285 research outputs found
Gravitational non-commutativity and G\"odel-like spacetimes
We derive general conditions under which geodesics of stationary spacetimes
resemble trajectories of charged particles in an electromagnetic field. For
large curvatures (analogous to strong magnetic fields), the quantum
mechanicical states of these particles are confined to gravitational analogs of
{\it lowest Landau levels}. Furthermore, there is an effective
non-commutativity between their spatial coordinates. We point out that the
Som-Raychaudhuri and G\"odel spacetime and its generalisations are precisely of
the above type and compute the effective non-commutativities that they induce.
We show that the non-commutativity for G\"odel spacetime is identical to that
on the fuzzy sphere. Finally, we show how the star product naturally emerges in
Som-Raychaudhuri spacetimes.Comment: Two sections added (Relation to the fuzzy sphere, Emergence of the
star product). 10 pages, Revtex. To appear in General Relativity and
Gravitatio
Radiation recoil from highly distorted black holes
We present results from numerical evolutions of single black holes distorted
by axisymmetric, but equatorially asymmetric, gravitational (Brill) waves. Net
radiated energies, apparent horizon embeddings, and recoil velocities are shown
for a range of Brill wave parameters, including both even and odd parity
distortions of Schwarzschild black holes. We find that a wave packet initially
concentrated on the black hole throat, a likely model also for highly
asymmetric stellar collapse and late stage binary mergers, can generate a
maximum recoil velocity of about 150 (23) km/sec for even (odd) parity
perturbations, significantly less than that required to eject black holes from
galactic cores.Comment: 15 pages, 8 figure
Strong Phase Separation in a Model of Sedimenting Lattices
We study the steady state resulting from instabilities in crystals driven
through a dissipative medium, for instance, a colloidal crystal which is
steadily sedimenting through a viscous fluid. The problem involves two coupled
fields, the density and the tilt; the latter describes the orientation of the
mass tensor with respect to the driving field. We map the problem to a 1-d
lattice model with two coupled species of spins evolving through conserved
dynamics. In the steady state of this model each of the two species shows
macroscopic phase separation. This phase separation is robust and survives at
all temperatures or noise levels--- hence the term Strong Phase Separation.
This sort of phase separation can be understood in terms of barriers to
remixing which grow with system size and result in a logarithmically slow
approach to the steady state. In a particular symmetric limit, it is shown that
the condition of detailed balance holds with a Hamiltonian which has
infinite-ranged interactions, even though the initial model has only local
dynamics. The long-ranged character of the interactions is responsible for
phase separation, and for the fact that it persists at all temperatures.
Possible experimental tests of the phenomenon are discussed.Comment: To appear in Phys Rev E (1 January 2000), 16 pages, RevTex, uses
epsf, three ps figure
Classical and Thermodynamic Stability of Black Branes
It is argued that many non-extremal black branes exhibit a classical
Gregory-Laflamme instability if, and only if, they are locally
thermodynamically unstable. For some black branes, the Gregory-Laflamme
instability must therefore disappear near extremality. For the black -branes
of the type II supergravity theories, the Gregory-Laflamme instability
disappears near extremality for but persists all the way down to
extremality for (the black D3-brane is not covered by the analysis of
this paper). This implies that the instability also vanishes for the
near-extremal black M2 and M5-brane solutions.Comment: 21 pages, LaTeX. v2: Various points clarified, typos corrected and
reference adde
Multiple Transitions to Chaos in a Damped Parametrically Forced Pendulum
We study bifurcations associated with stability of the lowest stationary
point (SP) of a damped parametrically forced pendulum by varying
(the natural frequency of the pendulum) and (the amplitude of the external
driving force). As is increased, the SP will restabilize after its
instability, destabilize again, and so {\it ad infinitum} for any given
. Its destabilizations (restabilizations) occur via alternating
supercritical (subcritical) period-doubling bifurcations (PDB's) and pitchfork
bifurcations, except the first destabilization at which a supercritical or
subcritical bifurcation takes place depending on the value of . For
each case of the supercritical destabilizations, an infinite sequence of PDB's
follows and leads to chaos. Consequently, an infinite series of period-doubling
transitions to chaos appears with increasing . The critical behaviors at the
transition points are also discussed.Comment: 20 pages + 7 figures (available upon request), RevTex 3.
