242 research outputs found
The von Neumann Hierarchy for Correlation Operators of Quantum Many-Particle Systems
The Cauchy problem for the von Neumann hierarchy of nonlinear equations is
investigated. One describes the evolution of all possible states of quantum
many-particle systems by the correlation operators. A solution of such
nonlinear equations is constructed in the form of an expansion over particle
clusters whose evolution is described by the corresponding order cumulant
(semi-invariant) of evolution operators for the von Neumann equations. For the
initial data from the space of sequences of trace class operators the existence
of a strong and a weak solution of the Cauchy problem is proved. We discuss the
relationships of this solution both with the -particle statistical
operators, which are solutions of the BBGKY hierarchy, and with the
-particle correlation operators of quantum systems.Comment: 26 page
Quantum Mechanics of Multi-Prong Potentials
We describe the bound state and scattering properties of a quantum mechanical
particle in a scalar -prong potential. Such a study is of special interest
since these situations are intermediate between one and two dimensions. The
energy levels for the special case of identical prongs exhibit an
alternating pattern of non-degeneracy and fold degeneracy. It is shown
that the techniques of supersymmetric quantum mechanics can be used to generate
new solutions. Solutions for prongs of arbitrary lengths are developed.
Discussions of tunneling in -well potentials and of scattering for piecewise
constant potentials are given. Since our treatment is for general values of
, the results can be studied in the large limit. A somewhat surprising
result is that a free particle incident on an -prong vertex undergoes
continuously increased backscattering as the number of prongs is increased.Comment: 17 pages. LATEX. On request, TOP_DRAW files or hard copies available
for 7 figure
Scattering theory on graphs
We consider the scattering theory for the Schr\"odinger operator
-\Dc_x^2+V(x) on graphs made of one-dimensional wires connected to external
leads. We derive two expressions for the scattering matrix on arbitrary graphs.
One involves matrices that couple arcs (oriented bonds), the other involves
matrices that couple vertices. We discuss a simple way to tune the coupling
between the graph and the leads. The efficiency of the formalism is
demonstrated on a few known examples.Comment: 21 pages, LaTeX, 10 eps figure
Kirchhoff's Rule for Quantum Wires
In this article we formulate and discuss one particle quantum scattering
theory on an arbitrary finite graph with open ends and where we define the
Hamiltonian to be (minus) the Laplace operator with general boundary conditions
at the vertices. This results in a scattering theory with channels. The
corresponding on-shell S-matrix formed by the reflection and transmission
amplitudes for incoming plane waves of energy is explicitly given in
terms of the boundary conditions and the lengths of the internal lines. It is
shown to be unitary, which may be viewed as the quantum version of Kirchhoff's
law. We exhibit covariance and symmetry properties. It is symmetric if the
boundary conditions are real. Also there is a duality transformation on the set
of boundary conditions and the lengths of the internal lines such that the low
energy behaviour of one theory gives the high energy behaviour of the
transformed theory. Finally we provide a composition rule by which the on-shell
S-matrix of a graph is factorizable in terms of the S-matrices of its
subgraphs. All proofs only use known facts from the theory of self-adjoint
extensions, standard linear algebra, complex function theory and elementary
arguments from the theory of Hermitean symplectic forms.Comment: 40 page
Galactic Rotation Parameters from Data on Open Star Clusters
Currently available data on the field of velocities Vr, Vl, Vb for open star
clusters are used to perform a kinematic analysis of various samples that
differ by heliocentric distance, age, and membership in individual structures
(the Orion, Carina--Sagittarius, and Perseus arms). Based on 375 clusters
located within 5 kpc of the Sun with ages up to 1 Gyr, we have determined the
Galactic rotation parameters
Wo =-26.0+-0.3 km/s/kpc,
W'o = 4.18+-0.17 km/s/kpc^2,
W''o=-0.45+-0.06 km/s/kpc^3, the system contraction parameter K = -2.4+-0.1
km/s/kpc, and the parameters of the kinematic center Ro =7.4+-0.3 kpc and lo =
0+-1 degrees. The Galactocentric distance Ro in the model used has been found
to depend significantly on the sample age. Thus, for example, it is 9.5+-0.7
kpc and 5.6+-0.3 kpc for the samples of young (50 Myr)
clusters, respectively. Our study of the kinematics of young open star clusters
in various spiral arms has shown that the kinematic parameters are similar to
the parameters obtained from the entire sample for the Carina-Sagittarius and
Perseus arms and differ significantly from them for the Orion arm. The
contraction effect is shown to be typical of star clusters with various ages.
