1,808 research outputs found
Slice Stretching at the Event Horizon when Geodesically Slicing the Schwarzschild Spacetime with Excision
Slice-stretching effects are discussed as they arise at the event horizon
when geodesically slicing the extended Schwarzschild black-hole spacetime while
using singularity excision. In particular, for Novikov and isotropic spatial
coordinates the outward movement of the event horizon (``slice sucking'') and
the unbounded growth there of the radial metric component (``slice wrapping'')
are analyzed. For the overall slice stretching, very similar late time behavior
is found when comparing with maximal slicing. Thus, the intuitive argument that
attributes slice stretching to singularity avoidance is incorrect.Comment: 5 pages, 2 figures, published version including minor amendments
suggested by the refere
Hexagons become second if symmetry is broken
Pattern formation on the free surface of a magnetic fluid subjected to a
magnetic field is investigated experimentally. By tilting the magnetic field
the symmetry can be broken in a controllable manner. When increasing the
amplitude of the tilted field, the flat surface gives way to liquid ridges. A
further increase results in a hysteretic transition to a pattern of stretched
hexagons. The instabilities are detected by means of a linear array of magnetic
hall sensors and compared with theoretical predictions.Comment: accepted for publication by Physical Review E/Rapid Communicatio
Density functional theory for strongly-correlated bosonic and fermionic ultracold dipolar and ionic gases
We introduce a density functional formalism to study the ground-state
properties of strongly-correlated dipolar and ionic ultracold bosonic and
fermionic gases, based on the self-consistent combination of the weak and the
strong coupling limits. Contrary to conventional density functional approaches,
our formalism does not require a previous calculation of the interacting
homogeneous gas, and it is thus very suitable to treat systems with tunable
long-range interactions. Due to its asymptotic exactness in the regime of
strong correlation, the formalism works for systems in which standard
mean-field theories fail.Comment: 5 pages, 2 figure
On the formation of Wigner molecules in small quantum dots
It was recently argued that in small quantum dots the electrons could
crystallize at much higher densities than in the infinite two-dimensional
electron gas. We compare predictions that the onset of spin polarization and
the formation of Wigner molecules occurs at a density parameter to the results of a straight-forward diagonalization of the Hamiltonian
matrix
Broken symmetries and directed collective energy transport
We study the appearance of directed energy current in homogeneous spatially
extended systems coupled to a heat bath in the presence of an external ac field
E(t). The systems are described by nonlinear field equations. By making use of
a symmetry analysis we predict the right choice of E(t) and obtain directed
energy transport for systems with a nonzero topological charge Q. We
demonstrate that the symmetry properties of motion of topological solitons
(kinks and antikinks) are equivalent to the ones for the energy current.
Numerical simulations confirm the predictions of the symmetry analysis and,
moreover, show that the directed energy current drastically increases as the
dissipation parameter reduces. Our results generalize recent rigorous
theories of currents generated by broken time-space symmetries to the case of
interacting many-particle systems.Comment: 4 pages, 2 figure
Weak noise approach to the logistic map
Using a nonperturbative weak noise approach we investigate the interference
of noise and chaos in simple 1D maps. We replace the noise-driven 1D map by an
area-preserving 2D map modelling the Poincare sections of a conserved dynamical
system with unbounded energy manifolds. We analyze the properties of the 2D map
and draw conclusions concerning the interference of noise on the nonlinear time
evolution. We apply this technique to the standard period-doubling sequence in
the logistic map. From the 2D area-preserving analogue we, in addition to the
usual period-doubling sequence, obtain a series of period doubled cycles which
are elliptic in nature. These cycles are spinning off the real axis at
parameters values corresponding to the standard period doubling events.Comment: 22 pages in revtex and 8 figures in ep
Constraint and gauge shocks in one-dimensional numerical relativity
We study how different types of blow-ups can occur in systems of hyperbolic
evolution equations of the type found in general relativity. In particular, we
discuss two independent criteria that can be used to determine when such
blow-ups can be expected. One criteria is related with the so-called geometric
blow-up leading to gradient catastrophes, while the other is based upon the
ODE-mechanism leading to blow-ups within finite time. We show how both
mechanisms work in the case of a simple one-dimensional wave equation with a
dynamic wave speed and sources, and later explore how those blow-ups can appear
in one-dimensional numerical relativity. In the latter case we recover the well
known ``gauge shocks'' associated with Bona-Masso type slicing conditions.
However, a crucial result of this study has been the identification of a second
family of blow-ups associated with the way in which the constraints have been
used to construct a hyperbolic formulation. We call these blow-ups ``constraint
shocks'' and show that they are formulation specific, and that choices can be
made to eliminate them or at least make them less severe.Comment: 19 pages, 8 figures and 1 table, revised version including several
amendments suggested by the refere
Correlation Induced Inhomogeneity in Circular Quantum Dots
Properties of the "electron gas" - in which conduction electrons interact by
means of Coulomb forces but ionic potentials are neglected - change
dramatically depending on the balance between kinetic energy and Coulomb
repulsion. The limits are well understood. For very weak interactions (high
density), the system behaves as a Fermi liquid, with delocalized electrons. In
contrast, in the strongly interacting limit (low density), the electrons
localize and order into a Wigner crystal phase. The physics at intermediate
densities, however, remains a subject of fundamental research. Here, we study
the intermediate-density electron gas confined to a circular disc, where the
degree of confinement can be tuned to control the density. Using accurate
quantum Monte Carlo techniques, we show that the electron-electron correlation
induced by an increase of the interaction first smoothly causes rings, and then
angular modulation, without any signature of a sharp transition in this density
range. This suggests that inhomogeneities in a confined system, which exist
even without interactions, are significantly enhanced by correlations.Comment: final version, modified introduction and clarifications, 4 page
Brownian motion exhibiting absolute negative mobility
We consider a single Brownian particle in a spatially symmetric, periodic
system far from thermal equilibrium. This setup can be readily realized
experimentally. Upon application of an external static force F, the average
particle velocity is negative for F>0 and positive for F<0 (absolute negative
mobility).Comment: 4 pages, 3 figures, to be published in PR
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