60,377 research outputs found
Equilibrium states of the pressure function for products of matrices
Let be a non-trivial family of complex
matrices, in the sense that for any , there exists such that . Let be the pressure function of . We show
that for each , there are at most ergodic -equilibrium states of
, and each of them satisfies certain Gibbs property.Comment: 12 pages. To appear in DCD
Global behavior of cosmological dynamics with interacting Veneziano ghost
In this paper, we shall study the dynamical behavior of the universe
accelerated by the so called Veneziano ghost dark energy component locally and
globally by using the linearization and nullcline method developed in this
paper. The energy density is generalized to be proportional to the Hawking
temperature defined on the trapping horizon instead of Hubble horizon of the
Friedmann-Robertson-Walker (FRW) universe. We also give a prediction of the
fate of the universe and present the bifurcation phenomenon of the dynamical
system of the universe. It seems that the universe could be dominated by dark
energy at present in some region of the parameter space.Comment: 8 pages, 7 figures, accepted for publication in JHE
Small-Recoil Approximation
In this review we discuss a technique to compute and to sum a class of
Feynman diagrams, and some of its applications. These are diagrams containing
one or more energetic particles that suffer very little recoil in their
interactions. When recoil is completely neglected, a decomposition formula can
be proven. This formula is a generalization of the well-known eikonal formula,
to non-abelian interactions. It expresses the amplitude as a sum of products of
irreducible amplitudes, with each irreducible amplitude being the amplitude to
emit one, or several mutually interacting, quasi-particles. For abelian
interaction a quasi-particle is nothing but the original boson, so this
decomposition formula reduces to the eikonal formula. In non-abelian situations
each quasi-particle can be made up of many bosons, though always with a total
quantum number identical to that of a single boson. This decomposition enables
certain amplitudes of all orders to be summed up into an exponential form, and
it allows subleading contributions of a certain kind, which is difficult to
reach in the usual way, to be computed. For bosonic emissions from a heavy
source with many constituents, a quasi-particle amplitude turns out to be an
amplitude in which all bosons are emitted from the same constituent. For
high-energy parton-parton scattering in the near-forward direction, the
quasi-particle turns out to be the Reggeon, and this formalism shows clearly
why gluons reggeize but photons do not. The ablility to compute subleading
terms in this formalism allows the BFKL-Pomeron amplitude to be extrapolated to
asymptotic energies, in a unitary way preserving the Froissart bound. We also
consider recoil corrections for abelian interactions in order to accommodate
the Landau-Pomeranchuk-Migdal effect.Comment: 21 pages with 4 figure
Coulomb blockade in silicon based structures at temperatures up to 50 K
Coulomb blockade has been observed in the current-voltage characteristics of structures fabricated in silicon germanium delta-doped material at temperatures up to 50 K. This is consistent with the estimated effective tunnel capacitance of 10 aF which is significantly smaller than the reported capacitances of tunnel junctions made from Al or GaAs/AlGaAs heterostructures
Comment on ``Capacity of the Hopfield model''
In a recent paper ``The capacity of the Hopfield model, J. Feng and B.
Tirozzi claim to prove rigorous results on the storage capacity that are in
conflict with the predictions of the replica approach. We show that their
results are in error and that their approach, even when the worst mistakes are
corrected, is not giving any mathematically rigorous results.Comment: 4pp, Plain Te
Achieving precise mechanical control in intrinsically noisy systems
How can precise control be realized in intrinsically noisy systems? Here, we develop a general theoretical framework that provides a way of achieving precise control in signal-dependent noisy environments. When the control signal has Poisson or supra-Poisson noise, precise control is not possible. If, however, the control signal has sub-Poisson noise, then precise control is possible. For this case, the precise control solution is not a function, but a rapidly varying random process that must be averaged with respect to a governing probability density functional. Our theoretical approach is applied to the control of straight-trajectory arm movement. Sub-Poisson noise in the control signal is shown to be capable of leading to precise control. Intriguingly, the control signal for this system has a natural counterpart, namely the bursting pulses of neurons-trains of Dirac-delta functions-in biological systems to achieve precise control performance
Magnetoelectric properties of magnetite thin films
Resistivity, DC Hall effect and transverse magnetoresistance measurements were made on polycrystalline thin films of magnetite (Fe3O4) from 104K to room temperature. The Verwey transition is observed at TV=123K, about 4K higher than reported for bulk magnetite. The ordinary and extraordinary Hall coefficients are negative over the entire temperature range, consistent with negatively charged carriers. The extraordinary Hall coefficient exhibits a rho 1/3 dependence on the resistivity above TV and a rho 2/3 dependence below TV. The magnetoresistance is negative at all temperatures and for all magnetic field strengths. The planar Hall effect signal was below the sensitivity of the present experiment
On Berenstein-Douglas-Seiberg Duality
I review the proposal of Berenstein-Douglas for a completely general
definition of Seiberg duality. To give evidence for their conjecture I present
the first example of a physical dual pair and explicitly check that it
satisfies the requirements. Then I explicitly show that a pair of toric dual
quivers is also dual according to their proposal. All these computations go
beyond tilting modules, and really work in the derived category. I introduce
all necessary mathematics where needed.Comment: 22 pages, LaTe
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