Dynamical differential equations compatible with rational qKZ equations

For the Lie algebra $gl_N$ we introduce a system of differential operators called the dynamical operators. We prove that the dynamical differential operators commute with the $gl_N$ rational quantized Knizhnik-Zamolodchikov difference operators. We describe the transformations of the dynamical operators under the natural action of the $gl_N$ Weyl group.Comment: 7 pages, AmsLaTe

Bethe subalgebras in affine Birman--Murakami--Wenzl algebras and flat connections for q-KZ equations

Commutative sets of Jucys-Murphyelements for affine braid groups of $A^{(1)},B^{(1)},C^{(1)},D^{(1)}$ types were defined. Construction of $R$-matrix representations of the affine braid group of type $C^{(1)}$ and its distinguish commutative subgroup generated by the $C^{(1)}$-type Jucys--Murphy elements are given. We describe a general method to produce flat connections for the two-boundary quantum Knizhnik-Zamolodchikov equations as necessary conditions for Sklyanin's type transfer matrix associated with the two-boundary multicomponent Zamolodchikov algebra to be invariant under the action of the $C^{(1)}$-type Jucys--Murphy elements. We specify our general construction to the case of the Birman--Murakami--Wenzl algebras. As an application we suggest a baxterization of the Dunkl--Cherednik elements $Y's$ in the double affine Hecke algebra of type $A$

Bethe eigenvectors of higher transfer matrices

We consider the XXX-type and Gaudin quantum integrable models associated with the Lie algebra $gl_N$. The models are defined on a tensor product irreducible $gl_N$-modules. For each model, there exist $N$ one-parameter families of commuting operators on the tensor product, called the transfer matrices. We show that the Bethe vectors for these models, given by the algebraic nested Bethe ansatz are eigenvectors of higher transfer matrices and compute the corresponding eigenvalues.Comment: 48 pages, amstex.tex (ver 2.2), misprints correcte

Interaction effects in assembly of magnetic nanoparticles

A specific absorption rate of a dilute assembly of various random clusters of iron oxide nanoparticles in alternating magnetic field has been calculated using Landau- Lifshitz stochastic equation. This approach simultaneously takes into account both the presence of thermal fluctuations of the nanoparticle magnetic moments, and magneto-dipole interaction between the nanoparticles of the clusters. It is shown that for usual 3D clusters the intensity of magneto- dipole interaction is determined mainly by the cluster packing density eta = Np*V/Vcl, where Np is the average number of the particles in the cluster, V is the nanoparticle volume, and Vcl is the cluster volume. The area of the low frequency hysteresis loop and the assembly specific absorption rate have been found to be considerably reduced when the packing density of the clusters increases in the range of 0.005 < eta < 0.4. The dependence of the specific absorption rate on the mean nanoparticle diameter is retained with increase of eta, but becomes less pronounced. For fractal clusters of nanoparticles, which arise in biological media, in addition to considerable reduction of the absorption rate, the absorption maximum is shifted to smaller particle diameters. It is found also that the specific absorption rate of fractal clusters increases appreciably with increase of the thickness of nonmagnetic shells at the nanoparticle surfaces.Comment: The paper is accepted for Nanoscale Res. Let

Fractional Fokker-Planck Equation for Fractal Media

We consider the fractional generalizations of equation that defines the medium mass. We prove that the fractional integrals can be used to describe the media with noninteger mass dimensions. Using fractional integrals, we derive the fractional generalization of the Chapman-Kolmogorov equation (Smolukhovski equation). In this paper fractional Fokker-Planck equation for fractal media is derived from the fractional Chapman-Kolmogorov equation. Using the Fourier transform, we get the Fokker-Planck-Zaslavsky equations that have fractional coordinate derivatives. The Fokker-Planck equation for the fractal media is an equation with fractional derivatives in the dual space.Comment: 17 page

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