120 research outputs found

### Fractional Generalization of Liouville Equations

In this paper fractional generalization of Liouville equation is considered.
We derive fractional analog of normalization condition for distribution
function. Fractional generalization of the Liouvile equation for dissipative
and Hamiltonian systems was derived from the fractional normalization
condition. This condition is considered considered as a normalization condition
for systems in fractional phase space. The interpretation of the fractional
space is discussed.Comment: 9 pages, LaTe

### Pure Stationary States of Open Quantum Systems

Using Liouville space and superoperator formalism we consider pure stationary
states of open and dissipative quantum systems. We discuss stationary states of
open quantum systems, which coincide with stationary states of closed quantum
systems. Open quantum systems with pure stationary states of linear oscillator
are suggested. We consider stationary states for the Lindblad equation. We
discuss bifurcations of pure stationary states for open quantum systems which
are quantum analogs of classical dynamical bifurcations.Comment: 7p., REVTeX

### Gravitational Field of Fractal Distribution of Particles

In this paper we consider the gravitational field of fractal distribution of
particles. To describe fractal distribution, we use the fractional integrals.
The fractional integrals are considered as approximations of integrals on
fractals. Using the fractional generalization of the Gauss's law, we consider
the simple examples of the fields of homogeneous fractal distribution. The
examples of gravitational moments for fractal distribution are considered.Comment: 14 pages, LaTe

### Scalar products in generalized models with SU(3)-symmetry

We consider a generalized model with SU(3)-invariant R-matrix, and review the
nested Bethe Ansatz for constructing eigenvectors of the transfer matrix. A sum
formula for the scalar product between generic Bethe vectors, originally
obtained by Reshetikhin [11], is discussed. This formula depends on a certain
partition function Z(\{\lambda\},\{\mu\}|\{w\},\{v\}), which we evaluate
explicitly. In the limit when the variables \{\mu\} or \{v\} approach infinity,
this object reduces to the domain wall partition function of the six-vertex
model Z(\{\lambda\}|\{w\}). Using this fact, we obtain a new expression for the
off-shell scalar product (between a generic Bethe vector and a Bethe
eigenvector), in the case when one set of Bethe variables tends to infinity.
The expression obtained is a product of determinants, one of which is the
Slavnov determinant from SU(2) theory. It extends a result of Caetano [13].Comment: 28 pages, 12 figures, greatly lengthened exposition in v3; 2
appendices and extra references adde

### Synthesis of Few-layer Graphene Sheets via Chemical and Thermal Reduction of Graphite Oxide

Few-layer graphene sheets were produced from graphite oxide (GO) chemical and thermal reduction.
For the chemical reduction of GO as reducing agents were used hydrazine hydrate, hydroxylammonium
chloride, sodium borohydride and sodium sulfite. The reduced material was characterized by elemental
analysis, thermo-gravimetric analysis, scanning electron microscopy, X-ray diffraction, Fourier transform
infrared and Raman spectroscopy. A comparison of the deoxygenation efficiency of graphene oxide suspension by different method or reductants has been made, revealing that the highest degree of reduction was
achieved by thermal reduction and using hydrazine hydrate and hydroxylammonium chloride as a reducing agents.
When you are citing the document, use the following link http://essuir.sumdu.edu.ua/handle/123456789/3506

### The Hubbard chain: Lieb-Wu equations and norm of the eigenfunctions

We argue that the square of the norm of the Hubbard wave function is
proportional to the determinant of a matrix, which is obtained by linearization
of the Lieb-Wu equations around a solution. This means that in the vicinity of
a solution the Lieb-Wu equations are non-degenerate, if the corresponding wave
function is non-zero. We further derive an action that generates the Lieb-Wu
equations and express our determinant formula for the square of the norm in
terms of the Hessian determinant of this action.Comment: 11 pages, Late

### Fractional Dynamics from Einstein Gravity, General Solutions, and Black Holes

We study the fractional gravity for spacetimes with non-integer dimensions.
Our constructions are based on a geometric formalism with the fractional Caputo
derivative and integral calculus adapted to nonolonomic distributions. This
allows us to define a fractional spacetime geometry with fundamental
geometric/physical objects and a generalized tensor calculus all being similar
to respective integer dimension constructions. Such models of fractional
gravity mimic the Einstein gravity theory and various Lagrange-Finsler and
Hamilton-Cartan generalizations in nonholonomic variables. The approach
suggests a number of new implications for gravity and matter field theories
with singular, stochastic, kinetic, fractal, memory etc processes. We prove
that the fractional gravitational field equations can be integrated in very
general forms following the anholonomic deformation method for constructing
exact solutions. Finally, we study some examples of fractional black hole
solutions, fractional ellipsoid gravitational configurations and imbedding of
such objects in fractional solitonic backgrounds.Comment: latex2e, 11pt, 40 pages with table of conten

### Preparation of Amino-Functionalized Graphene Sheets and their Conductive Properties

Amino-functionalized graphene sheets were prepared through chemical reduction by hydrazine hy-drate, amination or amidation of graphite oxide. For amination of graphite oxide were used polyamine such as ethylenediamine, diethylenetriamine and triethylenetetramine. Addition of amine groups to graphene is identified by Fourier transform infrared spectroscopy, Raman spectroscopy, elemental analysis and ther-mogravimetry. Scanning electron microscopy data indicate that the organic amine is not only as nitrogen sources to obtain the nitrogen-doped graphene but also as an important modification to control the assem-bly of graphene sheets in the 3D structures. The electrical conductivity of the materials obtained by amina-tion and amidation of graphene is much smaller than that of reduced graphite oxide.
When you are citing the document, use the following link http://essuir.sumdu.edu.ua/handle/123456789/3563

### Fractional Dynamics of Relativistic Particle

Fractional dynamics of relativistic particle is discussed. Derivatives of
fractional orders with respect to proper time describe long-term memory effects
that correspond to intrinsic dissipative processes. Relativistic particle
subjected to a non-potential four-force is considered as a nonholonomic system.
The nonholonomic constraint in four-dimensional space-time represents the
relativistic invariance by the equation for four-velocity u_{\mu}
u^{\mu}+c^2=0, where c is a speed of light in vacuum. In the general case, the
fractional dynamics of relativistic particle is described as non-Hamiltonian
and dissipative. Conditions for fractional relativistic particle to be a
Hamiltonian system are considered

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