350 research outputs found
Towards Rigorous Derivation of Quantum Kinetic Equations
We develop a rigorous formalism for the description of the evolution of
states of quantum many-particle systems in terms of a one-particle density
operator. For initial states which are specified in terms of a one-particle
density operator the equivalence of the description of the evolution of quantum
many-particle states by the Cauchy problem of the quantum BBGKY hierarchy and
by the Cauchy problem of the generalized quantum kinetic equation together with
a sequence of explicitly defined functionals of a solution of stated kinetic
equation is established in the space of trace class operators. The links of the
specific quantum kinetic equations with the generalized quantum kinetic
equation are discussed.Comment: 25 page
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
On the solutions of the nonlinear Liouville hierarchy
We investigate the initial-value problem of the non-linear Liouville
hierarchy. For the general form of the interaction potential we construct an
explicit solution in terms of an expansion over particle clusters whose
evolution is described by the corresponding-order cumulant of evolution
operators of a system of finitely many particles. For the initial data from the
space of integrable functions the existence of a strong solution of the Cauchy
problem is proved.Comment: 9 page
On Rigorous Derivation of the Enskog Kinetic Equation
We develop a rigorous formalism for the description of the kinetic evolution
of infinitely many hard spheres. On the basis of the kinetic cluster expansions
of cumulants of groups of operators of finitely many hard spheres the nonlinear
kinetic Enskog equation and its generalizations are justified. It is
established that for initial states which are specified in terms of
one-particle distribution functions the description of the evolution by the
Cauchy problem of the BBGKY hierarchy and by the Cauchy problem of the
generalized Enskog kinetic equation together with a sequence of explicitly
defined functionals of a solution of stated kinetic equation is an equivalent.
For the initial-value problem of the generalized Enskog equation the existence
theorem is proved in the space of integrable functions.Comment: 28 page
Approximations of singular vertex couplings in quantum graphs
We discuss approximations of the vertex coupling on a star-shaped quantum
graph of edges in the singular case when the wave functions are not
continuous at the vertex and no edge-permutation symmetry is present. It is
shown that the Cheon-Shigehara technique using interactions with
nonlinearly scaled couplings yields a -parameter family of boundary
conditions in the sense of norm resolvent topology. Moreover, using graphs with
additional edges one can approximate the -parameter family of
all time-reversal invariant couplings.Comment: LaTeX source file, 33 pages, with 3 eps figure
The spectral shift function and Levinson's theorem for quantum star graphs
We consider the Schr\"odinger operator on a star shaped graph with edges
joined at a single vertex. We derive an expression for the trace of the
difference of the perturbed and unperturbed resolvent in terms of a Wronskian.
This leads to representations for the perturbation determinant and the spectral
shift function, and to an analog of Levinson's formula
От идеи к синтезу модели образовательного стандарта подготовки ученых в аспирантуре
In a Quintessence form an idea and sequence is considered the synthesized decision of paradoxical problems in the system of preparation of research and scientifically-pedagogical workers of higher qualification.В квинтэссентной форме рассмотрено идею и последовательность синтезированного решения парадоксальных проблем в системе подготовки научных и научно-педагогических работников высшей квалификации
Virality of medical content in Russian social media
The work objective is to conduct a sociological study aimed at assessing validity (appropriateness) of the traditional characteristics and formation of a pool of specialized characteristics of the viral content, used in the promotion of health services by means of social media marketin
Structure and Biochemical Study of Nanocomposite Bioconstruction for Restoration of Bone-cartilaginous Defects
Porous and strong nanocomposite bioconstructions were formed by laser evaporation of an aqueous dispersion of carbon nanotubes in a protein matrix. The homogeneous dispersion was exposed to laser irradiation to create solid constructions. Continuous laser radiation with a wavelength of 970 nm and a power of 5-7 W was used. The porosity of nanocomposite bioconstructions was studied by the method of lowtemperature nitrogen porosimetry and X-ray microtomography, the tensile strength and relative elongation of bioconstructions were evaluated, and their biocompatibility was tested in vitro. It was found that with an increase of the carbon nanotube’s concentration, a slight decrease in strength (3-15 %), a decrease in the pore size (20- 40 %), and an increase in the degree of deformation (10-12 %) were observed. At the same time, the mechanical parameters of the bioconstructions met the requirements for the materials for the restoration of bone-cartilaginous defects. Using optical microscopy and the MTT-test, proliferative activity and structural features of bone tissue cells on the surface of nanocomposite bioconstructions were evaluated. Studies have shown no toxic or inhibitory effect on cells. The results of the studies can talk about the advantage of nanocomposite bioconstructions using as an implant material for improving the growth of biological cells and regenerating damaged biotissues.
Keywords: Nanocomposites, laser radiation, mechanical properties, porosity, X-ray microtomography, biocompatibilit
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