655 research outputs found
PT-symmetry and its spontaneous breakdown explained by anti-linearity
The impact of an anti-unitary symmetry on the spectrum of non-Hermitian operators is studied. Wigner's normal form of an anti-unitary operator accounts for the spectral properties of non-Hermitian, PE-symmetric Harniltonians. The occurrence of either single real or complex conjugate pairs of eigenvalues follows from this theory. The corresponding energy eigenstates span either one- or two-dimensional irreducible representations of the symmetry PE. In this framework, the concept of a spontaneously broken PE-symmetry is not needed
On the Absence of an Exponential Bound in Four Dimensional Simplicial Gravity
We have studied a model which has been proposed as a regularisation for four
dimensional quantum gravity. The partition function is constructed by
performing a weighted sum over all triangulations of the four sphere. Using
numerical simulation we find that the number of such triangulations containing
simplices grows faster than exponentially with . This property ensures
that the model has no thermodynamic limit.Comment: 8 pages, 2 figure
Corrections to Sirlin's Theorem in Chiral Perturbation Theory
We present the results of the first two-loop calculation of a form factor in
full Chiral Perturbation Theory. We choose a specific
linear combination of and form factors (the one
appearing in Sirlin's theorem) which does not get contributions from order
operators with unknown constants. For the charge radii, the correction to
the previous one-loop result turns out to be significant, but still there is no
agreement with the present data due to large experimental uncertainties in the
kaon charge radii.Comment: 6 pages, Latex, 2 LaTeX figure
Space of State Vectors in PT Symmetrical Quantum Mechanics
Space of states of PT symmetrical quantum mechanics is examined. Requirement
that eigenstates with different eigenvalues must be orthogonal leads to the
conclusion that eigenfunctions belong to the space with an indefinite metric.
The self consistent expressions for the probability amplitude and average value
of operator are suggested. Further specification of space of state vectors
yield the superselection rule, redefining notion of the superposition
principle. The expression for the probability current density, satisfying
equation of continuity and vanishing for the bound state, is proposed.Comment: Revised version, explicit expressions for average values and
probability amplitude adde
Numerical observation of non-axisymmetric vesicles in fluid membranes
By means of Surface Evolver (Exp. Math,1,141 1992), a software package of
brute-force energy minimization over a triangulated surface developed by the
geometry center of University of Minnesota, we have numerically searched the
non-axisymmetric shapes under the Helfrich spontaneous curvature (SC) energy
model. We show for the first time there are abundant mechanically stable
non-axisymmetric vesicles in SC model, including regular ones with intrinsic
geometric symmetry and complex irregular ones. We report in this paper several
interesting shapes including a corniculate shape with six corns, a
quadri-concave shape, a shape resembling sickle cells, and a shape resembling
acanthocytes. As far as we know, these shapes have not been theoretically
obtained by any curvature model before. In addition, the role of the
spontaneous curvature in the formation of irregular crenated vesicles has been
studied. The results shows a positive spontaneous curvature may be a necessary
condition to keep an irregular crenated shape being mechanically stable.Comment: RevTex, 14 pages. A hard copy of 8 figures is available on reques
Some properties of eigenvalues and eigenfunctions of the cubic oscillator with imaginary coupling constant
Comparison between the exact value of the spectral zeta function,
, and the results
of numeric and WKB calculations supports the conjecture by Bessis that all the
eigenvalues of this PT-invariant hamiltonian are real. For one-dimensional
Schr\"odinger operators with complex potentials having a monotonic imaginary
part, the eigenfunctions (and the imaginary parts of their logarithmic
derivatives) have no real zeros.Comment: 6 pages, submitted to J. Phys.
The Hierarchy Principle and the Large Mass Limit of the Linear Sigma Model
In perturbation theory we study the matching in four dimensions between the
linear sigma model in the large mass limit and the renormalized nonlinear sigma
model in the recently proposed flat connection formalism. We consider both the
chiral limit and the strong coupling limit of the linear sigma model. Our
formalism extends to Green functions with an arbitrary number of pion legs,at
one loop level,on the basis of the hierarchy as an efficient unifying principle
that governs both limits. While the chiral limit is straightforward, the
matching in the strong coupling limit requires careful use of the normalization
conditions of the linear theory, in order to exploit the functional equation
and the complete set of local solutions of its linearized form.Comment: Latex, 41 pages, corrected typos, final version accepted by IJT
Jost-Lehmann-Dyson Representation, Analyticity in Angle Variable and Upper Bounds in Noncommutative Quantum Field Theory
The existence of Jost-Lehmann-Dyson representation analogue has been proved
in framework of space-space noncommutative quantum field theory. On the basis
of this representation it has been found that some class of elastic amplitudes
admits an analytical continuation into complex \cos\vartheta plane and
corresponding domain of analyticity is Martin ellipse. This analyticity
combined with unitarity leads to Froissart-Martin upper bound on total cross
section.Comment: LaTeX, 15 pages, improved version, misprints corrected, the
references added, to appear in Theor. Math. Phy
Sums over Graphs and Integration over Discrete Groupoids
We show that sums over graphs such as appear in the theory of Feynman
diagrams can be seen as integrals over discrete groupoids. From this point of
view, basic combinatorial formulas of the theory of Feynman diagrams can be
interpreted as pull-back or push-forward formulas for integrals over suitable
groupoids.Comment: 27 pages, 4 eps figures; LaTeX2e; uses Xy-Pic. Some ambiguities
fixed, and several proofs simplifie
On Shape Transformations and Shape Fluctuations of Cellular Compartments and Vesicles
We discuss the shape formation and shape transitions of simple bilayer vesicles in context with their role in biology. In the first part several classes of shape changes of vesicles of one lipid component are described and it is shown that these can be explained in terms of the bending energy concept in particular augmented by the bilayer coupling hypothesis. In the second
part shape changes and vesicle fission of vesicles composed of membranes of lipid mixtures are reported. These are explained in terms of coupling between local curvature and phase separation
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