1,887 research outputs found
Explicit Free Parameterization of the Modified Tetrahedron Equation
The Modified Tetrahedron Equation (MTE) with affine Weyl quantum variables at
N-th root of unity is solved by a rational mapping operator which is obtained
from the solution of a linear problem. We show that the solutions can be
parameterized in terms of eight free parameters and sixteen discrete phase
choices, thus providing a broad starting point for the construction of
3-dimensional integrable lattice models. The Fermat curve points parameterizing
the representation of the mapping operator in terms of cyclic functions are
expressed in terms of the independent parameters. An explicit formula for the
density factor of the MTE is derived. For the example N=2 we write the MTE in
full detail. We also discuss a solution of the MTE in terms of bosonic
continuum functions.Comment: 28 pages, 3 figure
Quantum 2+1 evolution model
A quantum evolution model in 2+1 discrete space - time, connected with 3D
fundamental map R, is investigated. Map R is derived as a map providing a zero
curvature of a two dimensional lattice system called "the current system". In a
special case of the local Weyl algebra for dynamical variables the map appears
to be canonical one and it corresponds to known operator-valued R-matrix. The
current system is a kind of the linear problem for 2+1 evolution model. A
generating function for the integrals of motion for the evolution is derived
with a help of the current system. The subject of the paper is rather new, and
so the perspectives of further investigations are widely discussed.Comment: LaTeX, 37page
The modified tetrahedron equation and its solutions
A large class of 3-dimensional integrable lattice spin models is constructed.
The starting point is an invertible canonical mapping operator in the space of
a triple Weyl algebra. This operator is derived postulating a current branching
principle together with a Baxter Z-invariance. The tetrahedron equation for
this operator follows without further calculations. If the Weyl parameter is
taken to be a root of unity, the mapping operator decomposes into a matrix
conjugation and a C-number functional mapping. The operator of the matrix
conjugation satisfies a modified tetrahedron equation (MTE) in which the
"rapidities" are solutions of a classical integrable Hirota-type equation. The
matrix elements of this operator can be represented in terms of the
Bazhanov-Baxter Fermat curve cyclic functions, or alternatively in terms of
Gauss functions. The paper summarizes several recent publications on the
subject.Comment: 24 pages, 6 figures using epic/eepic package, Contribution to the
proceedings of the 6th International Conference on CFTs and Integrable
Models, Chernogolovka, Spetember 2002, reference adde
Studying of stowage massifs formation conditions in deep-laying rich KMA iron oxides developing and efficient stowage composition projection
On the example of Yakovlevsky iron-ore field which is characterized by composite hydro-geological and mining development conditions the natural monitoring technique of intense stowage massif strained state, which is formed in the descending layered dredging system of unstable rich iron oxides is proved and approve
On Spin Calogero-Moser system at infinity
We present a construction of a new integrable model as an infinite limit of Calogero models of N particles with spin. It is implemented in the multicomponent Fock space. Explicit formulas for Dunkl operators, the Yangian generators in the multicomponent Fock space are presented. The classical limit of the system is examined
Phase coherent transport in (Ga,Mn)As
Quantum interference effects and resulting quantum corrections of the
conductivity have been intensively studied in disordered conductors over the
last decades. The knowledge of phase coherence lengths and underlying dephasing
mechanisms are crucial to understand quantum corrections to the resistivity in
the different material systems. Due to the internal magnetic field and the
associated breaking of time-reversal symmetry quantum interference effects in
ferromagnetic materials have been scarcely explored. Below we describe the
investigation of phase coherent transport phenomena in the newly discovered
ferromagnetic semiconductor (Ga,Mn)As. We explore universal conductance
fluctuations in mesoscopic (Ga,Mn)As wires and rings, the Aharonov-Bohm effect
in nanoscale rings and weak localization in arrays of wires, made of the
ferromagnetic semiconductor material. The experiments allow to probe the phase
coherence length L_phi and the spin flip length L_SO as well as the temperature
dependence of dephasing.Comment: 22 pages, 10 figure
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