257 research outputs found
Noncompact SL(2,R) spin chain
We consider the integrable spin chain model - the noncompact SL(2,R) spin
magnet. The spin operators are realized as the generators of the unitary
principal series representation of the SL(2,R) group. In an explicit form, we
construct R-matrix, the Baxter Q-operator and the transition kernel to the
representation of the Separated Variables (SoV). The expressions for the energy
and quasimomentum of the eigenstates in terms of the Baxter Q-operator are
derived. The analytic properties of the eigenvalues of the Baxter operator as a
function of the spectral parameter are established. Applying the diagrammatic
approach, we calculate Sklyanin's integration measure in the separated
variables and obtain the solution to the spectral problem for the model in
terms of the eigenvalues of the Q-operator. We show that the transition kernel
to the SoV representation is factorized into a product of certain operators
each depending on a single separated variable.Comment: 29 pages, 12 figure
Electron-optical system of 200 kV gun for the VEPP-5 preinjector
The electron gun with a new electron-optical system to match project parameters of the VEPP-5 preinjector is
described. The gun produces the current with 10 A amplitude, pulse duration 2...3 ns at half-height and electron energy 200 keV. The gun has a dispenser cathode 20 mm in diameter and 100 mm spherical radius. The current control is performed by means of molybdenum equipotential grid with the cell size 0.4·0.4 mm and optical transparency
of about 0.68. The experimental results obtained are in good agreement with project parameters.Описано електронну гармату з новою електронно-оптичною системою, що відповідає проектним
параметрам передінжектора VEPP-5. Гармата дає струм 10 А с тривалістю імпульсу 2...3 нс на напіввисоті і
з енергією електронів 200 кеВ. Гармата має диспергуємий катод діаметром 20 мм і радіусом сфери 100 мм.
Керування здійснюється за допомогою молібденової еквіпотенційної сітки з коміркою розміром 0.4·0.4 мм і
оптичною прозорістю близько 0.68. Експериментально отримані результати знаходяться у відповідності з
проектними параметрами.Описана электронная пушка с новой электронно-оптической системой, соответствующая проектным параметрам предынжектора VEPP-5. Пушка дает ток 10 А с длительностью импульса 2…3 нс на полувысоте и
с энергией электронов 200 кэВ. Пушка имеет диспергируемый катод диаметром 20 мм и сферическим радиусом сферы 100 мм. Управление осуществляется посредством молибденовой эквипотенциальной сетки с
ячейкой размером 0.4·0.4 мм и оптической прозрачности около 0.68. Экспериментальные полученные результаты находятся в хорошем соответствии с проектными параметрами
Finite time singularities in a class of hydrodynamic models
Models of inviscid incompressible fluid are considered, with the kinetic
energy (i.e., the Lagrangian functional) taking the form in 3D Fourier representation, where
is a constant, . Unlike the case (the usual Eulerian
hydrodynamics), a finite value of results in a finite energy for a
singular, frozen-in vortex filament. This property allows us to study the
dynamics of such filaments without the necessity of a regularization procedure
for short length scales. The linear analysis of small symmetrical deviations
from a stationary solution is performed for a pair of anti-parallel vortex
filaments and an analog of the Crow instability is found at small wave-numbers.
A local approximate Hamiltonian is obtained for the nonlinear long-scale
dynamics of this system. Self-similar solutions of the corresponding equations
are found analytically. They describe the formation of a finite time
singularity, with all length scales decreasing like ,
where is the singularity time.Comment: LaTeX, 17 pages, 3 eps figures. This version is close to the journal
pape
Baxter Q-operator and Separation of Variables for the open SL(2,R) spin chain
We construct the Baxter Q-operator and the representation of the Separated
Variables (SoV) for the homogeneous open SL(2,R) spin chain. Applying the
diagrammatical approach, we calculate Sklyanin's integration measure in the
separated variables and obtain the solution to the spectral problem for the
model in terms of the eigenvalues of the Q-operator. We show that the
transition kernel to the SoV representation is factorized into the product of
certain operators each depending on a single separated variable. As a
consequence, it has a universal pyramid-like form that has been already
observed for various quantum integrable models such as periodic Toda chain,
closed SL(2,R) and SL(2,C) spin chains.Comment: 29 pages, 9 figures, Latex styl
Instabilities in the two-dimensional cubic nonlinear Schrodinger equation
The two-dimensional cubic nonlinear Schrodinger equation (NLS) can be used as
a model of phenomena in physical systems ranging from waves on deep water to
pulses in optical fibers. In this paper, we establish that every
one-dimensional traveling wave solution of NLS with trivial phase is unstable
with respect to some infinitesimal perturbation with two-dimensional structure.
