213,244 research outputs found
Solitary Waves Bifurcated from Bloch Band Edges in Two-dimensional Periodic Media
Solitary waves bifurcated from edges of Bloch bands in two-dimensional
periodic media are determined both analytically and numerically in the context
of a two-dimensional nonlinear Schr\"odinger equation with a periodic
potential. Using multi-scale perturbation methods, envelope equations of
solitary waves near Bloch bands are analytically derived. These envelope
equations reveal that solitary waves can bifurcate from edges of Bloch bands
under either focusing or defocusing nonlinearity, depending on the signs of
second-order dispersion coefficients at the edge points. Interestingly, at edge
points with two linearly independent Bloch modes, the envelope equations lead
to a host of solitary wave structures including reduced-symmetry solitons,
dipole-array solitons, vortex-cell solitons, and so on -- many of which have
never been reported before. It is also shown analytically that the centers of
envelope solutions can only be positioned at four possible locations at or
between potential peaks. Numerically, families of these solitary waves are
directly computed both near and far away from band edges. Near the band edges,
the numerical solutions spread over many lattice sites, and they fully agree
with the analytical solutions obtained from envelope equations. Far away from
the band edges, solitary waves are strongly localized with intensity and phase
profiles characteristic of individual families.Comment: 23 pages, 15 figures. To appear in Phys. Rev.
Antiferromagnetic spin phase transition in nuclear matter with effective Gogny interaction
The possibility of ferromagnetic and antiferromagnetic phase transitions in
symmetric nuclear matter is analyzed within the framework of a Fermi liquid
theory with the effective Gogny interaction. It is shown that at some critical
density nuclear matter with D1S effective force undergoes a phase transition to
the antiferromagnetic spin state (the opposite direction of neutron and proton
spins). The self--consistent equations of spin polarized nuclear matter with
D1S force have no solutions, corresponding to the ferromagnetic spin ordering
(the same direction of neutron and proton spins) and, hence, the ferromagnetic
transition does not appear. The dependence of antiferromagnetic spin
polarization parameter as a function of density is found at zero temperature.Comment: Report at the workshop "Hot points in astrophysics and cosmology",
Dubna, August, 2-13, 2004. REVTeX4, 9 pages, 3 figure
Asymmetric vortex solitons in nonlinear periodic lattices
We reveal the existence of asymmetric vortex solitons in ideally symmetric
periodic lattices, and show how such nonlinear localized structures describing
elementary circular flows can be analyzed systematically using the
energy-balance relations. We present the examples of rhomboid, rectangular, and
triangular vortex solitons on a square lattice, and also describe novel
coherent states where the populations of clockwise and anti-clockwise vortex
modes change periodically due to a nonlinearity-induced momentum exchange
through the lattice. Asymmetric vortex solitons are expected to exist in
different nonlinear lattice systems including optically-induced photonic
lattices, nonlinear photonic crystals, and Bose-Einstein condensates in optical
lattices.Comment: 4 pages, 5 figure
Spin polarized states in neutron matter at a strong magnetic field
Spin polarized states in neutron matter at a strong magnetic field are
considered in the model with the Skyrme effective interaction (SLy4, SLy7
parametrizations). Analyzing the self-consistent equations at zero temperature,
it is shown that a thermodynamically stable branch of solutions for the spin
polarization parameter as a function of density corresponds to the negative
spin polarization when the majority of neutron spins are oriented oppositely to
the direction of the magnetic field. Besides, beginning from some threshold
density being dependent on the magnetic field strength the self-consistent
equations have also two other branches (upper and lower) of solutions for the
spin polarization parameter with the positive spin polarization.
The free energy corresponding to the upper branch turns out to be very close
to the free energy corresponding to the thermodynamically preferable branch
with the negative spin polarization. As a consequence, at a strong magnetic
field, the state with the positive spin polarization can be realized as a
metastable state at the high density region in neutron matter which under
decreasing density at some threshold density changes into a thermodynamically
stable state with the negative spin polarization. The calculations of the
neutron spin polarization parameter and energy per neutron as functions of the
magnetic field strength show that the influence of the magnetic field remains
small at the field strengths up to G.Comment: Prepared with RevTeX4, 8pp., 5 figs; v.2: matches published versio
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