186 research outputs found
Theory for a dissipative droplet soliton excited by a spin torque nanocontact
A novel type of solitary wave is predicted to form in spin torque oscillators
when the free layer has a sufficiently large perpendicular anisotropy. In this
structure, which is a dissipative version of the conservative droplet soliton
originally studied in 1977 by Ivanov and Kosevich, spin torque counteracts the
damping that would otherwise destroy the mode. Asymptotic methods are used to
derive conditions on perpendicular anisotropy strength and applied current
under which a dissipative droplet can be nucleated and sustained. Numerical
methods are used to confirm the stability of the droplet against various
perturbations that are likely in experiments, including tilting of the applied
field, non-zero spin torque asymmetry, and non-trivial Oersted fields. Under
certain conditions, the droplet experiences a drift instability in which it
propagates away from the nanocontact and is then destroyed by damping.Comment: 15 pages, 12 figure
On phenomenon of scattering on resonances associated with discretisation of systems with fast rotating phase
Numerical integration of ODEs by standard numerical methods reduces a
continuous time problems to discrete time problems. Discrete time problems have
intrinsic properties that are absent in continuous time problems. As a result,
numerical solution of an ODE may demonstrate dynamical phenomena that are
absent in the original ODE. We show that numerical integration of system with
one fast rotating phase lead to a situation of such kind: numerical solution
demonstrate phenomenon of scattering on resonances that is absent in the
original system.Comment: 10 pages, 5 figure
Optimal Constraint Projection for Hyperbolic Evolution Systems
Techniques are developed for projecting the solutions of symmetric hyperbolic
evolution systems onto the constraint submanifold (the constraint-satisfying
subset of the dynamical field space). These optimal projections map a field
configuration to the ``nearest'' configuration in the constraint submanifold,
where distances between configurations are measured with the natural metric on
the space of dynamical fields. The construction and use of these projections is
illustrated for a new representation of the scalar field equation that exhibits
both bulk and boundary generated constraint violations. Numerical simulations
on a black-hole background show that bulk constraint violations cannot be
controlled by constraint-preserving boundary conditions alone, but are
effectively controlled by constraint projection. Simulations also show that
constraint violations entering through boundaries cannot be controlled by
constraint projection alone, but are controlled by constraint-preserving
boundary conditions. Numerical solutions to the pathological scalar field
system are shown to converge to solutions of a standard representation of the
scalar field equation when constraint projection and constraint-preserving
boundary conditions are used together.Comment: final version with minor changes; 16 pages, 14 figure
Vector-soliton collision dynamics in nonlinear optical fibers
We consider the interactions of two identical, orthogonally polarized vector
solitons in a nonlinear optical fiber with two polarization directions,
described by a coupled pair of nonlinear Schroedinger equations. We study a
low-dimensional model system of Hamiltonian ODE derived by Ueda and Kath and
also studied by Tan and Yang. We derive a further simplified model which has
similar dynamics but is more amenable to analysis. Sufficiently fast solitons
move by each other without much interaction, but below a critical velocity the
solitons may be captured. In certain bands of initial velocities the solitons
are initially captured, but separate after passing each other twice, a
phenomenon known as the two-bounce or two-pass resonance. We derive an analytic
formula for the critical velocity. Using matched asymptotic expansions for
separatrix crossing, we determine the location of these "resonance windows."
Numerical simulations of the ODE models show they compare quite well with the
asymptotic theory.Comment: 32 pages, submitted to Physical Review
Duality in Perturbation Theory and the Quantum Adiabatic Approximation
Duality is considered for the perturbation theory by deriving, given a series
solution in a small parameter, its dual series with the development parameter
being the inverse of the other. A dual symmetry in perturbation theory is
identified. It is then shown that the dual to the Dyson series in quantum
mechanics is given by a recent devised series having the adiabatic
approximation as leading order. A simple application of this result is given by
rederiving a theorem for strongly perturbed quantum systems.Comment: 9 pages, revtex. Improved english and presentation. Final version
accepted for publication by Physical Review
Rosen-Zener model in cold molecule formation
The Rosen-Zener model for association of atoms in a Bose-Einstein condensate
is studied. Using a nonlinear Volterra integral equation, we obtain an analytic
formula for final probability of the transition to the molecular state for weak
interaction limit. Considering the strong coupling limit of high field
intensities, we show that the system reveals two different time-evolution
pictures depending on the detuning of the frequency of the associating field.
For both limit cases we derive highly accurate formulas for the molecular state
probability valid for the whole range of variation of time. Using these
formulas, we show that at large detuning regime the molecule formation process
occurs almost non-oscillatory in time and a Rosen-Zener pulse is not able to
associate more than one third of atoms at any time point. The system returns to
its initial all-atomic state at the end of the process and the maximal
transition probability is achieved when the field intensity reaches its peak.
In contrast, at small detuning the evolution of the system displays
large-amplitude oscillations between atomic and molecular populations. We find
that the shape of the oscillations in the first approximation is defined by the
field detuning only. Finally, a hidden singularity of the Rosen-Zener model due
to the specific time-variation of the field amplitude at the beginning of the
interaction is indicated. It is this singularity that stands for many of the
qualitative and quantitative properties of the model. The singularity may be
viewed as an effective resonance-touching
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