122 research outputs found
Pseudo-Hermitian Hamiltonians, indefinite inner product spaces and their symmetries
We extend the definition of generalized parity , charge-conjugation
and time-reversal operators to nondiagonalizable pseudo-Hermitian
Hamiltonians, and we use these generalized operators to describe the full set
of symmetries of a pseudo-Hermitian Hamiltonian according to a fourfold
classification. In particular we show that and are the generators of
the antiunitary symmetries; moreover, a necessary and sufficient condition is
provided for a pseudo-Hermitian Hamiltonian to admit a -reflecting
symmetry which generates the -pseudounitary and the -pseudoantiunitary
symmetries. Finally, a physical example is considered and some hints on the
-unitary evolution of a physical system are also given.Comment: 20 page
Impact assessment of the options for surface preparation of glass ionomer cement on the bond strength to the composite material in a series of experiments
Laminate technique, or the so-called sandwich technique restoration of posterior group of teeth involves the use of glass ionomer cement and composite material in sequence. The relatively weak mechanical bond between glass ionomer cement and composite at the end of time could lead to the disruption of adhesion. With the advent of new materials, adhesive systems, we believe it is necessary to review the classical technique of the combined use of glass ionomer cement and composite materials. This article is aimed to evaluate the adhesion force between glass ionomer cement and composite material using different adhesive systems and curing techniques.Двухслойная техника, или так называемая сэндвич-техника восстановления боковой группы зубов, предусматривает использование стеклоиономерного цемента и композитного материала в определенной последовательности. Относительно слабая механическая связь между стеклоиономерным цементом и композитом по истечении времени может приводить к нарушению адгезии. С появлением новых материалов, а также адгезивных систем мы считаем необходимым пересмотреть классическую технику комбинированного использования стеклоиономерного цемента и композитных материалов. Данное исследование посвящено оценке силы сцепления между стеклоиономерным цементом и композитным материалом, с использованием различных адгезивных систем и техник полимеризации
-self-adjoint operators with -symmetries: extension theory approach
A well known tool in conventional (von Neumann) quantum mechanics is the
self-adjoint extension technique for symmetric operators. It is used, e.g., for
the construction of Dirac-Hermitian Hamiltonians with point-interaction
potentials. Here we reshape this technique to allow for the construction of
pseudo-Hermitian (-self-adjoint) Hamiltonians with complex
point-interactions. We demonstrate that the resulting Hamiltonians are
bijectively related with so called hypermaximal neutral subspaces of the defect
Krein space of the symmetric operator. This symmetric operator is allowed to
have arbitrary but equal deficiency indices . General properties of the
$\cC$ operators for these Hamiltonians are derived. A detailed study of
$\cC$-operator parametrizations and Krein type resolvent formulas is provided
for $J$-self-adjoint extensions of symmetric operators with deficiency indices
. The technique is exemplified on 1D pseudo-Hermitian Schr\"odinger and
Dirac Hamiltonians with complex point-interaction potentials
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Kinetic theory of plasma adiabatic major radius compression in tokamaks
A kinetic approach is developed to understand the individual charged particle behavior as well as plasma macro parameters (temperature, density, etc.) during the adiabatic R-compression in a tokamak. The perpendicular electric field from Ohm`s law at zero resistivity E = {minus}v{sub E} x B/c is made use of to obtain the equation for particle velocity evolution in order to describe the particle motion during the R-compression. Expressions for both passing and trapped particle energy and pitch angle change are obtained for a plasma with high aspect ratio and circular magnetic surfaces. The particle behavior near the trapped passing boundary during the compression is also studied to understand the shift induced loss of alpha particles produced by D-T fusion reactions in Tokamak Fusion Test Reactor experiments. Qualitative agreement is obtained with the experiments. Solving the drift kinetic equation in the collisional case, i.e., when the collisional frequency {nu}{sub coll} of given species exceeds the inverse compression time {tau}{sub compr}{sup {minus}1}, the authors obtain that the temperature and the density evolution is reduced to the MHD results T {approximately} R{sup {minus}4/3} and n {approximately} R{sup {minus}2}, respectively. In the opposite case, {nu}{sub coll} {much_lt} {tau}{sub compr}{sup {minus}1}, the longitudinal component of the temperature evolve like R(superscript)-2(end superscript) and perpendicular components of the temperature evolve like T{sub {parallel}} {approximately} R{sup {minus}2} and T{sub {perpendicular}} {approximately} R{sup {minus}1}. The effect of toroidicity is negligible in both cases
Schroedinger equation for joint bidirectional motion in time
The conventional, time-dependent Schroedinger equation describes only
unidirectional time evolution of the state of a physical system, i.e., forward
or, less commonly, backward. This paper proposes a generalized quantum dynamics
for the description of joint, and interactive, forward and backward time
evolution within a physical system. [...] Three applications are studied: (1) a
formal theory of collisions in terms of perturbation theory; (2) a
relativistically invariant quantum field theory for a system that kinematically
comprises the direct sum of two quantized real scalar fields, such that one
field evolves forward and the other backward in time, and such that there is
dynamical coupling between the subfields; (3) an argument that in the latter
field theory, the dynamics predicts that in a range of values of the coupling
constants, the expectation value of the vacuum energy of the universe is forced
to be zero to high accuracy. [...]Comment: 30 pages, no figures. Related material is in quant-ph/0404012.
