3,413 research outputs found
Motion Caused by Magnetic Field in Lobachevsky Space
We study motion of a relativistic particle in the 3-dimensional Lobachevsky
space in the presence of an external magnetic field which is analogous to a
constant uniform magnetic field in the Euclidean space. Three integrals of
motion are found and equations of motion are solved exactly in the special
cylindrical coordinates. Motion on surface of the cylinder of constant radius
is considered in detail.Comment: 4 page
Classical Particle in Presence of Magnetic Field, Hyperbolic Lobachevsky and Spherical Riemann Models
Motion of a classical particle in 3-dimensional Lobachevsky and Riemann
spaces is studied in the presence of an external magnetic field which is
analogous to a constant uniform magnetic field in Euclidean space. In both
cases three integrals of motions are constructed and equations of motion are
solved exactly in the special cylindrical coordinates on the base of the method
of separation of variables. In Lobachevsky space there exist trajectories of
two types, finite and infinite in radial variable, in Riemann space all motions
are finite and periodical. The invariance of the uniform magnetic field in
tensor description and gauge invariance of corresponding 4-potential
description is demonstrated explicitly. The role of the symmetry is clarified
in classification of all possible solutions, based on the geometric symmetry
group, SO(3,1) and SO(4) respectively
Study of Stability of a Charged Topological Soliton in the System of Two Interacting Scalar Fields
An analytical-numerical analysis of the singular self-adjoint spectral
problem for a system of three linear ordinary second-order differential
equations defined on the entire real exis is presented. This problem comes to
existence in the nonlinear field theory. The dependence of the differential
equations on the spectral parameter is nonlinear, which results in a quadratic
operator Hermitian pencil.Comment: 22 pages, 2 figure
Practical cryptographic strategies in the post-quantum era
We review new frontiers in information security technologies in
communications and distributed storage technologies with the use of classical,
quantum, hybrid classical-quantum, and post-quantum cryptography. We analyze
the current state-of-the-art, critical characteristics, development trends, and
limitations of these techniques for application in enterprise information
protection systems. An approach concerning the selection of practical
encryption technologies for enterprises with branched communication networks is
introduced.Comment: 5 pages, 2 figures; review pape
Synthesis of the Einstein-Podolsky-Rosen entanglement in a sequence of two single-mode squeezers
Synthesis of the Einstein-Podolsky-Rosen entangled state --- the primary
entangled resource in continuous-variable quantum-optical information
processing --- is a technological challenge of great importance. Here we
propose and implement a new scheme of generating this state. Two nonlinear
optical crystals, positioned back-to-back in the waist of a pump beam, function
as single-pass degenerate optical parametric amplifiers and produce single-mode
squeezed vacuum states in orthogonal polarization modes, but in the same
spatiotemporal mode. A subsequent pair of waveplates acts as a beam splitter,
entangling the two polarization modes to generate the Einstein-Podolsky-Rosen
state. This technique takes advantage of the strong nonlinearity associated
with type-I phase-matching configuration while at the same time eliminating the
need for actively stabilizing the optical phase between the two squeezers,
which typically arises if these squeezers are spatially separated. We
demonstrate our method in an experiment, preparing a 1.4 dB two-mode squeezed
state and characterizing it via two-mode homodyne tomography.Comment: 4 pages, 3 figure
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