1,615 research outputs found
Weakly-nonlocal Symplectic Structures, Whitham method, and weakly-nonlocal Symplectic Structures of Hydrodynamic Type
We consider the special type of the field-theoretical Symplectic structures
called weakly nonlocal. The structures of this type are in particular very
common for the integrable systems like KdV or NLS. We introduce here the
special class of the weakly nonlocal Symplectic structures which we call the
weakly nonlocal Symplectic structures of Hydrodynamic Type. We investigate then
the connection of such structures with the Whitham averaging method and propose
the procedure of "averaging" of the weakly nonlocal Symplectic structures. The
averaging procedure gives the weakly nonlocal Symplectic Structure of
Hydrodynamic Type for the corresponding Whitham system. The procedure gives
also the "action variables" corresponding to the wave numbers of -phase
solutions of initial system which give the additional conservation laws for the
Whitham system.Comment: 64 pages, Late
Quasiperiodic functions theory and the superlattice potentials for a two-dimensional electron gas
We consider Novikov problem of the classification of level curves of
quasiperiodic functions on the plane and its connection with the conductivity
of two-dimensional electron gas in the presence of both orthogonal magnetic
field and the superlattice potentials of special type. We show that the
modulation techniques used in the recent papers on the 2D heterostructures
permit to obtain the general quasiperiodic potentials for 2D electron gas and
consider the asymptotic limit of conductivity when . Using the
theory of quasiperiodic functions we introduce here the topological
characteristics of such potentials observable in the conductivity. The
corresponding characteristics are the direct analog of the "topological
numbers" introduced previously in the conductivity of normal metals.Comment: Revtex, 16 pages, 12 figure
Calculation of the moscovium ground-state energy by quantum algorithms
We investigate the possibility to calculate the ground-state energy of the
atomic systems on a quantum computer. For this purpose we evaluate the lowest
binding energy of the moscovium atom with the use of the iterative phase
estimation and variational quantum eigensolver. The calculations by the
variational quantum eigensolver are performed with a disentangled unitary
coupled cluster ansatz and with various types of hardware-efficient ansatze.
The optimization is performed with the use of the Adam and Quantum Natural
Gradients procedures. The scalability of the ansatze and optimizers is tested
by increasing the size of the basis set and the number of active electrons. The
number of gates required for the iterative phase estimation and variational
quantum eigensolver is also estimated.Comment: 29 pages, 5 figure
Relativistic calculations of the K-K charge transfer and K-vacancy production probabilities in low-energy ion-atom collisions
The previously developed technique for evaluation of charge-transfer and
electron-excitation processes in low-energy heavy-ion collisions [I.I. Tupitsyn
et al., Phys. Rev. A 82, 042701(2010)] is extended to collisions of ions with
neutral atoms. The method employs the active electron approximation, in which
only the active electron participates in the charge transfer and excitation
processes while the passive electrons provide the screening DFT potential. The
time-dependent Dirac wave function of the active electron is represented as a
linear combination of atomic-like Dirac-Fock-Sturm orbitals, localized at the
ions (atoms). The screening DFT potential is calculated using the overlapping
densities of each ions (atoms), derived from the atomic orbitals of the passive
electrons. The atomic orbitals are generated by solving numerically the
one-center Dirac-Fock and Dirac-Fock-Sturm equations by means of a
finite-difference approach with the potential taken as the sum of the exact
reference ion (atom) Dirac-Fock potential and of the Coulomb potential from the
other ion within the monopole approximation. The method developed is used to
calculate the K-K charge transfer and K-vacancy production probabilties for the
Ne -- F collisions at the F projectile
energies 130 keV/u and 230 keV/u. The obtained results are compared with
experimental data and other theoretical calculations. The K-K charge transfer
and K-vacancy production probabilities are also calculated for the Xe --
Xe collision.Comment: 16 pages, 4 figure
Vibrational spectroscopy of GdCr3(BO3)4: Quantitative separation of crystalline phases
This work is devoted to the investigation of GdCr3(BO3)4 crystals by the method of infrared spectroscopy. Incongruently melting borate GdCr3(BO3)4 was obtained as a result of spontaneous crystallization. Crystal structures were identified by the method of infrared spectroscopy. Ab initio calculations in the frame of density functional theory enabled us to separate modes belonging to the R32 and C2/c phases and to estimate the ratio of these phases in GdCr3(BO3)4 crystals. We have found that the content of the rhombohedral R32 (non- centrosymmetric) modification is about 85%. © Published under licence by IOP Publishing Ltd
Reciprocal transformations of Hamiltonian operators of hydrodynamic type: nonlocal Hamiltonian formalism for linearly degenerate systems
Reciprocal transformations of Hamiltonian operators of hydrodynamic type are
investigated. The transformed operators are generally nonlocal, possessing a
number of remarkable algebraic and differential-geometric properties. We apply
our results to linearly degenerate semi-Hamiltonian systems in Riemann
invariants. Since all such systems are linearizable by appropriate
(generalized) reciprocal transformations, our formulae provide an infinity of
mutually compatible nonlocal Hamiltonian structures, explicitly parametrized by
arbitrary functions of one variable.Comment: 26 page
High-Speed Traffic Is the Future Railway Transport
В статье рассмотрены основные аспекты программы строительства высокоскоростной магистрали в России и новые технологии для создания скоростных железных дорог.The article discusses the main aspects of the high-speed railway construction program in Russia and new technologies for creating high-speed Railways
On the water-bag model of dispersionless KP hierarchy
We investigate the bi-Hamiltonian structure of the waterbag model of dKP for
two component case. One can establish the third-order and first-order
Hamiltonian operator associated with the waterbag model. Also, the dispersive
corrections are discussed.Comment: 19 page
Solvable Lie algebras with triangular nilradicals
All finite-dimensional indecomposable solvable Lie algebras , having
the triangular algebra T(n) as their nilradical, are constructed. The number of
nonnilpotent elements in satisfies and the
dimension of the Lie algebra is
Whitham systems and deformations
We consider the deformations of Whitham systems including the "dispersion
terms" and having the form of Dubrovin-Zhang deformations of Frobenius
manifolds. The procedure is connected with B.A. Dubrovin problem of
deformations of Frobenius manifolds corresponding to the Whitham systems of
integrable hierarchies. Under some non-degeneracy requirements we suggest a
general scheme of the deformation of the hyperbolic Whitham systems using the
initial non-linear system. The general form of the deformed Whitham system
coincides with the form of the "low-dispersion" asymptotic expansions used by
B.A. Dubrovin and Y. Zhang in the theory of deformations of Frobenius
manifolds.Comment: 27 pages, Late
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