Differs from published version by a few added remarks on the possibility of a
large-scale-average negative energy density in spac
Krein-Space Formulation of PT-Symmetry, CPT-Inner Products, and Pseudo-Hermiticity
Emphasizing the physical constraints on the formulation of a quantum theory
based on the standard measurement axiom and the Schroedinger equation, we
comment on some conceptual issues arising in the formulation of PT-symmetric
quantum mechanics. In particular, we elaborate on the requirements of the
boundedness of the metric operator and the diagonalizability of the
Hamiltonian. We also provide an accessible account of a Krein-space derivation
of the CPT-inner product that was widely known to mathematicians since 1950's.
We show how this derivation is linked with the pseudo-Hermitian formulation of
PT-symmetric quantum mechanics.Comment: published version, 17 page
PT symmetry, Cartan decompositions, Lie triple systems and Krein space related Clifford algebras
Gauged PT quantum mechanics (PTQM) and corresponding Krein space setups are
studied. For models with constant non-Abelian gauge potentials and extended
parity inversions compact and noncompact Lie group components are analyzed via
Cartan decompositions. A Lie triple structure is found and an interpretation as
PT-symmetrically generalized Jaynes-Cummings model is possible with close
relation to recently studied cavity QED setups with transmon states in
multilevel artificial atoms. For models with Abelian gauge potentials a hidden
Clifford algebra structure is found and used to obtain the fundamental symmetry
of Krein space related J-selfadjoint extensions for PTQM setups with
ultra-localized potentials.Comment: 11 page
Statistical Origin of Pseudo-Hermitian Supersymmetry and Pseudo-Hermitian Fermions
We show that the metric operator for a pseudo-supersymmetric Hamiltonian that
has at least one negative real eigenvalue is necessarily indefinite. We
introduce pseudo-Hermitian fermion (phermion) and abnormal phermion algebras
and provide a pair of basic realizations of the algebra of N=2
pseudo-supersymmetric quantum mechanics in which pseudo-supersymmetry is
identified with either a boson-phermion or a boson-abnormal-phermion exchange
symmetry. We further establish the physical equivalence (non-equivalence) of
phermions (abnormal phermions) with ordinary fermions, describe the underlying
Lie algebras, and study multi-particle systems of abnormal phermions. The
latter provides a certain bosonization of multi-fermion systems.Comment: 20 pages, to appear in J.Phys.
Solvability and PT-symmetry in a double-well model with point interactions
We show that and how point interactions offer one of the most suitable guides
towards a quantitative analysis of properties of certain specific non-Hermitian
(usually called PT-symmetric) quantum-mechanical systems. A double-well model
is chosen, an easy solvability of which clarifies the mechanisms of the
unavoided level crossing and of the spontaneous PT-symmetry breaking. The
latter phenomenon takes place at a certain natural boundary of the domain of
the "acceptable" parameters of the model. Within this domain the model mediates
a nice and compact explicit illustration of the not entirely standard
probabilistic interpretation of the physical bound states in the very recently
developed (so called PT symmetric or, in an alternative terminology,
pseudo-Hermitian) new, fairly exciting and very quickly developing branch of
Quantum Mechanics.Comment: 24 p., written for the special journal issue "Singular Interactions
in Quantum Mechanics: Solvable Models". Will be also presented to the int.
conference "Pseudo-Hermitian Hamiltonians in Quantum Physics III" (Instanbul,
Koc University, June 20 - 22, 2005)
http://home.ku.edu.tr/~amostafazadeh/workshop/workshop.ht
Relativistic supersymmetric quantum mechanics based on Klein-Gordon equation
Witten's non-relativistic formalism of supersymmetric quantum mechanics was
based on a factorization and partnership between Schroedinger equations. We
show how it accommodates a transition to the partnership between relativistic
Klein-Gordon equations. In such a class of models the requirement of
supersymmetry is shown to lead to a certain "exceptional-point" instability of
ground states.Comment: 20 page
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