1,788 research outputs found
Introduction to PT-Symmetric Quantum Theory
In most introductory courses on quantum mechanics one is taught that the
Hamiltonian operator must be Hermitian in order that the energy levels be real
and that the theory be unitary (probability conserving). To express the
Hermiticity of a Hamiltonian, one writes , where the symbol
denotes the usual Dirac Hermitian conjugation; that is, transpose and
complex conjugate. In the past few years it has been recognized that the
requirement of Hermiticity, which is often stated as an axiom of quantum
mechanics, may be replaced by the less mathematical and more physical
requirement of space-time reflection symmetry (PT symmetry) without losing any
of the essential physical features of quantum mechanics. Theories defined by
non-Hermitian PT-symmetric Hamiltonians exhibit strange and unexpected
properties at the classical as well as at the quantum level. This paper
explains how the requirement of Hermiticity can be evaded and discusses the
properties of some non-Hermitian PT-symmetric quantum theories
Vacuum Stability of the wrong sign Scalar Field Theory
We apply the effective potential method to study the vacuum stability of the
bounded from above (unstable) quantum field potential. The
stability ( and the mass renormalization
( conditions force the effective
potential of this theory to be bounded from below (stable). Since bounded from
below potentials are always associated with localized wave functions, the
algorithm we use replaces the boundary condition applied to the wave functions
in the complex contour method by two stability conditions on the effective
potential obtained. To test the validity of our calculations, we show that our
variational predictions can reproduce exactly the results in the literature for
the -symmetric theory. We then extend the applications
of the algorithm to the unstudied stability problem of the bounded from above
scalar field theory where classical analysis prohibits the
existence of a stable spectrum. Concerning this, we calculated the effective
potential up to first order in the couplings in space-time dimensions. We
find that a Hermitian effective theory is instable while a non-Hermitian but
-symmetric effective theory characterized by a pure imaginary
vacuum condensate is stable (bounded from below) which is against the classical
predictions of the instability of the theory. We assert that the work presented
here represents the first calculations that advocates the stability of the
scalar potential.Comment: 21pages, 12 figures. In this version, we updated the text and added
some figure
Solvable model of quantum microcanonical states
Accepted versio
Complexified dynamical systems.
Accepted versio
Geometric aspects of space-time reflection symmetry in quantum mechanics
For nearly two decades, much research has been carried out on properties of physical systems described by Hamiltonians that are not Hermitian in the conventional sense, but are symmetric under space-time reflection; that is, they exhibit PT symmetry. Such Hamiltonians can be used to model the behavior of closed quantum systems, but they can also be replicated in open systems for which gain and loss are carefully balanced, and this has been implemented in laboratory experiments for a wide range of systems. Motivated by these ongoing research activities, we investigate here a particular theoretical aspect of the subject by unraveling the geometric structures of Hilbert spaces endowed with the parity and time-reversal operations, and analyze the characteristics ofPT -symmetric Hamiltonians. A canonical relation between aPT -symmetric operator and a Hermitian operator is established in a geometric setting. The quadratic form corresponding to the parity operator, in particular, gives rise to a natural partition of the Hilbert space into two halves corresponding to states having positive and negative PT norm. Positive definiteness of the norm can be restored by introducing a conjugation operator C ; this leads to a positive-definite inner product in terms of CPT conjugation
A possible method for non-Hermitian and non--symmetric Hamiltonian systems
A possible method to investigate non-Hermitian Hamiltonians is suggested
through finding a Hermitian operator and defining the annihilation and
creation operators to be -pseudo-Hermitian adjoint to each other. The
operator represents the -pseudo-Hermiticity of Hamiltonians.
As an example, a non-Hermitian and non--symmetric Hamiltonian with
imaginary linear coordinate and linear momentum terms is constructed and
analyzed in detail. The operator is found, based on which, a real
spectrum and a positive-definite inner product, together with the probability
explanation of wave functions, the orthogonality of eigenstates, and the
unitarity of time evolution, are obtained for the non-Hermitian and
non--symmetric Hamiltonian. Moreover, this Hamiltonian turns out to be
coupled when it is extended to the canonical noncommutative space with
noncommutative spatial coordinate operators and noncommutative momentum
operators as well. Our method is applicable to the coupled Hamiltonian. Then
the first and second order noncommutative corrections of energy levels are
calculated, and in particular the reality of energy spectra, the
positive-definiteness of inner products, and the related properties (the
probability explanation of wave functions, the orthogonality of eigenstates,
and the unitarity of time evolution) are found not to be altered by the
noncommutativity.Comment: 15 pages, no figures; v2: clarifications added; v3: 16 pages, 1
figure, clarifications made clearer; v4: 19 pages, the main context is
completely rewritten; v5: 25 pages, title slightly changed, clarifications
added, the final version to appear in PLOS ON
Genetic analysis of wheat rust resistance genes segregating in a Kariega x Avocet S population
Item does not contain fulltext14 mei 201
Simplicial gauge theory on spacetime
We define a discrete gauge-invariant Yang-Mills-Higgs action on spacetime
simplicial meshes. The formulation is a generalization of classical lattice
gauge theory, and we prove consistency of the action in the sense of
approximation theory. In addition, we perform numerical tests of convergence
towards exact continuum results for several choices of gauge fields in pure
gauge theory.Comment: 18 pages, 2 figure
Stem rust resistance in South African wheat cultivars
The aim of this study was to attempt to identify reliable factors associated with dropout risk in a sample of 161 panic disorder patients treated with manualized cognitive behavior therapy. Four possible predictors of dropout were selected from the literature: level of education, treatment motivation, personality psychopathology, and initial symptom severity. Thirty-two patients (19.9%) were dropouts. Level of education and motivation were significantly associated with dropout, but the associations were small. Personality psychopathology and initial symptom severity were not associated with dropout. It is concluded that, at present, we are unable to make precise dropout risk predictions, even in a homogeneous group of patients treated using standardized treatment
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