The quantum vacuum at the foundations of classical electrodynamics
In the classical theory of electromagnetism, the permittivity and the
permeability of free space are constants whose magnitudes do not seem to
possess any deeper physical meaning. By replacing the free space of classical
physics with the quantum notion of the vacuum, we speculate that the values of
the aforementioned constants could arise from the polarization and
magnetization of virtual pairs in vacuum. A classical dispersion model with
parameters determined by quantum and particle physics is employed to estimate
their values. We find the correct orders of magnitude. Additionally, our simple
assumptions yield an independent estimate for the number of charged elementary
particles based on the known values of the permittivity and the permeability,
and for the volume of a virtual pair. Such interpretation would provide an
intriguing connection between the celebrated theory of classical
electromagnetism and the quantum theory in the weak field limit.Comment: Accepted in Applied Physics B: Special Issue for the 50 years of the
laser. Comments are welcome
Coulomb Effects on Electromagnetic Pair Production in Ultrarelativistic Heavy-Ion Collisions
We discuss the implications of the eikonal amplitude on the pair production
probability in ultrarelativistic heavy-ion transits. In this context the
Weizs\"acker-Williams method is shown to be exact in the ultrarelativistic
limit, irrespective of the produced particles' mass. A new equivalent
single-photon distribution is derived which correctly accounts for the Coulomb
distortions. As an immediate application, consequences for unitarity violation
in photo-dissociation processes in peripheral heavy-ion encounters are
discussed.Comment: 13 pages, 4 .eps figure
Landau Damping and Coherent Structures in Narrow-Banded 1+1 Deep Water Gravity Waves
We study the nonlinear energy transfer around the peak of the spectrum of
surface gravity waves by taking into account nonhomogeneous effects. In the
narrow-banded approximation the kinetic equation resulting from a
nonhomogeneous wave field is a Vlasov-Poisson type equation which includes at
the same time the random version of the Benjamin-Feir instability and the
Landau damping phenomenon. We analytically derive the values of the Phillips'
constant and the enhancement factor for which the
narrow-banded approximation of the JONSWAP spectrum is unstable. By performing
numerical simulations of the nonlinear Schr\"{o}dinger equation we check the
validity of the prediction of the related kinetic equation. We find that the
effect of Landau damping is to suppress the formation of coherent structures.
The problem of predicting freak waves is briefly discussed.Comment: 4 pages, 3 figure
Critical Dynamics of Magnets
We review our current understanding of the critical dynamics of magnets above
and below the transition temperature with focus on the effects due to the
dipole--dipole interaction present in all real magnets. Significant progress in
our understanding of real ferromagnets in the vicinity of the critical point
has been made in the last decade through improved experimental techniques and
theoretical advances in taking into account realistic spin-spin interactions.
We start our review with a discussion of the theoretical results for the
critical dynamics based on recent renormalization group, mode coupling and spin
wave theories. A detailed comparison is made of the theory with experimental
results obtained by different measuring techniques, such as neutron scattering,
hyperfine interaction, muon--spin--resonance, electron--spin--resonance, and
magnetic relaxation, in various materials. Furthermore we discuss the effects
of dipolar interaction on the critical dynamics of three--dimensional isotropic
antiferromagnets and uniaxial ferromagnets. Special attention is also paid to a
discussion of the consequences of dipolar anisotropies on the existence of
magnetic order and the spin--wave spectrum in two--dimensional ferromagnets and
antiferromagnets. We close our review with a formulation of critical dynamics
in terms of nonlinear Langevin equations.Comment: Review article (154 pages, figures included
Breakdown of superfluidity of an atom laser past an obstacle
The 1D flow of a continuous beam of Bose-Einstein condensed atoms in the
presence of an obstacle is studied as a function of the beam velocity and of
the type of perturbing potential (representing the interaction of the obstacle
with the atoms of the beam). We identify the relevant regimes:
stationary/time-dependent and superfluid/dissipative; the absence of drag is
used as a criterion for superfluidity. There exists a critical velocity below
which the flow is superfluid. For attractive obstacles, we show that this
critical velocity can reach the value predicted by Landau's approach. For
penetrable obstacles, it is shown that superfluidity is recovered at large beam
velocity. Finally, enormous differences in drag occur when switching from
repulsive to attractive potential.Comment: 15 pages, 6 figure
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