1,802 research outputs found
Quasi-exactly solvable problems and the dual (q-)Hahn polynomials
A second-order differential (q-difference) eigenvalue equation is constructed
whose solutions are generating functions of the dual (q-)Hahn polynomials. The
fact is noticed that these generating functions are reduced to the (little
q-)Jacobi polynomials, and implications of this for quasi-exactly solvable
problems are studied. A connection with the Azbel-Hofstadter problem is
indicated.Comment: 15 pages, LaTex; final version, presentation improved, title changed,
to appear in J.Math.Phy
The Determinant Representation for a Correlation Function in Scaling Lee-Yang Model
We consider the scaling Lee-Yang model. It corresponds to the unique
perturbation of the minimal CFT model M(2,5). This is not a unitary model. We
used known expression for form factors in order to obtain a closed expression
for a correlation function of a trace of energy-momentum tensor. This
expression is a determinant of an integral operator. Similar determinant
representation were proven to be useful not only for quantum correlation
functions but also in matrix models.Comment: 14 pages, LaTeX, no figure
Synthesis and tribological properties of new fluoro-containing oligomers
Oligomers based on (polyfluoroalkyl)methyl oxiranes and thiiranes was first synthesized by the cationic polymerization in the presence of boron trifluoride etherate. Molecular weights of the products were defined by cryoscopic method. It was found that synthesized oligomers can be used as additives to industrial lubricants and sulfur oligomers are of the greatest positive tribological effect. © Pleiades Publishing, Ltd., 2013
Estimation of coupling between oscillators from short time series via phase dynamics modeling: limitations and application to EEG data
We demonstrate in numerical experiments that estimators of strength and
directionality of coupling between oscillators based on modeling of their phase
dynamics [D.A. Smirnov and B.P. Bezruchko, Phys. Rev. E 68, 046209 (2003)] are
widely applicable. Namely, although the expressions for the estimators and
their confidence bands are derived for linear uncoupled oscillators under the
influence of independent sources of Gaussian white noise, they turn out to
allow reliable characterization of coupling from relatively short time series
for different properties of noise, significant phase nonlinearity of the
oscillators, and non-vanishing coupling between them. We apply the estimators
to analyze a two-channel human intracranial epileptic electroencephalogram
(EEG) recording with the purpose of epileptic focus localization.Comment: 22 pages, 7 figures, the paper is to be published in Chaos, 2005,
vol.15, issue 2, see http://chaos.aip.org
Sine-Gordon breather form factors and quantum field equations
Using the results of previous investigations on sine-Gordon form factors
exact expressions of all breather matrix elements are obtained for several
operators: all powers of the fundamental bose field, general exponentials of
it, the energy momentum tensor and all higher currents. Formulae for the
asymptotic behavior of bosonic form factors are presented which are motivated
by Weinberg's power counting theorem in perturbation theory. It is found that
the quantum sine-Gordon field equation holds and an exact relation between the
``bare'' mass and the renormalized mass is obtained. Also a quantum version of
a classical relation for the trace of the energy momentum is proven. The
eigenvalue problem for all higher conserved charges is solved. All results are
compared with perturbative Feynman graph expansions and full agreement is
found.Comment: LaTeX, 31 page
The determinant representation for quantum correlation functions of the sinh-Gordon model
We consider the quantum sinh-Gordon model in this paper. Using known formulae
for form factors we sum up all their contributions and obtain a closed
expression for a correlation function. This expression is a determinant of an
integral operator. Similar determinant representations were proven to be useful
not only in the theory of correlation functions, but also in the matrix models.Comment: 21 pages, Latex, no figure
The quasiclassical theory of the Dirac equation with a scalar-vector interaction and its applications in the theory of heavy-light mesons
We construct a relativistic potential quark model of , , , and
mesons in which the light quark motion is described by the Dirac equation
with a scalar-vector interaction and the heavy quark is considered a local
source of the gluon field. The effective interquark interaction is described by
a combination of the perturbative one-gluon exchange potential
and the long-range Lorentz-scalar and
Lorentz-vector linear potentials and , where
. Within the quasiclassical approximation, we obtain
simple asymptotic formulas for the energy and mass spectra and for the mean
radii of , , , and mesons, which ensure a high accuracy of
calculations even for states with the radial quantum number . We
show that the fine structure of P-wave states in heavy-light mesons is
primarily sensitive to the choice of two parameters: the strong-coupling
constant and the coefficient of mixing of the long-range
scalar and vector potentials and .
The quasiclassical formulas for asymptotic coefficients of wave function at
zero and infinity are obtained.Comment: 22 pages, 6 figure
p-Adic Mathematical Physics
A brief review of some selected topics in p-adic mathematical physics is
presented.Comment: 36 page
Paramagnetic and antiferromagnetic resonances in the diamagnetically diluted Haldane magnet PbNi2V2O8
The impurity-induced antiferromagnetic ordering of the doped Haldane magnet
Pb(Ni{1-x}Mg{x})2V2O8 (0 < x <0.06) was studied by electron spin resonance
(ESR) on ceramic samples in the frequency range 9-110 GHz. Below the N\'{e}el
temperature a transformation of the ESR spectrum was found, indicating an
antiferromagnetic resonance mode of spin precession. The excitation gap of the
spin-wave spectrum increases with increasing Mg-concentration in the same
manner as the N\'{e}el temperature, reaching its maximum value of 80 GHz at x >
0.04. At small concentrations x < 0.02 the signals of antiferromagnetic
resonance were found to coexist with the signal of the paramagnetic resonance
indicating a microscopic separation of the magnetic phases.Comment: 10 pages, 9 figure
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