanics ◽  
Spectral Properties ◽  
Block Structure ◽  
Circulant Matrices ◽  
Real Spectrum ◽  
Star Graph ◽  
Quantum Graphs ◽  
Star Graphs ◽  
Rotationally Symmetric ◽  
Symmetric Quantum

How ideas ofPT-symmetric quantum mechanics can be applied to quantum graphs is analyzed, in particular to the star graph. The class of rotationally symmetric vertex conditions is analyzed. It is shown that all such conditions can effectively be described by circulant matrices: real in the case of odd number of edges and complex having particular block structure in the even case. Spectral properties of the corresponding operators are discussed.

scholarly journals New Advancements in AdS/CFT in Lower Dimensions

Universe ◽  
2021 ◽  
Vol 7 (7) ◽  
pp. 250
Author(s):  
Yolanda Lozano ◽  
Anayeli Ramirez
Keyword(s):  
Quantum Mechanics ◽  
Light Cone ◽  
Field Theories ◽  
New Class ◽  
Recent Developments ◽  
M Theory

We review recent developments in the study of the AdS/CFT correspondence in lower dimensions. We start by summarising the classification of AdS3×S2 solutions in massive type IIA supergravity with (0, 4) supersymmetries and the construction of their 2D dual quiver CFTs. These theories are the seed for further developments that we review next. First, we construct a new class of AdS3 solutions in M-theory that describe M-strings in M5-brane intersections. Second, we generate a new class of AdS2×S3 solutions in massive IIA with four supercharges that we interpret as describing backreacted baryon vertices within the 5D N=1 QFT living in D4-D8 branes. Third, we construct two classes of AdS2 solutions in Type IIB. The first are dual to discrete light-cone quantised quantum mechanics living in null cylinders. The second class is interpreted as dual to backreacted baryon vertices within 4D N=2 QFT living in D3-D7 branes. Explicit dual quiver field theories are given for all classes of solutions. These are used to compute the central charges of the CFTs that are shown to agree with the holographic expressions.

NON-HERMITIAN QUANTUM FIELD THEORY

2005 ◽  
Vol 20 (19) ◽  
pp. 4646-4652 ◽  
Author(s):  
CARL. M. BENDER
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Quantum Mechanics ◽  
Degrees Of Freedom ◽  
Real Spectrum ◽  
Quantum Field ◽  
Unitary Theory ◽  
Symmetric Quantum ◽  
Quantum Mechanical Systems ◽  
Bounded Below

In my talk at the Seventh QCD Workshop held in Villefranche in January 2003 I showed that a non-Hermitian Hamiltonian H possessing an unbroken [Formula: see text] symmetry (i) has a real spectrum that is bounded below, and (ii) defines a unitary theory of quantum mechanics with positive norm. The proof of unitarity requires a linear operator [Formula: see text], which was originally defined as a sum over the eigenfunctions of H. However, using this definition to calculate [Formula: see text] is cumbersome in quantum mechanics and impossible in quantum field theory. I describe here an alternative method for calculating [Formula: see text] directly in terms of the operator dynamical variables of the quantum theory. This new method is general and applies to a variety of quantum mechanical systems having several degrees of freedom. More importantly, this method gives the [Formula: see text] operator in quantum field theory. The [Formula: see text] operator is a new time-independent observable in [Formula: see text]-symmetric quantum field theory.

scholarly journals A New Class of Higher-Order Hypergeometric Bernoulli Polynomials Associated with Lagrange–Hermite Polynomials

Symmetry ◽  
2021 ◽  
Vol 13 (4) ◽  
pp. 648
Author(s):  
Ghulam Muhiuddin ◽  
Waseem Ahmad Khan ◽  
Ugur Duran ◽  
Deena Al-Kadi
Keyword(s):  
Generating Function ◽  
Functional Equations ◽  
Laguerre Polynomials ◽  
Hermite Polynomials ◽  
Bernoulli Polynomials ◽  
Higher Order ◽  
New Class

The purpose of this paper is to construct a unified generating function involving the families of the higher-order hypergeometric Bernoulli polynomials and Lagrange–Hermite polynomials. Using the generating function and their functional equations, we investigate some properties of these polynomials. Moreover, we derive several connected formulas and relations including the Miller–Lee polynomials, the Laguerre polynomials, and the Lagrange Hermite–Miller–Lee polynomials.

