526 research outputs found
Modified Gibbs's representation of rotation matrix
A modified Gibbs's rotation matrix is derived and the connection with the
Euler angles, quaternions, and CayleyKlein parameters is established. As
particular cases, the Rodrigues and Gibbs parameterizations of the rotation are
obtained. The composition law of two rotations from the quaternion
representation is presented showing a convenient expression for calculating the
successive rotations.Comment: 17 page
A dense Bose fluid at zero temperature: condensation and clusters in liquid He-4
We present a full set of wave equations describing a dense Bose fluid,
applicable both to non- ideal gases and to liquid 4He. The phonon spectrum in
liquid 4He is found and the fraction of condensed particles is calculated at
zero temperature for a wide range of densities. The theory also yields the
ground-state energy for the quantum liquid 4He in agreement to high accuracy
with Monte Carlo simulations and experimental data at low pressure. We also
present the derivation of a generalized Hartree-Fock equation describing roton
clusters in low temperature liquid 4He, allowing us to confirm that, at low
enough temperatures and for a wide range of pressures, the stable clusters
consist of 13 bound atoms.Comment: 16 pages, 7 figure
Kalb-Ramond fields in the Petiau-Duffin-Kemmer formalism and scale invariance
Kalb-Ramond equations for massive and massless particles are considered in
the framework of the Petiau-Duffin-Kemmer formalism. We obtain
matrices of the relativistic wave equation of the first-order and solutions in
the form of density matrix. The canonical and Belinfante energy-momentum
tensors are found. We investigate the scale invariance and obtain the conserved
dilatation current. It was demonstrated that the conformal symmetry is broken
even for massless fields.Comment: 9 pages, no figure
Effective Lagrangian and Dynamical Symmetry Breaking in the SU(2)XU(1) NJL Model
Dynamical symmetry breaking and the formation of scalar condensates in the
SU(2)XU(1) Nambu-Jona-Lasinio model with two coupling constants has been
studied in the framework of the mean field approximation. The bosonization
procedures of the model are performed using the functional integration method.
The possibility of the spontaneous CP symmetry breaking in the model under
consideration has been shown. The mass spectrum of the bound states of
fermions, as well as the effective Lagrangian of interacting scalar and
pseudoscalar mesons are obtained.Comment: 7 pages, LaTeX. Minor correction
Solutions of Podolsky's Electrodynamics Equation in the First-Order Formalism
The Podolsky generalized electrodynamics with higher derivatives is
formulated in the first-order formalism. The first-order relativistic wave
equation in the 20-dimensional matrix form is derived. We prove that the
matrices of the equation obey the Petiau-Duffin-Kemmer algebra. The
Hermitianizing matrix and Lagrangian in the first-order formalism are given.
The projection operators extracting solutions of field equations for states
with definite energy-momentum and spin projections are obtained, and we find
the density matrix for the massive state. The -matrix Schrodinger
form of the equation is derived, and the Hamiltonian is obtained. Projection
operators extracting the physical eigenvalues of the Hamiltonian are found.Comment: 17 pages, minor corrections, published versio
Effects of x(3) nonlinearities in traveling-wave second-harmonic generation
We investigate the effects of self-phase and cross-phase chi ((3)) nonlinearities, in the process of traveling-wave second-harmonic generation. We derive a semiclassical analytical solution for the field intensities, comparing this with the numerically obtained fully quantum solutions. We also investigate the effects of the cross-phase modulation on the quantum statistical properties of the fields. We find that, as the chi ((3)) components increase, there are qualitative changes to both the field intensities and the quantum statistics
On Hyperbolic Attractors in Complex Shimizu -- Morioka Model
We present a modified complex-valued Shimizu -- Morioka system with uniformly
hyperbolic attractor. The numerically observed attractor in Poincar\'{e}
cross-section is topologically close to Smale -- Williams solenoid. The
arguments of the complex variables undergo Bernoulli-type map, essential for
Smale -- Williams attractor, due to the geometrical arrangement of the phase
space and an additional perturbation term. The transformation of the phase
space near the saddle equilibrium "scatters" trajectories to new angles, then
trajectories run from the saddle and return to it for the next "scatter". We
provide the results of numerical simulations of the model and demonstrate
typical features of the appearing hyperbolic attractor of Smale -- Williams
type. Importantly, we show in numerical tests the transversality of tangent
subspaces -- a pivotal property of uniformly hyperbolic attractor.Comment: 9 pages, 8 figure
Stabilization of a light bullet in a layered Kerr medium with sign-changing nonlinearity
Using the numerical solution of the nonlinear Schr\"odinger equation and a
variational method it is shown that (3+1)-dimensional spatiotemporal optical
solitons, known as light bullets, can be stabilized in a layered Kerr medium
with sign-changing nonlinearity along the propagation direction.Comment: 4 pages, 3 PS figure
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