It is most pronounced for clusters with a mean age of 100 Myr, with the
contraction velocity being Kr = -4.3+-1.0 km/s.Comment: 14 pages, 4 figures, 2 table
Band spectra of rectangular graph superlattices
We consider rectangular graph superlattices of sides l1, l2 with the
wavefunction coupling at the junctions either of the delta type, when they are
continuous and the sum of their derivatives is proportional to the common value
at the junction with a coupling constant alpha, or the "delta-prime-S" type
with the roles of functions and derivatives reversed; the latter corresponds to
the situations where the junctions are realized by complicated geometric
scatterers. We show that the band spectra have a hidden fractal structure with
respect to the ratio theta := l1/l2. If the latter is an irrational badly
approximable by rationals, delta lattices have no gaps in the weak-coupling
case. We show that there is a quantization for the asymptotic critical values
of alpha at which new gap series open, and explain it in terms of
number-theoretic properties of theta. We also show how the irregularity is
manifested in terms of Fermi-surface dependence on energy, and possible
localization properties under influence of an external electric field.
KEYWORDS: Schroedinger operators, graphs, band spectra, fractals,
quasiperiodic systems, number-theoretic properties, contact interactions, delta
coupling, delta-prime coupling.Comment: 16 pages, LaTe
A single-mode quantum transport in serial-structure geometric scatterers
We study transport in quantum systems consisting of a finite array of N
identical single-channel scatterers. A general expression of the S matrix in
terms of the individual-element data obtained recently for potential scattering
is rederived in this wider context. It shows in particular how the band
spectrum of the infinite periodic system arises in the limit . We
illustrate the result on two kinds of examples. The first are serial graphs
obtained by chaining loops or T-junctions. A detailed discussion is presented
for a finite-periodic "comb"; we show how the resonance poles can be computed
within the Krein formula approach. Another example concerns geometric
scatterers where the individual element consists of a surface with a pair of
leads; we show that apart of the resonances coming from the decoupled-surface
eigenvalues such scatterers exhibit the high-energy behavior typical for the
delta' interaction for the physically interesting couplings.Comment: 36 pages, a LaTeX source file with 2 TeX drawings, 3 ps and 3 jpeg
figures attache
Analysis of the Situation on Anthrax in the World in 2022, the Forecast for the Russian Federation for 2023
The paper provides the results of analysis of the epizootiological and epidemiological situation on anthrax in the world in 2022, also, the forecast of incidence rates for the Russian Federation in 2023 is presented. In 2022, two cases of anthrax in farm animals and two cases of cutaneous form of infection in humans were registered in Russia, in the constituent entities of the North Caucasian Federal District: the Republic of Dagestan and the Stavropol Territory. The tense situation on anthrax was reported in the neighboring countries: Azerbaijan, Georgia, Kazakhstan, Kyrgyzstan, Tajikistan, Uzbekistan, and Ukraine. Epizootics of infection with the highest number of affected farm and wild animals were recorded in the countries of Africa, Asia, North America and Europe. The incidence of anthrax among people in the far abroad (mainly in Africa and Asia) was mostly associated with consuming the meat of sick and fallen farm animals, contact with infected animals, animal products. The incidence of anthrax in animals and humans in the Russian Federation in 2023 will largely depend on the scale of coverage with specific immunization of susceptible animals and persons at risk of infection and, given the strict implementation of comprehensive surveillance measures, will be limited to the registration of potentially possible single cases of infection
- …