1,535 research outputs found

### Spin and orbital Hall effects for diffracting optical beams in gradient-index media

We examine the evolution of paraxial beams carrying intrinsic spin and
orbital angular momenta (AM) in gradient-index media. A parabolic-type equation
is derived which describes the beam diffraction in curvilinear coordinates
accompanying the central ray. The center of gravity of the beam experiences
transverse AM-dependent deflections -- the spin and orbital Hall effects. The
spin Hall effect generates a transverse translation of the beam as a whole, in
precise agreement with recent geometrical optics predictions. At the same time,
the orbital Hall effect is significantly affected by the diffraction in the
inhomogeneous medium and is accompanied by changes in the intrinsic orbital AM
and deformations of the beam.Comment: 4 pages, 2 figures, to appear in Phys. Rev.

### Non-Universality in Random Matrix Ensembles with Soft Level Confinement

Two families of strongly non-Gaussian random matrix ensembles (RME) are
considered. They are statistically equivalent to a one-dimensional plasma of
particles interacting logarithmically and confined by the potential that has
the long-range behavior $V(\epsilon)\sim |\epsilon|^{\alpha}$ ($0<\alpha<1$),
or $V(\epsilon)\sim \ln^{2}|\epsilon|$. The direct Monte Carlo simulations on
the effective plasma model shows that the spacing distribution function (SDF)
in such RME can deviate from that of the classical Gaussian ensembles. For
power-law potentials, this deviation is seen only near the origin $\epsilon\sim
0$, while for the double-logarithmic potential the SDF shows the cross-over
from the Wigner-Dyson to Poisson behavior in the bulk of the spectrum.Comment: 4 pages, REVTEX, 3 postscript figures appended, ICTP/9/94/ckw.

### Theoretical and numerical studies of wave-packet propagation in tokamak plasmas

Theoretical and numerical studies of wave-packet propagation are presented to
analyze the time varying 2D mode structures of electrostatic fluctuations in
tokamak plasmas, using general flux coordinates. Instead of solving the 2D wave
equations directly, the solution of the initial value problem is used to obtain
the 2D mode structure, following the propagation of wave-packets generated by a
source and reconstructing the time varying field. As application, the 2D WKB
method is applied to investigate the shaping effects (elongation and
triangularity) of tokamak geometry on the lower hybrid wave propagation and
absorbtion. Meanwhile, the Mode Structure Decomposition (MSD) method is used to
handle the boundary conditions and simplify the 2D problem to two nested 1D
problems. The MSD method is related to that discussed earlier by Zonca and Chen
[Phys. Fluids B 5, 3668 (1993)], and reduces to the well-known "ballooning
formalism" [J. W. Connor, R. J. Hastie, and J. B. Taylor, Phys. Rev. Lett. 40,
396 (1978)], when spatial scale separation applies. This method is used to
investigate the time varying 2D electrostatic ITG mode structure with a mixed
WKB-full-wave technique. The time varying field pattern is reconstructed and
the time asymptotic structure of the wave-packet propagation gives the 2D
eigenmode and the corresponding eigenvalue. As a general approach to
investigate 2D mode structures in tokamak plasmas, our method also applies for
electromagnetic waves with general source/sink terms, either by an
internal/external antenna or nonlinear wave interaction with zonal structures.Comment: 24 pages, 14 figure

### Langmuir wave linear evolution in inhomogeneous nonstationary anisotropic plasma

Equations describing the linear evolution of a non-dissipative Langmuir wave
in inhomogeneous nonstationary anisotropic plasma without magnetic field are
derived in the geometrical optics approximation. A continuity equation is
obtained for the wave action density, and the conditions for the action
conservation are formulated. In homogeneous plasma, the wave field E
universally scales with the electron density N as E ~ N^{3/4}, whereas the
wavevector evolution varies depending on the wave geometry

### Random Matrix Theory of the Energy-Level Statistics of Disordered Systems at the Anderson Transition

We consider a family of random matrix ensembles (RME) invariant under
similarity transformations and described by the probability density $P({\bf
H})= \exp[-{\rm Tr}V({\bf H})]$. Dyson's mean field theory (MFT) of the
corresponding plasma model of eigenvalues is generalized to the case of weak
confining potential, $V(\epsilon)\sim {A\over 2}\ln ^2(\epsilon)$. The
eigenvalue statistics derived from MFT are shown to deviate substantially from
the classical Wigner-Dyson statistics when $A<1$. By performing systematic
Monte Carlo simulations on the plasma model, we compute all the relevant
statistical properties of the RME with weak confinement. For $A_c\approx 0.4$
the distribution function of the energy-level spacings (LSDF) of this RME
coincides in a large energy window with the LSDF of the three dimensional
Anderson model at the metal-insulator transition. For the same $A_c$, the
variance of the number of levels, $\langle n^2\rangle -\langle n\rangle^2$, in
an interval containing $\langle n\rangle$ levels on average, grows linearly
with $\langle n\rangle$, and its slope is equal to $0.32 \pm 0.02$, which is
consistent with the value found for the Anderson model at the critical point.Comment: 32 pages, REVTEX 3.0, 10 postscript (uuencoded) figures include

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