15 research outputs found
Hamiltonian Formalism of the de-Sitter Invariant Special Relativity
Lagrangian of the Einstein's special relativity with universal parameter
() is invariant under Poincar\'e transformation which preserves
Lorentz metric . The has been extended to be
one which is invariant under de Sitter transformation that preserves so called
Beltrami metric . There are two universal parameters and in
this Special Relativity (denote it as ). The
Lagrangian-Hamiltonian formulism of is formulated in this
paper. The canonic energy, canonic momenta, and 10 Noether charges
corresponding to the space-time's de Sitter symmetry are derived. The canonical
quantization of the mechanics for -free particle is
performed. The physics related to it is discussed.Comment: 24 pages, no figur
Vortex Pinball Under Crossed AC Drives in Superconductors with Periodic Pinning Arrays
Vortices driven with both a transverse and a longitudinal AC drive which are
out of phase are shown to exhibit a novel commensuration-incommensuration
effect when interacting with periodic substrates. For different AC driving
parameters, the motion of the vortices forms commensurate orbits with the
periodicity of the pinning array. When the commensurate orbits are present,
there is a finite DC critical depinning threshold, while for the incommensurate
phases the vortices are delocalized and the DC depinning threshold is absent.Comment: 4 pages, 4 postscript figure
Transverse phase-locking in fully frustrated Josephson junction arrays: a new type of fractional giant steps
We study, analytically and numerically, phase locking of driven vortex
lattices in fully-frustrated Josephson junction arrays at zero temperature. We
consider the case when an ac current is applied {\it perpendicular} to a dc
current. We observe phase locking, steps in the current-voltage
characteristics, with a dependence on external ac-drive amplitude and frequency
qualitatively different from the Shapiro steps, observed when the ac and dc
currents are applied in parallel. Further, the critical current increases with
increasing transverse ac-drive amplitude, while it decreases for longitudinal
ac-drive. The critical current and the phase-locked current step width,
increase quadratically with (small) amplitudes of the ac-drive. For larger
amplitudes of the transverse ac-signal, we find windows where the critical
current is hysteretic, and windows where phase locking is suppressed due to
dynamical instabilities. We characterize the dynamical states around the
phase-locking interference condition in the curve with voltage noise,
Lyapunov exponents and Poincar\'e sections. We find that zero temperature
phase-locking behavior in large fully frustrated arrays is well described by an
effective four plaquette model.Comment: 12 pages, 11 figure
Transverse Phase Locking for Vortex Motion in Square and Triangular Pinning Arrays
We analyze transverse phase locking for vortex motion in a superconductor
with a longitudinal DC drive and a transverse AC drive. For both square and
triangular arrays we observe a variety of fractional phase locking steps in the
velocity versus DC drive which correspond to stable vortex orbits. The locking
steps are more pronounced for the triangular arrays which is due to the fact
that the vortex motion has a periodic transverse velocity component even for
zero transverse AC drive. All the steps increase monotonically in width with AC
amplitude. We confirm that the width of some fractional steps in the square
arrays scales as the square of the AC driving amplitude. In addition we
demonstrate scaling in the velocity versus applied DC driving curves at
depinning and on the main step, similar to that seen for phase locking in
charge-density wave systems. The phase locking steps are most prominent for
commensurate vortex fillings where the interstitial vortices form symmetrical
ground states. For increasing temperature, the fractional steps are washed out
very quickly, while the main step gains a linear component and disappears at
melting. For triangular pinning arrays we again observe transverse phase
locking, with the main and several of the fractional step widths scaling
linearly with AC amplitude.Comment: 10 pages, 14 postscript figure