If the coefficients of the linear dispersion terms have the same sign then the
only unstable perturbations have transverse wavelength longer than a
well-defined cut-off. If the coefficients of the linear dispersion terms have
opposite signs, then there is no such cut-off and as the wavelength decreases,
the maximum growth rate approaches a well-defined limit.Comment: 4 pages, 4 figure
Stability of trapped Bose-Einstein condensates
In three-dimensional trapped Bose-Einstein condensate (BEC), described by the
time-dependent Gross-Pitaevskii-Ginzburg equation, we study the effect of
initial conditions on stability using a Gaussian variational approach and exact
numerical simulations. We also discuss the validity of the criterion for
stability suggested by Vakhitov and Kolokolov. The maximum initial chirp
(initial focusing defocusing of cloud) that can lead a stable condensate to
collapse even before the number of atoms reaches its critical limit is obtained
for several specific cases. When we consider two- and three-body nonlinear
terms, with negative cubic and positive quintic terms, we have the conditions
for the existence of two phases in the condensate. In this case, the magnitude
of the oscillations between the two phases are studied considering sufficient
large initial chirps. The occurrence of collapse in a BEC with repulsive
two-body interaction is also shown to be possible.Comment: 15 pages, 11 figure
Transverse instability and its long-term development for solitary waves of the (2+1)-Boussinesq equation
The stability properties of line solitary wave solutions of the
(2+1)-dimensional Boussinesq equation with respect to transverse perturbations
and their consequences are considered. A geometric condition arising from a
multi-symplectic formulation of this equation gives an explicit relation
between the parameters for transverse instability when the transverse
wavenumber is small. The Evans function is then computed explicitly, giving the
eigenvalues for transverse instability for all transverse wavenumbers. To
determine the nonlinear and long time implications of transverse instability,
numerical simulations are performed using pseudospectral discretization. The
numerics confirm the analytic results, and in all cases studied, transverse
instability leads to collapse.Comment: 16 pages, 8 figures; submitted to Phys. Rev.
Measurement of and Structure Functions in Low Region with the IHEP-JINR Neutrino Detector
The isoscalar structure functions and are measured as functions
of averaged over all permissible for the range of 6 to 28 GeV of
incident neutrino (anti-neutrino) energy at the IHEP-JINR Neutrino Detector.
The QCD analysis of structure function provides
MeV under the assumption of QCD
validity in the region of low . The corresponding value of the strong
interaction constant agrees with the
recent result of the CCFR collaboration and with the combined LEP/SLC result.Comment: 11 pages, 1 Postscript figure, LaTeX. Talk given at the 7th
International Workshop on Deep Inelastic Scattering and QCD (DIS 99),
Zeuthen, Germany, 19-23 Apr 199
Separation of variables for the quantum SL(2,R) spin chain
We construct representation of the Separated Variables (SoV) for the quantum
SL(2,R) Heisenberg closed spin chain and obtain the integral representation for
the eigenfunctions of the model. We calculate explicitly the Sklyanin measure
defining the scalar product in the SoV representation and demonstrate that the
language of Feynman diagrams is extremely useful in establishing various
properties of the model. The kernel of the unitary transformation to the SoV
representation is described by the same "pyramid diagram" as appeared before in
the SoV representation for the SL(2,C) spin magnet. We argue that this kernel
is given by the product of the Baxter Q-operators projected onto a special
reference state.Comment: 26 pages, Latex style, 9 figures. References corrected, minor
stylistic changes, version to be publishe
Current-sheet formation in incompressible electron magnetohydrodynamics
The nonlinear dynamics of axisymmetric, as well as helical, frozen-in vortex
structures is investigated by the Hamiltonian method in the framework of ideal
incompressible electron magnetohydrodynamics. For description of current-sheet
formation from a smooth initial magnetic field, local and nonlocal nonlinear
approximations are introduced and partially analyzed that are generalizations
of the previously known exactly solvable local model neglecting electron
inertia. Finally, estimations are made that predict finite-time singularity
formation for a class of hydrodynamic models intermediate between that local
model and the Eulerian hydrodynamics.Comment: REVTEX4, 5 pages, no figures. Introduction rewritten, new material
and references adde
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