8,544 research outputs found
Average output entropy for quantum channels
We study the regularized average Renyi output entropy \bar{S}_{r}^{\reg} of
quantum channels. This quantity gives information about the average noisiness
of the channel output arising from a typical, highly entangled input state in
the limit of infinite dimensions. We find a closed expression for
\beta_{r}^{\reg}, a quantity which we conjecture to be equal to \Srreg. We
find an explicit form for \beta_{r}^{\reg} for some entanglement-breaking
channels, and also for the qubit depolarizing channel as a
function of the parameter . We prove equality of the two quantities in
some cases, in particular we conclude that for both are
non-analytic functions of the variable .Comment: 32 pages, several plots and figures; positivity condition added for
Theorem on entanglement breaking channels; new result for entrywise positive
channel
Laboratory simulations of astrophysical jets and solar coronal loops: new results
An experimental program underway at Caltech has produced plasmas where the shape is neither fixed by the vacuum chamber nor fixed by an external coil set, but instead is determined by self-organization. The plasma dynamics is highly reproducible and so can be studied in considerable detail even though the morphology of the plasma is both complex and time-dependent. A surprising result has been the observation that self-collimating MHD-driven plasma jets are ubiquitous and play a fundamental role in the self-organization. The jets can be considered lab-scale simulations of astrophysical jets and in addition are intimately related to solar coronal loops. The jets are driven by the combination of the axial component of the J×B force and the axial pressure gradient resulting from the non-uniform pinch force associated with the flared axial current density. Behavior is consistent with a model showing that collimation results from axial non-uniformity of the jet velocity. In particular, flow stagnation in the jet frame compresses frozen-in azimuthal magnetic flux, squeezes together toroidal magnetic field lines, thereby amplifying the embedded toroidal magnetic field, enhancing the pinch force, and hence causing collimation of the jet
Discrete Lagrangian systems on the Virasoro group and Camassa-Holm family
We show that the continuous limit of a wide natural class of the
right-invariant discrete Lagrangian systems on the Virasoro group gives the
family of integrable PDE's containing Camassa-Holm, Hunter-Saxton and
Korteweg-de Vries equations. This family has been recently derived by Khesin
and Misiolek as Euler equations on the Virasoro algebra for
-metrics. Our result demonstrates a universal nature of
these equations.Comment: 6 pages, no figures, AMS-LaTeX. Version 2: minor changes. Version 3:
minor change
Scattering off an oscillating target: Basic mechanisms and their impact on cross sections
We investigate classical scattering off a harmonically oscillating target in
two spatial dimensions. The shape of the scatterer is assumed to have a
boundary which is locally convex at any point and does not support the presence
of any periodic orbits in the corresponding dynamics. As a simple example we
consider the scattering of a beam of non-interacting particles off a circular
hard scatterer. The performed analysis is focused on experimentally accessible
quantities, characterizing the system, like the differential cross sections in
the outgoing angle and velocity. Despite the absence of periodic orbits and
their manifolds in the dynamics, we show that the cross sections acquire rich
and multiple structure when the velocity of the particles in the beam becomes
of the same order of magnitude as the maximum velocity of the oscillating
target. The underlying dynamical pattern is uniquely determined by the phase of
the first collision between the beam particles and the scatterer and possesses
a universal profile, dictated by the manifolds of the parabolic orbits, which
can be understood both qualitatively as well as quantitatively in terms of
scattering off a hard wall. We discuss also the inverse problem concerning the
possibility to extract properties of the oscillating target from the
differential cross sections.Comment: 18 page
Integrability and Ergodicity of Classical Billiards in a Magnetic Field
We consider classical billiards in plane, connected, but not necessarily
bounded domains. The charged billiard ball is immersed in a homogeneous,
stationary magnetic field perpendicular to the plane. The part of dynamics
which is not trivially integrable can be described by a "bouncing map". We
compute a general expression for the Jacobian matrix of this map, which allows
to determine stability and bifurcation values of specific periodic orbits. In
some cases, the bouncing map is a twist map and admits a generating function
which is useful to do perturbative calculations and to classify periodic
orbits. We prove that billiards in convex domains with sufficiently smooth
boundaries possess invariant tori corresponding to skipping trajectories.