scholarly journals Simpson type inequalities and applications

2021 ◽  
Author(s):  
Muhammad Uzair Awan ◽  
Muhammad Zakria Javed ◽  
Michael Th. Rassias ◽  
Muhammad Aslam Noor ◽  
Khalida Inayat Noor
Keyword(s):  
Quadrature Formula ◽  
Convex Functions ◽  
Integral Identity ◽  
Higher Order ◽  
Auxiliary Result ◽  
First Order ◽  
New Class ◽  
Differentiable Functions

AbstractA new generalized integral identity involving first order differentiable functions is obtained. Using this identity as an auxiliary result, we then obtain some new refinements of Simpson type inequalities using a new class called as strongly (s, m)-convex functions of higher order of $$\sigma >0$$ σ > 0 . We also discuss some interesting applications of the obtained results in the theory of means. In last we present applications of the obtained results in obtaining Simpson-like quadrature formula.

scholarly journals Difference formula defined by a new differential symmetric operator for a class of meromorphically multivalent functions

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Rabha W. Ibrahim ◽  
Ibtisam Aldawish
Keyword(s):  
Differential Operator ◽  
Boundary Value Problems ◽  
Unit Disk ◽  
Spectral Theory ◽  
Analytic Functions ◽  
Special Class ◽  
Symmetric Operator ◽  
New Class ◽  
Difference Formula ◽  
Symmetric Operators

AbstractSymmetric operators have benefited in different fields not only in mathematics but also in other sciences. They appeared in the studies of boundary value problems and spectral theory. In this note, we present a new symmetric differential operator associated with a special class of meromorphically multivalent functions in the punctured unit disk. This study explores some of its geometric properties. We consider a new class of analytic functions employing the suggested symmetric differential operator.

scholarly journals Interesting Examples of Violation of the Classical Equivalence Principle but Not of the Weak One

2018 ◽  
Vol 2018 ◽  
pp. 1-13
Author(s):  
Antonio Accioly ◽  
Wallace Herdy
Keyword(s):  
Wave Function ◽  
Quantum Mechanics ◽  
Gravitational Field ◽  
Experimental Test ◽  
Equivalence Principle ◽  
Free Fall ◽  
Higher Order ◽  
Tree Level ◽  
Quantum Particles ◽  
Bohr Atom

The equivalence principle (EP) and Schiff’s conjecture are discussed en passant, and the connection between the EP and quantum mechanics is then briefly analyzed. Two semiclassical violations of the classical equivalence principle (CEP) but not of the weak one (WEP), i.e., Greenberger gravitational Bohr atom and the tree-level scattering of different quantum particles by an external weak higher-order gravitational field, are thoroughly investigated afterwards. Next, two quantum examples of systems that agree with the WEP but not with the CEP, namely, COW experiment and free fall in a constant gravitational field of a massive object described by its wave-function Ψ, are discussed in detail. Keeping in mind that, among the four examples focused on in this work only COW experiment is based on an experimental test, some important details related to it are presented as well.

Properties of Classes of Random Graphs

1994 ◽  
Vol 3 (4) ◽  
pp. 435-454 ◽  
Author(s):  
Neal Brand ◽  
Steve Jackson
Keyword(s):  
Random Graphs ◽  
Higher Order ◽  
Order Property ◽  
First Order ◽  
New Class ◽  
Vertex Transitive ◽  
Vertex Transitive Graphs ◽  
Almost All ◽  
Transitive Graphs

In [11] it is shown that the theory of almost all graphs is first-order complete. Furthermore, in [3] a collection of first-order axioms are given from which any first-order property or its negation can be deduced. Here we show that almost all Steinhaus graphs satisfy the axioms of almost all graphs and conclude that a first-order property is true for almost all graphs if and only if it is true for almost all Steinhaus graphs. We also show that certain classes of subgraphs of vertex transitive graphs are first-order complete. Finally, we give a new class of higher-order axioms from which it follows that large subgraphs of specified type exist in almost all graphs.

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