4,153 research outputs found
Internal Time Peculiarities as a Cause of Bifurcations Arising in Classical Trajectory Problem and Quantum Chaos Creation in Three-Body System
A new formulation of the theory of quantum mechanical multichannel scattering
for three-body collinear systems is proposed. It is shown, that in this simple
case the principle of quantum determinism in the general case breaks down and
we have a micro-irreversible quantum mechanics. The first principle
calculations of the quantum chaos (wave chaos) were pursued on the example of
an elementary chemical reaction Li+(FH)->(LiFH)*->(LiF)+H.Comment: 7 pages, 3 figures, accepted for publication in Int. J. of
Bifurcation & Chao
Grassmannians Gr(N-1,N+1), closed differential N-1 forms and N-dimensional integrable systems
Integrable flows on the Grassmannians Gr(N-1,N+1) are defined by the
requirement of closedness of the differential N-1 forms of rank
N-1 naturally associated with Gr(N-1,N+1). Gauge-invariant parts of these
flows, given by the systems of the N-1 quasi-linear differential equations,
describe coisotropic deformations of (N-1)-dimensional linear subspaces. For
the class of solutions which are Laurent polynomials in one variable these
systems coincide with N-dimensional integrable systems such as Liouville
equation (N=2), dispersionless Kadomtsev-Petviashvili equation (N=3),
dispersionless Toda equation (N=3), Plebanski second heavenly equation (N=4)
and others. Gauge invariant part of the forms provides us with
the compact form of the corresponding hierarchies. Dual quasi-linear systems
associated with the projectively dual Grassmannians Gr(2,N+1) are defined via
the requirement of the closedness of the dual forms . It
is shown that at N=3 the self-dual quasi-linear system, which is associated
with the harmonic (closed and co-closed) form , coincides with the
Maxwell equations for orthogonal electric and magnetic fields.Comment: 26 pages, references adde
On the heavenly equation hierarchy and its reductions
Second heavenly equation hierarchy is considered using the framework of
hyper-K\"ahler hierarchy developed by Takasaki. Generating equations for the
hierarchy are introduced, they are used to construct generating equations for
reduced hierarchies. General -reductions, logarithmic reduction and rational
reduction for one of the Lax-Sato functions are discussed. It is demonstrated
that rational reduction is equivalent to the symmetry constraint.Comment: 13 pages, LaTeX, minor misprints corrected, references adde
Chiral Skyrmionic matter in non-centrosymmetric magnets
Axisymmetric magnetic strings with a fixed sense of rotation and nanometer
sizes (chiral magnetic vortices or Skyrmions) have been predicted to exist in a
large group of non-centrosymmetric crystals more than two decades ago. Recently
these extraordinary magnetic states have been directly observed in thin layers
of cubic helimagnet (Fe,Co)Si. In this report we apply our earlier theoretical
findings to review main properties of chiral Skyrmions, to elucidate their
physical nature, and to analyse these recent experimental results on
magnetic-field-driven evolution of Skyrmions and helicoids in chiral
helimagnets.Comment: 13 pages, 7 figures, invited talk - JEMS-2010 ( 23-28 August, Krakow,
Poland
Lattice and q-difference Darboux-Zakharov-Manakov systems via -dressing method
A general scheme is proposed for introduction of lattice and q-difference
variables to integrable hierarchies in frame of -dressing
method . Using this scheme, lattice and q-difference Darboux-Zakharov-Manakov
systems of equations are derived. Darboux, B\"acklund and Combescure
transformations and exact solutions for these systems are studied.Comment: 8 pages, LaTeX, to be published in J Phys A, Letters
New Perturbation Theory for Nonstationary Anharmonic Oscillator
The new perturbation theory for the problem of nonstationary anharmonic
oscillator with polynomial nonstationary perturbation is proposed. As a zero
order approximation the exact wave function of harmonic oscillator with
variable frequency in external field is used. Based on some intrinsic
properties of unperturbed wave function the variational-iterational method is
proposed, that make it possible to correct both the amplitude and the phase of
wave function. As an application the first order correction are proposed both
for wave function and S-matrix elements for asymmetric perturbation potential
of type The transition amplitude
''ground state - ground state'' is analyzed in detail
depending on perturbation parameter (including strong coupling
region ) and one-dimensional refraction coefficient .Comment: LaTeX, 13 page
Statistical Estimation of Quantum Tomography Protocols Quality
A novel operational method for estimating the efficiency of quantum state
tomography protocols is suggested. It is based on a-priori estimation of the
quality of an arbitrary protocol by means of universal asymptotic fidelity
distribution and condition number, which takes minimal value for better
protocol. We prove the adequacy of the method both with numerical modeling and
through the experimental realization of several practically important protocols
of quantum state tomography
Intermediate phase in the spiral antiferromagnet Ba_2CuGe_2O_7
The magnetic compound Ba_2CuGe_2O_7 has recently been shown to be an
essentially two-dimensional spiral antiferromagnet that exhibits an
incommensurate-to-commensurate phase transition when a magnetic field applied
along the c-axis exceeds a certain critical value H_c. The T=0 dynamics is
described here in terms of a continuum field theory in the form of a nonlinear
sigma model. We are thus in a position to carry out a complete calculation of
the low-energy magnon spectrum for any strength of the applied field throughout
the phase transition. In particular, our spin-wave analysis reveals
field-induced instabilities at two distinct critical fields H_1 and H_2 such
that H_1 < H_c < H_2. Hence we predict the existence of an intermediate phase
whose detailed nature is also studied to some extent in the present paper.Comment: 15 pages, 11 figures, 2 table
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