1,195 research outputs found
Dynamical differential equations compatible with rational qKZ equations
For the Lie algebra we introduce a system of differential operators
called the dynamical operators. We prove that the dynamical differential
operators commute with the rational quantized Knizhnik-Zamolodchikov
difference operators. We describe the transformations of the dynamical
operators under the natural action of the Weyl group.Comment: 7 pages, AmsLaTe
Fractional Variations for Dynamical Systems: Hamilton and Lagrange Approaches
Fractional generalization of an exterior derivative for calculus of
variations is defined. The Hamilton and Lagrange approaches are considered.
Fractional Hamilton and Euler-Lagrange equations are derived. Fractional
equations of motion are obtained by fractional variation of Lagrangian and
Hamiltonian that have only integer derivatives.Comment: 21 pages, LaTe
Fractional Generalization of Gradient Systems
We consider a fractional generalization of gradient systems. We use
differential forms and exterior derivatives of fractional orders. Examples of
fractional gradient systems are considered. We describe the stationary states
of these systems.Comment: 11 pages, LaTe
Results of the investigation of the otolith function in manned space flights
The effects of conditions of long term and short term space flights on the otolith function of cosmonauts were investigated via pre and post examinations. The results show that after long term flight, the intensity of the otolith reflex increased and asymmetry occurred in the indicators of the otolith function. Large changes in terms of expression and duration in the indicators of the otolith function after long term flight as compared with short term flight were also noted
Weyl Quantization of Fractional Derivatives
The quantum analogs of the derivatives with respect to coordinates q_k and
momenta p_k are commutators with operators P_k and $Q_k. We consider quantum
analogs of fractional Riemann-Liouville and Liouville derivatives. To obtain
the quantum analogs of fractional Riemann-Liouville derivatives, which are
defined on a finite interval of the real axis, we use a representation of these
derivatives for analytic functions. To define a quantum analog of the
fractional Liouville derivative, which is defined on the real axis, we can use
the representation of the Weyl quantization by the Fourier transformation.Comment: 9 pages, LaTe
Fractional Liouville and BBGKI Equations
We consider the fractional generalizations of Liouville equation. The
normalization condition, phase volume, and average values are generalized for
fractional case.The interpretation of fractional analog of phase space as a
space with fractal dimension and as a space with fractional measure are
discussed. The fractional analogs of the Hamiltonian systems are considered as
a special class of non-Hamiltonian systems. The fractional generalization of
the reduced distribution functions are suggested. The fractional analogs of the
BBGKI equations are derived from the fractional Liouville equation.Comment: 20 page
Banks-Zaks fixed point analysis in momentum subtraction schemes
We analyse the critical exponents relating to the quark mass anomalous
dimension and beta-function at the Banks-Zaks fixed point in Quantum
Chromodynamics (QCD) in a variety of representations for the quark in the
momentum subtraction (MOM) schemes of Celmaster and Gonsalves. For a specific
range of values of the number of quark flavours, estimates of the exponents
appear to be scheme independent. Using the recent five loop modified minimal
subtraction (MSbar) scheme quark mass anomalous dimension and estimates of the
fixed point location we estimate the associated exponent as 0.263-0.268 for the
SU(3) colour group and 12 flavours when the quarks are in the fundamental
representation.Comment: 33 latex pages, 25 tables, anc directory contains txt file with
electronic version of renormalization group function
Path Integral for Quantum Operations
In this paper we consider a phase space path integral for general
time-dependent quantum operations, not necessarily unitary. We obtain the path
integral for a completely positive quantum operation satisfied Lindblad
equation (quantum Markovian master equation). We consider the path integral for
quantum operation with a simple infinitesimal generator.Comment: 24 pages, LaTe
Psi-Series Solution of Fractional Ginzburg-Landau Equation
One-dimensional Ginzburg-Landau equations with derivatives of noninteger
order are considered. Using psi-series with fractional powers, the solution of
the fractional Ginzburg-Landau (FGL) equation is derived. The leading-order
behaviours of solutions about an arbitrary singularity, as well as their
resonance structures, have been obtained. It was proved that fractional
equations of order with polynomial nonlinearity of order have the
noninteger power-like behavior of order near the singularity.Comment: LaTeX, 19 pages, 2 figure
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