1,649 research outputs found
Hall drift of axisymmetric magnetic fields in solid neutron-star matter
Hall drift, i. e., transport of magnetic flux by the moving electrons giving
rise to the electrical current, may be the dominant effect causing the
evolution of the magnetic field in the solid crust of neutron stars. It is a
nonlinear process that, despite a number of efforts, is still not fully
understood. We use the Hall induction equation in axial symmetry to obtain some
general properties of nonevolving fields, as well as analyzing the evolution of
purely toroidal fields, their poloidal perturbations, and current-free, purely
poloidal fields. We also analyze energy conservation in Hall instabilities and
write down a variational principle for Hall equilibria. We show that the
evolution of any toroidal magnetic field can be described by Burgers' equation,
as previously found in plane-parallel geometry. It leads to sharp current
sheets that dissipate on the Hall time scale, yielding a stationary field
configuration that depends on a single, suitably defined coordinate. This
field, however, is unstable to poloidal perturbations, which grow as their
field lines are stretched by the background electron flow, as in instabilities
earlier found numerically. On the other hand, current-free poloidal
configurations are stable and could represent a long-lived crustal field
supported by currents in the fluid stellar core.Comment: 8 pages, 5 figure panels; new version with very small correction;
accepted by Astronomy & Astrophysic
Generation of frequency sidebands on single photons with indistinguishability from quantum dots
Generation and manipulation of the quantum state of a single photon is at the
heart of many quantum information protocols. There has been growing interest in
using phase modulators as quantum optics devices that preserve coherence. In
this Letter, we have used an electro-optic phase modulator to shape the state
vector of single photons emitted by a quantum dot to generate new frequency
components (modes) and explicitly demonstrate that the phase modulation process
agrees with the theoretical prediction at a single photon level. Through
two-photon interference measurements we show that for an output consisting of
three modes (the original mode and two sidebands), the indistinguishability of
the mode engineered photon, measured through the secondorder intensity
correlation (g2(0)) is preserved. This work demonstrates a robust means to
generate a photonic qubit or more complex state (e.g., a qutrit) for quantum
communication applications by encoding information in the sidebands without the
loss of coherence
Modelling bacterial behaviour close to a no-slip plane boundary: the influence of bacterial geometry
We describe a boundary-element method used to model the hydrodynamics of a bacterium propelled by a single helical flagellum. Using this model, we optimize the power efficiency of swimming with respect to cell body and flagellum geometrical parameters, and find that optima for swimming in unbounded fluid and near a no-slip plane boundary are nearly indistinguishable. We also consider the novel optimization objective of torque efficiency and find a very different optimal shape. Excluding effects such as Brownian motion and electrostatic interactions, it is demonstrated that hydrodynamic forces may trap the bacterium in a stable, circular orbit near the boundary, leading to the empirically observable surface accumulation of bacteria. Furthermore, the details and even the existence of this stable orbit depend on geometrical parameters of the bacterium, as described in this article. These results shed some light on the phenomenon of surface accumulation of micro-organisms and offer hydrodynamic explanations as to why some bacteria may accumulate more readily than others based on morphology
Exact joint density-current probability function for the asymmetric exclusion process
We study the asymmetric exclusion process with open boundaries and derive the
exact form of the joint probability function for the occupation number and the
current through the system. We further consider the thermodynamic limit,
showing that the resulting distribution is non-Gaussian and that the density
fluctuations have a discontinuity at the continuous phase transition, while the
current fluctuations are continuous. The derivations are performed by using the
standard operator algebraic approach, and by the introduction of new operators
satisfying a modified version of the original algebra.Comment: 4 pages, 3 figure
Clocked Atom Delivery to a Photonic Crystal Waveguide
Experiments and numerical simulations are described that develop quantitative
understanding of atomic motion near the surfaces of nanoscopic photonic crystal
waveguides (PCWs). Ultracold atoms are delivered from a moving optical lattice
into the PCW. Synchronous with the moving lattice, transmission spectra for a
guided-mode probe field are recorded as functions of lattice transport time and
frequency detuning of the probe beam. By way of measurements such as these, we
have been able to validate quantitatively our numerical simulations, which are
based upon detailed understanding of atomic trajectories that pass around and
through nanoscopic regions of the PCW under the influence of optical and
surface forces. The resolution for mapping atomic motion is roughly 50 nm in
space and 100 ns in time. By introducing auxiliary guided mode (GM) fields that
provide spatially varying AC-Stark shifts, we have, to some degree, begun to
control atomic trajectories, such as to enhance the flux into to the central
vacuum gap of the PCW at predetermined times and with known AC-Stark shifts.
Applications of these capabilities include enabling high fractional filling of
optical trap sites within PCWs, calibration of optical fields within PCWs, and
utilization of the time-dependent, optically dense atomic medium for novel
nonlinear optical experiments
Power Spectra of the Total Occupancy in the Totally Asymmetric Simple Exclusion Process
As a solvable and broadly applicable model system, the totally asymmetric
exclusion process enjoys iconic status in the theory of non-equilibrium phase
transitions. Here, we focus on the time dependence of the total number of
particles on a 1-dimensional open lattice, and its power spectrum. Using both
Monte Carlo simulations and analytic methods, we explore its behavior in
different characteristic regimes. In the maximal current phase and on the
coexistence line (between high/low density phases), the power spectrum displays
algebraic decay, with exponents -1.62 and -2.00, respectively. Deep within the
high/low density phases, we find pronounced \emph{oscillations}, which damp
into power laws. This behavior can be understood in terms of driven biased
diffusion with conserved noise in the bulk.Comment: 4 pages, 4 figure
Shock statistics in higher-dimensional Burgers turbulence
We conjecture the exact shock statistics in the inviscid decaying Burgers
equation in D>1 dimensions, with a special class of correlated initial
velocities, which reduce to Brownian for D=1. The prediction is based on a
field-theory argument, and receives support from our numerical calculations. We
find that, along any given direction, shocks sizes and locations are
uncorrelated.Comment: 4 pages, 8 figure
Freezing Transition in Decaying Burgers Turbulence and Random Matrix Dualities
We reveal a phase transition with decreasing viscosity at \nu=\nu_c>0
in one-dimensional decaying Burgers turbulence with a power-law correlated
random profile of Gaussian-distributed initial velocities
\sim|x-x'|^{-2}. The low-viscosity phase exhibits non-Gaussian
one-point probability density of velocities, continuously dependent on \nu,
reflecting a spontaneous one step replica symmetry breaking (RSB) in the
associated statistical mechanics problem. We obtain the low orders cumulants
analytically. Our results, which are checked numerically, are based on
combining insights in the mechanism of the freezing transition in random
logarithmic potentials with an extension of duality relations discovered
recently in Random Matrix Theory. They are essentially non mean-field in nature
as also demonstrated by the shock size distribution computed numerically and
different from the short range correlated Kida model, itself well described by
a mean field one step RSB ansatz. We also provide some insights for the finite
viscosity behaviour of velocities in the latter model.Comment: Published version, essentially restructured & misprints corrected. 6
pages, 5 figure
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