38 research outputs found
On the driven Frenkel-Kontorova model: I. Uniform sliding states and dynamical domains of different particle densities
The dynamical behavior of a harmonic chain in a spatially periodic potential
(Frenkel-Kontorova model, discrete sine-Gordon equation) under the influence of
an external force and a velocity proportional damping is investigated. We do
this at zero temperature for long chains in a regime where inertia and damping
as well as the nearest-neighbor interaction and the potential are of the same
order. There are two types of regular sliding states: Uniform sliding states,
which are periodic solutions where all particles perform the same motion
shifted in time, and nonuniform sliding states, which are quasi-periodic
solutions where the system forms patterns of domains of different uniform
sliding states. We discuss the properties of this kind of pattern formation and
derive equations of motion for the slowly varying average particle density and
velocity. To observe these dynamical domains we suggest experiments with a
discrete ring of at least fifty Josephson junctions.Comment: Written in RevTeX, 9 figures in PostScrip
Stability of traveling waves in a driven Frenkel–Kontorova model
In this work we revisit a classical problem of traveling waves in a damped Frenkel–Kontorova lattice driven by a constant external force. We compute these solutions as fixed points of a nonlinear map and obtain the corresponding kinetic relation between the driving force and the velocity of the wave for different values of the damping coefficient. We show that the kinetic curve can become non-monotone at small velocities, due to resonances with linear modes, and also at large velocities where the kinetic relation becomes multivalued. Exploring the spectral stability of the obtained waveforms, we identify, at the level of numerical accuracy of our computations, a precise criterion for instability of the traveling wave solutions: monotonically decreasing portions of the kinetic curve always bear an unstable eigendirection. We discuss why the validity of this criterion in the dissipative setting is a rather remarkable feature offering connections to the Hamiltonian variant of the model and of lattice traveling waves more generally. Our stability results are corroborated by direct numerical simulations which also reveal the possible outcomes of dynamical instabilities.AEI/FEDER, (UE) MAT2016-79866-
Fragmentation of Fast Josephson Vortices and Breakdown of Ordered States by Moving Topological Defects
Topological defects such as vortices, dislocations or domain walls define
many important effects in superconductivity, superfluidity, magnetism, liquid
crystals, and plasticity of solids. Here we address the breakdown of the
topologically-protected stability of such defects driven by strong external
forces. We focus on Josephson vortices that appear at planar weak links of
suppressed superconductivity which have attracted much attention for electronic
applications, new sources of THz radiation, and low-dissipative computing. Our
numerical simulations show that a rapidly moving vortex driven by a constant
current becomes unstable with respect to generation of vortex-antivortex pairs
caused by Cherenkov radiation. As a result, vortices and antivortices become
spatially separated and accumulate continuously on the opposite sides of an
expanding dissipative domain. This effect is most pronounced in thin film edge
Josephson junctions at low temperatures where a single vortex can switch the
whole junction into a resistive state at currents well below the Josephson
critical current. Our work gives a new insight into instability of a moving
topological defect which destroys global long-range order in a way that is
remarkably similar to the crack propagation in solids.Comment: Sci. Rep. 5, 1782
Resonant steps and spatiotemporal dynamics in the damped dc-driven Frenkel-Kontorova chain
Kink dynamics of the damped Frenkel-Kontorova (discrete sine-Gordon) chain
driven by a constant external force are investigated. Resonant steplike
transitions of the average velocity occur due to the competitions between the
moving kinks and their radiated phasonlike modes. A mean-field consideration is
introduced to give a precise prediction of the resonant steps. Slip-stick
motion and spatiotemporal dynamics on those resonant steps are discussed. Our
results can be applied to studies of the fluxon dynamics of 1D
Josephson-junction arrays and ladders, dislocations, tribology and other
fields.Comment: 20 Plain Latex pages, 10 Eps figures, to appear in Phys. Rev.
Spontaneous nucleation of structural defects in inhomogeneous ion chains
Structural defects in ion crystals can be formed during a linear quench of
the transverse trapping frequency across the mechanical instability from a
linear chain to the zigzag structure. The density of defects after the sweep
can be conveniently described by the Kibble-Zurek mechanism. In particular, the
number of kinks in the zigzag ordering can be derived from a time-dependent
Ginzburg-Landau equation for the order parameter, here the zigzag transverse
size, under the assumption that the ions are continuously laser cooled. In a
linear Paul trap the transition becomes inhomogeneous, being the charge density
larger in the center and more rarefied at the edges. During the linear quench
the mechanical instability is first crossed in the center of the chain, and a
front, at which the mechanical instability is crossed during the quench, is
identified which propagates along the chain from the center to the edges. If
the velocity of this front is smaller than the sound velocity, the dynamics
becomes adiabatic even in the thermodynamic limit and no defect is produced.
Otherwise, the nucleation of kinks is reduced with respect to the case in which
the charges are homogeneously distributed, leading to a new scaling of the
density of kinks with the quenching rate. The analytical predictions are
verified numerically by integrating the Langevin equations of motion of the
ions, in presence of a time-dependent transverse confinement. We argue that the
non-equilibrium dynamics of an ion chain in a Paul trap constitutes an ideal
scenario to test the inhomogeneous extension of the Kibble-Zurek mechanism,
which lacks experimental evidence to date.Comment: 19 pages, 5 figure