425 research outputs found
Canonical, squeezed and fermionic coherent states in a right quaternionic Hilbert space with a left multiplication on it
Using a left multiplication defined on a right quaternionic Hilbert space, we
shall demonstrate that various classes of coherent states such as the canonical
coherent states, pure squeezed states, fermionic coherent states can be defined
with all the desired properties on a right quaternionic Hilbert space. Further,
we shall also demonstrate squeezed states can be defined on the same Hilbert
space, but the noncommutativity of quaternions prevents us in getting the
desired results.Comment: Conference paper. arXiv admin note: text overlap with
arXiv:1704.02946; substantial text overlap with arXiv:1706.0068
Boundary interpolation for slice hyperholomorphic Schur functions
A boundary Nevanlinna-Pick interpolation problem is posed and solved in the
quaternionic setting. Given nonnegative real numbers , quaternions all of modulus , so that the
-spheres determined by each point do not intersect and for , and quaternions , we wish to find a slice
hyperholomorphic Schur function so that and
Our arguments relies on the theory of slice hyperholomorphic
functions and reproducing kernel Hilbert spaces
First Principles Modeling of Topological Insulators: Structural Optimization and Exchange Correlation Functionals
Topological insulators (TIs) are materials that are insulating in the bulk
but have zero band gap surface states with linear dispersion and are protected
by time reversal symmetry. These unique characteristics could pave the way for
many promising applications that include spintronic devices and quantum
computations. It is important to understand and theoretically describe TIs as
accurately as possible in order to predict properties. Quantum mechanical
approaches, specifically first principles density functional theory (DFT) based
methods, have been used extensively to model electronic properties of TIs.
Here, we provide a comprehensive assessment of a variety of DFT formalisms and
how these capture the electronic structure of TIs. We concentrate on
BiSe and BiTe as examples of prototypical TI materials. We find
that the generalized gradient (GGA) and kinetic density functional (metaGGA)
produce displacements increasing the thickness of the TI slab, whereas we see
an opposite behavior in DFT computations using LDA. Accounting for van der
Waals (vdW) interactions overcomes the apparent over-relaxations and retraces
the atomic positions towards the bulk. Based on an intensive computational
study, we show that GGA with vdW treatment is the most appropriate method for
structural optimization. Electronic structures derived from GGA or metaGGA
employing experimental lattice parameters are also acceptable. In this regard,
we express a slight preference for metaGGA in terms of accuracy, but an overall
preference for GGA due to compensatory improvements in computability in
capturing TI behavior
Inducing Quantum Phase Transitions in Non-Topological Insulators Via Atomic Control of Sub-Structural Elements
Topological insulators (TIs) are an important family of quantum materials
that exhibit a Dirac point (DP) in the surface band structure but have a finite
band gap in bulk. A large degree of spin-orbit interaction and low bandgap is a
prerequisite for stabilizing DPs on selective atomically flat cleavage planes.
Tuning of the DP in these materials has been suggested via modifications to the
atomic structure of the entire system. Using the example of AsTe and
ZnTe, which are not TIs, we show that a quantum phase transition can be
induced in atomically flat and stepped surfaces, for AsTe and ZrTe,
respectively. This is achieved by establishing a framework for controlling
electronic properties that is focused on local perturbations at key locations
that we call sub-structural elements (SSEs). We exemplify this framework
through a novel method of isovalent sublayer anion doping and biaxial strain.Comment: 13 pages, 3 figures, 1 tabl
The importance of protein expression sod2 in response to oxidative stress for different cancer cells
de Branges-Rovnyak spaces: basics and theory
For a contractive analytic operator-valued function on the unit disk
, de Branges and Rovnyak associate a Hilbert space of analytic
functions and related extension space
consisting of pairs of analytic functions on the unit disk . This
survey describes three equivalent formulations (the original geometric de
Branges-Rovnyak definition, the Toeplitz operator characterization, and the
characterization as a reproducing kernel Hilbert space) of the de
Branges-Rovnyak space , as well as its role as the underlying
Hilbert space for the modeling of completely non-isometric Hilbert-space
contraction operators. Also examined is the extension of these ideas to handle
the modeling of the more general class of completely nonunitary contraction
operators, where the more general two-component de Branges-Rovnyak model space
and associated overlapping spaces play key roles. Connections
with other function theory problems and applications are also discussed. More
recent applications to a variety of subsequent applications are given in a
companion survey article
Applications of Hilbert Module Approach to Multivariable Operator Theory
A commuting -tuple of bounded linear operators on a
Hilbert space \clh associate a Hilbert module over
in the following sense: where and
. A companion survey provides an introduction to the theory
of Hilbert modules and some (Hilbert) module point of view to multivariable
operator theory. The purpose of this survey is to emphasize algebraic and
geometric aspects of Hilbert module approach to operator theory and to survey
several applications of the theory of Hilbert modules in multivariable operator
theory. The topics which are studied include: generalized canonical models and
Cowen-Douglas class, dilations and factorization of reproducing kernel Hilbert
spaces, a class of simple submodules and quotient modules of the Hardy modules
over polydisc, commutant lifting theorem, similarity and free Hilbert modules,
left invertible multipliers, inner resolutions, essentially normal Hilbert
modules, localizations of free resolutions and rigidity phenomenon.
This article is a companion paper to "An Introduction to Hilbert Module
Approach to Multivariable Operator Theory".Comment: 46 pages. This is a companion paper to arXiv:1308.6103. To appear in
Handbook of Operator Theory, Springe
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