Moreover, in strong field we construct adiabatic invariants over exponentially
large times. On the other hand, we present evidence that the billiard in a
square is ergodic for some large enough values of the magnetic field. A
numerical study reveals that the scattering on two circles is essentially
chaotic.Comment: Explanations added in Section 5, Section 6 enlarged, small errors
corrected; Large figures have been bitmapped; 40 pages LaTeX, 15 figures,
uuencoded tar.gz. file. To appear in J. Stat. Phys. 8
New Algorithm for Mixmaster Dynamics
We present a new numerical algorithm for evolving the Mixmaster spacetimes.
By using symplectic integration techniques to take advantage of the exact Taub
solution for the scattering between asymptotic Kasner regimes, we evolve these
spacetimes with higher accuracy using much larger time steps than previously
possible. The longer Mixmaster evolution thus allowed enables detailed
comparison with the Belinskii, Khalatnikov, Lifshitz (BKL) approximate
Mixmaster dynamics. In particular, we show that errors between the BKL
prediction and the measured parameters early in the simulation can be
eliminated by relaxing the BKL assumptions to yield an improved map. The
improved map has different predictions for vacuum Bianchi Type IX and magnetic
Bianchi Type VI Mixmaster models which are clearly matched in the
simulation.Comment: 12 pages, Revtex, 4 eps figure
The electronic structure of the high-symmetry perovskite iridate Ba2IrO4
We report angle-resolved photoemission (ARPES) measurements, density
functional and model tight-binding calculations on BaIrO (Ba-214), an
antiferromagnetic ( K) insulator. Ba-214 does not exhibit the
rotational distortion of the IrO octahedra that is present in its sister
compound SrIrO (Sr-214), and is therefore an attractive reference
material to study the electronic structure of layered iridates. We find that
the band structures of Ba-214 and Sr-214 are qualitatively similar, hinting at
the predominant role of the spin-orbit interaction in these materials.
Temperature-dependent ARPES data show that the energy gap persists well above
, and favour a Mott over a Slater scenario for this compound.Comment: 13 pages, 9 figure
Explicit Integration of the Full Symmetric Toda Hierarchy and the Sorting Property
We give an explicit formula for the solution to the initial value problem of
the full symmetric Toda hierarchy. The formula is obtained by the
orthogonalization procedure of Szeg\"{o}, and is also interpreted as a
consequence of the QR factorization method of Symes \cite{symes}. The sorting
property of the dynamics is also proved for the case of a generic symmetric
matrix in the sense described in the text, and generalizations of tridiagonal
formulae are given for the case of matrices with nonzero diagonals.Comment: 13 pages, Latex
Integrability and chaos: the classical uncertainty
In recent years there has been a considerable increase in the publishing of
textbooks and monographs covering what was formerly known as random or
irregular deterministic motion, now named by the more fashionable term of
deterministic chaos. There is still substantial interest in a matter that is
included in many graduate and even undergraduate courses on classical
mechanics. Based on the Hamiltonian formalism, the main objective of this
article is to provide, from the physicist's point of view, an overall and
intuitive review of this broad subject (with some emphasis on the KAM theorem
and the stability of planetary motions) which may be useful to both students
and instructors.Comment: 24 pages, 10 figure
Derivative pricing under the possibility of long memory in the supOU stochastic volatility model
We consider the supOU stochastic volatility model which is able to exhibit
long-range dependence. For this model we give conditions for the discounted
stock price to be a martingale, calculate the characteristic function, give a
strip where it is analytic and discuss the use of Fourier pricing techniques.
Finally, we present a concrete specification with polynomially decaying
autocorrelations and calibrate it to observed market prices of plain vanilla
options
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