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

PsiPsi - Vectors for Three Dimensional Models

In this paper we apply the method of psi-vectors to three dimensional statistical models. This method gives the correspondence between the Bazhanov -- Baxter model and its vertex formulation. Considering psi-vectors for the Planar model, we obtain its self-duality.Comment: 11 pages, LaTeX, no figure

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

Defensive response to humans in farm-bred sables (Martes zibellina)

The formation of behavior type in the postnatal development of sables is studied insufficiently. Studies of this hot topic showed that the anthropogenic factor has a great influence on behavior formation in sables. Identification of other components that can influence the formation of sable behavior of sables in relation to a human is of obvious interest. The objectives of our work were: (1) variation of behavior type in pups with age and (2) correlation of behavior with pup sex and coloration, litter size, and origin of parents. A total of 262 pups were tested. Part of their parents belonged to animals, thoroughbred for coloration («black sable» breed), whose selection had been conducted in farms for 40 years. Other parents originated from sables caught in 1990s in Kamchatka and the Urals (mongrels). The type of behavior was determined by the standard hand test. Animals avoiding contact were scored zero. Animals communicating with the experimenter and demonstrating calm behavior (friendly response) were scored +1 to +5. Animals that demonstrated aggressive behavior (fearful response) were scored –1 to –4. Tests of the same animals were repeated at ages of 4, 5, and 6 months. In the final test at 6 months, 78,6 % of pups of both sexes showed the avoidance response, 20,2 % were attributed to the calm type, and 1,2 % to aggressive. The experi- ment proved that the formation of behavioral reactions in young sables was influenced by the sex of animals. The calm response was more frequently demonstrated by males than by females (p > 0,99–0,999). Behavior type in young sables showed no association with age, but the proportion of calm animals increased in each successive test (differences statistically insignificant, p < 0,90). No statistically significant correlation could be found between coloration and tame behavior of pups because of small numbers of such animals. Litter size or parent breed did not affect the formation of behavior type in pups

Single Cycle Thin Film Compressor Opening the door to Zeptosecond-Exawatt Physics

This article demonstrates a new compression scheme that has the potential to compress a high energy pulse as high as a few hundred Joules in a pulse as short as one optical cycle at 0.8{\mu}m making a true ultra-relativistic {\lambda}^3 pulse. This pulse could have a focused intensity of 10^24W/cm2 or a0 of 1000. It could form an efficient, 10%, relativistic mirror that could compress the pulse to the atto-zeptosecond regime, with an upshifted wavelength of 1-10keV. This technique could be a watershed making the entry of petawatt pulses into the exawatt and zeptosecond regime possible.Comment: 6 pages, 6 figure

Conserved Charges in the Principal Chiral Model on a Supergroup

The classical principal chiral model in 1+1 dimensions with target space a compact Lie supergroup is investigated. It is shown how to construct a local conserved charge given an invariant tensor of the Lie superalgebra. We calculate the super-Poisson brackets of these currents and argue that they are finitely generated. We show how to derive an infinite number of local charges in involution. We demonstrate that these charges Poisson commute with the non-local charges of the model

Variability of Fe II Emission Features in the Seyfert 1 Galaxy NGC 5548

We study the low-contrast Fe II emission blends in the ultraviolet (1250--2200A) and optical (4000--6000A) spectra of the Seyfert 1 galaxy NGC 5548 and show that these features vary in flux and that these variations are correlated with those of the optical continuum. The amplitude of variability of the optical Fe II emission is 50% - 75% that of Hbeta and the ultraviolet Fe II emission varies with an even larger amplitude than Hbeta. However, accurate measurement of the flux in these blends proves to be very difficult even using excellent Fe II templates to fit the spectra. We are able to constrain only weakly the optical Fe II emission-line response timescale to a value less than several weeks; this upper limit exceeds all the reliably measured emission-line lags in this source so it is not particularly meaningful. Nevertheless, the fact that the optical Fe II and continuum flux variations are correlated indicates that line fluorescence in a photoionized plasma, rather than collisional excitation, is responsible for the Fe II emission. The iron emission templates are available upon request.Comment: 34 pages including 12 figures and 2 tables. Accepted for publication by ApJ (tentatively in vol. 626 June 10, 2005

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

Interaction of ballistic quasiparticles and vortex configurations in superfluid He3-B

The vortex line density of turbulent superfluid He3-B at very low temperature is deduced by detecting the shadow of ballistic quasiparticles which are Andreev reflected by quantized vortices. Until now the measured total shadow has been interpreted as the sum of shadows arising from interactions of a single quasiparticle with a single vortex. By integrating numerically the quasi-classical Hamiltonian equations of motion of ballistic quasiparticles in the presence of nontrivial but relatively simple vortex systems (such as vortex-vortex and vortex-antivortex pairs and small clusters of vortices) we show that partial screening can take place, and the total shadow is not necessarily the sum of the shadows. We have also found that it is possible that, upon impinging on complex vortex configurations, quasiparticles experience multiple reflections, which can be classical, Andreev, or both.Comment: To appear in Phys Rev