787 research outputs found
Fibre bundle formulation of nonrelativistic quantum mechanics. III. Pictures and integrals of motion
We propose a new systematic fibre bundle formulation of nonrelativistic
quantum mechanics. The new form of the theory is equivalent to the usual one
but it is in harmony with the modern trends in theoretical physics and
potentially admits new generalizations in different directions. In it a pure
state of some quantum system is described by a state section (along paths) of a
(Hilbert) fibre bundle. It's evolution is determined through the bundle
(analogue of the) Schr\"odinger equation. Now the dynamical variables and the
density operator are described via bundle morphisms (along paths). The
mentioned quantities are connected by a number of relations derived in this
work.
In this third part of our series we investigate the bundle analogues of the
conventional pictures of motion. In particular, there are found the state
sections and bundle morphisms corresponding to state vectors and observables
respectively. The equations of motion for these quantities are derived too.
Using the results obtained, we consider from the bundle view-point problems
concerning the integrals of motion. An invariant (bundle) necessary and
sufficient conditions for a dynamical variable to be an integral of motion are
found.Comment: 19 standard (11pt, A4) LaTeX 2e pages. The packages AMS-LaTeX and
amsfonts are required. New references and comments are added. Minor style
chages. Continuation of quant-ph/9803083, quant-ph/9803084 and
quant-ph/9804062. For continuation of the series view
http://www.inrne.bas.bg/mathmod/bozhome
Phonons and Magnetic Excitations in Mott-Insulator LaTiO
The polarized Raman spectra of stoichiometric LaTiO (T K) were
measured between 6 and 300 K. In contrast to earlier report on half-metallic
LaTiO, neither strong background scattering, nor Fano shape of the
Raman lines was observed. The high frequency phonon line at 655 cm
exhibits anomalous softening below T: a signature for structural
rearrangement. The assignment of the Raman lines was done by comparison to the
calculations of lattice dynamics and the nature of structural changes upon
magnetic ordering are discussed. The broad Raman band, which appears in the
antiferromagnetic phase, is assigned to two-magnon scattering. The estimated
superexchange constant meV is in excellent agreement with the
result of neutron scattering studies.Comment: 4 pages, 5 figure
Raman and Infrared-Active Phonons in Hexagonal HoMnO Single Crystals: Magnetic Ordering Effects
Polarized Raman scattering and infrared reflection spectra of hexagonal
HoMnO single crystals in the temperature range 10-300 K are reported.
Group-theoretical analysis is performed and scattering selection rules for the
second order scattering processes are presented. Based on the results of
lattice dynamics calculations, performed within the shell model, the observed
lines in the spectra are assigned to definite lattice vibrations. The magnetic
ordering of Mn ions, which occurs below T=76 K, is shown to effect both
Raman- and infrared-active phonons, which modulate Mn-O-Mn bonds and,
consequently, Mn exchange interaction.Comment: 8 pages, 6 figure
Smrtnost od akutnih otrovanja u području Plovdiva u Bugarskoj
The severe recession in Bulgaria which followed the collapse of the totalitarian regime in 1989 had an unfavourable impact on the health status of the population. Systematic studies of acute poisoning mortality rate in the transitional period (1990-98) are scarce in the post-totalitarian Eastern European countries and are lacking in Bulgaria. This retrospective study analysed 1,150 deaths due to acute poisoning in Plovdiv Region for the period 1961-98. Acute poisoning mortality rate was moderately high in the period between 1990 and 1998 with respect to the average of 4.99 per 100,000 a year. It grew steadily during rapid socialist industrialization (1961-90) and showed a trend of slight decrease during transition (1991-1998). The decrease may largely be accounted for by the foundation of the regional toxicological centre and to a certain degree by a drop in industrial and agricultural production and exposure to hazards.Nakon pada totalitarnog režima 1989. godine, socioekonomska kriza što je zahvatila zemlju odrazila se negativno na zdravstveno stanje populacije. Sustavna praćenja akutnih otrovanja tijekom tranzicijskog razdoblja u Istočnoj Europi su oskudna, a u Bugarskoj ih nije ni bilo. U ovom se radu retrospektivno analizira 1150 slučajeva akutnih smrtnih otrovanja u području Plovdiva, i to u razdoblju 1961-1990. u vrijeme intenzivne industrijalizacije. U tom je razdoblju stopa smrtnosti od akutnih otrovanja stalno rasla dosegnuvši maksimum između 1986. i 1989., a nakon toga je počela lagano opadati. U razdoblju između 1990. i 1998. smrtnost od akutnih otrovanja iznosila je 4,99 na 100.000 stanovnika. Spomenuti trend opadanja smrtnosti pripisuje se osnivanju regionalnoga toksikološkog centra, kao i usporavanju industrijske i poljoprivredne aktivnosti s posljedicom smanjenja ekspozicije toksičnim tvarima. U smanjivanju stope smrtnosti od akutnih otrovanja posebnu ulogu imaju dobro planirane i provođene preventivne mjere
Frames of reference in spaces with affine connections and metrics
A generalized definition of a frame of reference in spaces with affine
connections and metrics is proposed based on the set of the following
differential-geometric objects:
(a) a non-null (non-isotropic) vector field,
(b) the orthogonal to the vector field sub space,
(c) an affine connection and the related to it covariant differential
operator determining a transport along the given non-null vector filed.
On the grounds of this definition other definitions related to the notions of
accelerated, inertial, proper accelerated and proper inertial frames of
reference are introduced and applied to some mathematical models for the
space-time. The auto-parallel equation is obtained as an Euler-Lagrange's
equation. Einstein's theory of gravitation appears as a theory for
determination of a special frame of reference (with the gravitational force as
inertial force) by means of the metrics and the characteristics of a material
distribution.
PACS numbers: 0490, 0450, 1210G, 0240VComment: 17 pages, LaTeX 2
Apolarity, Hessian and Macaulay polynomials
A result by Macaulay states that an Artinian graded Gorenstein ring R of
socle dimension one and socle degree b can be realized as the apolar ring of a
homogeneous polynomial f of degree b. If R is the Jacobian ring of a smooth
hypersurface g=0, then b is just equal to the degree of the Hessian polynomial
of g. In this paper we investigate the relationship between f and the Hessian
polynomial of g.Comment: 12 pages. Improved exposition, minor correction
Flows and particles with shear-free and expansion-free velocities in (L^-_n,g)- and Weyl's spaces
Conditions for the existence of flows with non-null shear-free and
expansion-free velocities in spaces with affine connections and metrics are
found. On their basis, generalized Weyl's spaces with shear-free and
expansion-free conformal Killing vectors as velocity's vectors of spinless test
particles moving in a Weyl's space are considered. The necessary and sufficient
conditions are found under which a free spinless test particle could move in
spaces with affine connections and metrics on a curve described by means of an
auto-parallel equation. In Weyl's spaces with Weyl's covector, constructed by
the use of a dilaton field, the dilaton field appears as a scaling factor for
the rest mass density of the test particle. PACS numbers: 02.40.Ky, 04.20.Cv,
04.50.+h, 04.90.+eComment: 20 pages, LaTeX, to appear in Classical and Quantum Gravity. arXiv
admin note: substantial text overlap with arXiv:gr-qc/001104
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