1,569 research outputs found
Controlling the direction, topological charge, and spectrum of transition radiation with holographic metasurfaces
We show experimentally that wavefront - the direction, spectral composition and phase profile of light emission - stimulated by free electron injection into plasmonic and dielectric media can be controlled with high finesse using holographic nanostructures
Long Range Hops and the Pair Annihilation Reaction A+A->0: Renormalization Group and Simulation
A simple example of a non-equilibrium system for which fluctuations are
important is a system of particles which diffuse and may annihilate in pairs on
contact. The renormalization group can be used to calculate the time dependence
of the density of particles, and provides both an exact value for the exponent
governing the decay of particles and an epsilon-expansion for the amplitude of
this power law. When the diffusion is anomalous, as when the particles perform
Levy flights, the critical dimension depends continuously on the control
parameter for the Levy distribution. The epsilon-expansion can then become an
expansion in a small parameter. We present a renormalization group calculation
and compare these results with those of a simulation.Comment: As-published version; two significant errors fixed, two references
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Reaction, Levy Flights, and Quenched Disorder
We consider the A + A --> emptyset reaction, where the transport of the
particles is given by Levy flights in a quenched random potential. With a
common literature model of the disorder, the random potential can only increase
the rate of reaction. With a model of the disorder that obeys detailed balance,
however, the rate of reaction initially increases and then decreases as a
function of the disorder strength. The physical behavior obtained with this
second model is in accord with that for reactive turbulent flow, indicating
that Levy flight statistics can model aspects of turbulent fluid transport.Comment: 6 pages, 5 pages. Phys. Rev. E. 65 (2002) 011109--1-
Numerical simulations of a non-commutative theory: the scalar model on the fuzzy sphere
We address a detailed non-perturbative numerical study of the scalar theory
on the fuzzy sphere. We use a novel algorithm which strongly reduces the
correlation problems in the matrix update process, and allows the investigation
of different regimes of the model in a precise and reliable way. We study the
modes associated to different momenta and the role they play in the ``striped
phase'', pointing out a consistent interpretation which is corroborated by our
data, and which sheds further light on the results obtained in some previous
works. Next, we test a quantitative, non-trivial theoretical prediction for
this model, which has been formulated in the literature: The existence of an
eigenvalue sector characterised by a precise probability density, and the
emergence of the phase transition associated with the opening of a gap around
the origin in the eigenvalue distribution. The theoretical predictions are
confirmed by our numerical results. Finally, we propose a possible method to
detect numerically the non-commutative anomaly predicted in a one-loop
perturbative analysis of the model, which is expected to induce a distortion of
the dispersion relation on the fuzzy sphere.Comment: 1+36 pages, 18 figures; v2: 1+55 pages, 38 figures: added the study
of the eigenvalue distribution, added figures, tables and references, typos
corrected; v3: 1+20 pages, 10 eps figures, new results, plots and references
added, technical details about the tests at small matrix size skipped,
version published in JHE
The Spectrum of the Dirac Operator on Coset Spaces with Homogeneous Gauge Fields
The spectrum and degeneracies of the Dirac operator are analysed on compact
coset spaces when there is a non-zero homogeneous background gauge field which
is compatible with the symmetries of the space, in particular when the gauge
field is derived from the spin-connection. It is shown how the degeneracy of
the lowest Landau level in the recently proposed higher dimensional quantum
Hall effect is related to the Atiyah-Singer index theorem for the Dirac
operator on a compact coset space.Comment: 25 pages, typeset in LaTeX, uses youngtab.st
Angular momenta creation in relativistic electron-positron plasma
Creation of angular momentum in a relativistic electron-positron plasma is
explored. It is shown that a chain of angular momentum carrying vortices is a
robust asymptotic state sustained by the generalized nonlinear Schrodinger
equation characteristic to the system. The results may suggest a possible
electromagnetic origin of angular momenta when it is applied to the MeV epoch
of the early Universe.Comment: 20 pages, 6 figure
Exact solution of Schrodinger equation for Pseudoharmonic potential
Exact solution of Schrodinger equation for the pseudoharmonic potential is
obtained for an arbitrary angular momentum. The energy eigenvalues and
corresponding eigenfunctions are calculated by Nikiforov-Uvarov method.
Wavefunctions are expressed in terms of Jacobi polynomials. The energy
eigenvalues are calculated numerically for some values of l and n with n<5 for
some diatomic molecules.Comment: 10 page
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