WW--geometry of the Toda systems associated with non-exceptional simple Lie algebras

The present paper describes the $W$--geometry of the Abelian finite non-periodic (conformal) Toda systems associated with the $B,C$ and $D$ series of the simple Lie algebras endowed with the canonical gradation. The principal tool here is a generalization of the classical Pl\"ucker embedding of the $A$-case to the flag manifolds associated with the fundamental representations of $B_n$, $C_n$ and $D_n$, and a direct proof that the corresponding K\"ahler potentials satisfy the system of two--dimensional finite non-periodic (conformal) Toda equations. It is shown that the $W$--geometry of the type mentioned above coincide with the differential geometry of special holomorphic (W) surfaces in target spaces which are submanifolds (quadrics) of $CP^N$ with appropriate choices of $N$. In addition, these W-surfaces are defined to satisfy quadratic holomorphic differential conditions that ensure consistency of the generalized Pl\"ucker embedding. These conditions are automatically fulfiled when Toda equations hold.Comment: 30 pages, no figur

Classical A_n--W-Geometry

This is a detailed development for the $A_n$ case, of our previous article entitled "W-Geometries" to be published in Phys. Lett. It is shown that the $A_n$--W-geometry corresponds to chiral surfaces in $CP^n$. This is comes out by discussing 1) the extrinsic geometries of chiral surfaces (Frenet-Serret and Gauss-Codazzi equations) 2) the KP coordinates (W-parametrizations) of the target-manifold, and their fermionic (tau-function) description, 3) the intrinsic geometries of the associated chiral surfaces in the Grassmannians, and the associated higher instanton- numbers of W-surfaces. For regular points, the Frenet-Serret equations for $CP^n$--W-surfaces are shown to give the geometrical meaning of the $A_n$-Toda Lax pair, and of the conformally-reduced WZNW models, and Drinfeld-Sokolov equations. KP coordinates are used to show that W-transformations may be extended as particular diffeomorphisms of the target-space. This leads to higher-dimensional generalizations of the WZNW and DS equations. These are related with the Zakharov- Shabat equations. For singular points, global Pl\"ucker formulae are derived by combining the $A_n$-Toda equations with the Gauss-Bonnet theorem written for each of the associated surfaces.Comment: (60 pages

Plasma rotation diagnostics at the FT-2 tokamak based on the upper hybrid resonance backscattering enhanced doppler effect

Observations of enhanced Doppler frequency shift effect of the highly localized microwave backscattering in the upper hybrid resonance are reported. The experiment is performed at FT-2 tokamak, where a steerable focusing antenna set, allowing off equatorial plane plasma extraordinary wave probing from high magnetic field side, was installed. A separate line less than 1.5 MHz wide and shifted by up to 2 MHz is routinely observed in the backscattering spectrum under condition of accessible upper hybrid resonance. The enhanced frequency shift is explained by the growth of poloidal wave number of the probing wave in the resonance. Development of a new scheme for local diagnostics of fluctuations poloidal rotation based on this effect is started.У статті описуються спостереження посиленого ефекту Доплера в спектрі сигналу розсіяного назад у верхньому гібридному резонансі зондувальної хвилі. Експеримент виконаний на токамаці ФТ-2, на якому недавно були встановлені рухливі антени, що дозволяють здійснювати зондування плазми електромагнітними хвилями в незвичайній поляризації з боку сильного магнітного поля. За умови доступного верхнього гібридного резонансу в спектрі розсіювання спостерігалася лінія шириною менш 1.5 МГц, зрушена до 2 МГц. Ефект пояснений ростом полоідального хвильового числа зондувальної хвилі в резонансі. Почато розвиток нової схеми локальної діагностики обертання плазмових флуктуацій, заснованої на цьому ефекті.В статье описываются наблюдения усиленного эффекта Доплера в спектре сигнала рассеянного назад в верхнем гибридном резонансе зондирующей волны. Эксперимент выполнен на токамаке ФТ-2, на котором недавно были установлены подвижные антенны, позволяющие осуществлять зондирование плазмы электромагнитными волнами в необыкновенной поляризации со стороны сильного магнитного поля. При условии доступного верхнего гибридного резонанса в спектре рассеяния наблюдалась линия шириной менее 1.5 МГц, сдвинутая до 2 МГц. Эффект объяснён ростом полоидального волнового числа зондирующей волны в резонансе. Начато развитие новой схемы локальной диагностики вращения плазменных флуктуаций, основанной на этом эффекте

Lorentz breaking Effective Field Theory and observational tests

Analogue models of gravity have provided an experimentally realizable test field for our ideas on quantum field theory in curved spacetimes but they have also inspired the investigation of possible departures from exact Lorentz invariance at microscopic scales. In this role they have joined, and sometime anticipated, several quantum gravity models characterized by Lorentz breaking phenomenology. A crucial difference between these speculations and other ones associated to quantum gravity scenarios, is the possibility to carry out observational and experimental tests which have nowadays led to a broad range of constraints on departures from Lorentz invariance. We shall review here the effective field theory approach to Lorentz breaking in the matter sector, present the constraints provided by the available observations and finally discuss the implications of the persisting uncertainty on the composition of the ultra high energy cosmic rays for the constraints on the higher order, analogue gravity inspired, Lorentz violations.Comment: 47 pages, 4 figures. Lecture Notes for the IX SIGRAV School on "Analogue Gravity", Como (Italy), May 2011. V.3. Typo corrected, references adde

Anomalous phenomena in ECRH experiments at toroidal devices and low-threshold parametric decay instabilities

In the paper the possibility of total 3D trapping of electron Bernstein (EB) waves in the tokamak equatorial plane in the vicinity of the local density maximum produced by electron pump-out-effect is demonstrated. Thresholds and growth rates of the associated absolute (temporally growing) parametric decay instability (PDI) leading to anomalous absorption is predicted in the range of less than 100 kW. Its possible role in explanation of ion acceleration observed in ECRH experiments as well as in redistribution of the deposited power is discussed

White Nanoluminophores Based on Monodisperse Carbon Nanodots Modified with Europium Ions

Monodisperse carbon nanodots modified with europium ions possessing photoluminescence in the entire visible region of the spectrum were synthesized by the template method. The chemical composition and structure of the resulting white nanoluminophore were studied by X ray spectral and microscopic method