111 research outputs found
From Forbidden Coronal Lines to Meaningful Coronal Magnetic Fields
We review methods to measure magnetic fields within the corona using the
polarized light in magnetic-dipole (M1) lines. We are particularly interested
in both the global magnetic-field evolution over a solar cycle, and the local
storage of magnetic free energy within coronal plasmas. We address commonly
held skepticisms concerning angular ambiguities and line-of-sight confusion. We
argue that ambiguities are in principle no worse than more familiar remotely
sensed photospheric vector-fields, and that the diagnosis of M1 line data would
benefit from simultaneous observations of EUV lines. Based on calculations and
data from eclipses, we discuss the most promising lines and different
approaches that might be used. We point to the S-like [Fe {\sc XI}] line (J=2
to J=1) at 789.2nm as a prime target line (for ATST for example) to augment the
hotter 1074.7 and 1079.8 nm Si-like lines of [Fe {\sc XIII}] currently observed
by the Coronal Multi-channel Polarimeter (CoMP). Significant breakthroughs will
be made possible with the new generation of coronagraphs, in three distinct
ways: (i) through single point inversions (which encompasses also the analysis
of MHD wave modes), (ii) using direct comparisons of synthetic MHD or
force-free models with polarization data, and (iii) using tomographic
techniques.Comment: Accepted by Solar Physics, April 201
Nonequilibrium dynamics of random field Ising spin chains: exact results via real space RG
Non-equilibrium dynamics of classical random Ising spin chains are studied
using asymptotically exact real space renormalization group. Specifically the
random field Ising model with and without an applied field (and the Ising spin
glass (SG) in a field), in the universal regime of a large Imry Ma length so
that coarsening of domains after a quench occurs over large scales. Two types
of domain walls diffuse in opposite Sinai random potentials and mutually
annihilate. The domain walls converge rapidly to a set of system-specific
time-dependent positions {\it independent of the initial conditions}. We obtain
the time dependent energy, magnetization and domain size distribution
(statistically independent). The equilibrium limits agree with known exact
results. We obtain exact scaling forms for two-point equal time correlation and
two-time autocorrelations. We also compute the persistence properties of a
single spin, of local magnetization, and of domains. The analogous quantities
for the spin glass are obtained. We compute the two-point two-time correlation
which can be measured by experiments on spin-glass like systems. Thermal
fluctuations are found to be dominated by rare events; all moments of truncated
correlations are computed. The response to a small field applied after waiting
time , as measured in aging experiments, and the fluctuation-dissipation
ratio are computed. For ,
, it equals its equilibrium value X=1, though time
translational invariance fails. It exhibits for aging regime
with non-trivial , different from mean field.Comment: 55 pages, 9 figures, revte
Pascal Principle for Diffusion-Controlled Trapping Reactions
"All misfortune of man comes from the fact that he does not stay peacefully
in his room", has once asserted Blaise Pascal. In the present paper we evoke
this statement as the "Pascal principle" in regard to the problem of survival
of an "A" particle, which performs a lattice random walk in presence of a
concentration of randomly moving traps "B", and gets annihilated upon
encounters with any of them. We prove here that at sufficiently large times for
both perfect and imperfect trapping reactions, for arbitrary spatial dimension
"d" and for a rather general class of random walks, the "A" particle survival
probability is less than or equal to the survival probability of an immobile
target in the presence of randomly moving traps.Comment: 4 pages, RevTex, appearing in PR
Lattice theory of trapping reactions with mobile species
We present a stochastic lattice theory describing the kinetic behavior of
trapping reactions , in which both the and particles
perform an independent stochastic motion on a regular hypercubic lattice. Upon
an encounter of an particle with any of the particles, is
annihilated with a finite probability; finite reaction rate is taken into
account by introducing a set of two-state random variables - "gates", imposed
on each particle, such that an open (closed) gate corresponds to a reactive
(passive) state. We evaluate here a formal expression describing the time
evolution of the particle survival probability, which generalizes our
previous results. We prove that for quite a general class of random motion of
the species involved in the reaction process, for infinite or finite number of
traps, and for any time , the particle survival probability is always
larger in case when stays immobile, than in situations when it moves.Comment: 12 pages, appearing in PR
Stratorotational instability in MHD Taylor-Couette flows
The stability of dissipative Taylor-Couette flows with an axial stable
density stratification and a prescribed azimuthal magnetic field is considered.
Global nonaxisymmetric solutions of the linearized MHD equations with toroidal
magnetic field, axial density stratification and differential rotation are
found for both insulating and conducting cylinder walls. Flat rotation laws
such as the quasi-Kepler law are unstable against the nonaxisymmetric
stratorotational instability (SRI). The influence of a current-free toroidal
magnetic field depends on the magnetic Prandtl number Pm: SRI is supported by
Pm > 1 and it is suppressed by Pm \lsim 1. For too flat rotation laws a smooth
transition exists to the instability which the toroidal magnetic field produces
in combination with the differential rotation. This nonaxisymmetric azimuthal
magnetorotational instability (AMRI) has been computed under the presence of an
axial density gradient. If the magnetic field between the cylinders is not
current-free then also the Tayler instability occurs and the transition from
the hydrodynamic SRI to the magnetic Tayler instability proves to be rather
complex. Most spectacular is the `ballooning' of the stability domain by the
density stratification: already a rather small rotation stabilizes magnetic
fields against the Tayler instability. An azimuthal component of the resulting
electromotive force only exists for density-stratified flows. The related
alpha-effect for magnetic SRI of Kepler rotation appears to be positive for
negative d\rho/dz <0.Comment: 10 pages, 13 figures, submitted to Astron. Astrophy
Soliton Lattices in the Incommensurate Spin-Peierls Phase: Local Distortions and Magnetizations
It is shown that nonadiabatic fluctuations of the soliton lattice in the
spin-Peierls system CuGeO_3 lead to an important reduction of the NMR line
widths. These fluctuations are the zero-point motion of the massless phasonic
excitations. Furthermore, we show that the discrepancy of X-ray and NMR soliton
widths can be understood as the difference between a distortive and a magnetic
width. Their ratio is controlled by the frustration of the spin system. By this
work, theoretical and experimental results can be reconciled in two important
points.Comment: 9 pages, 5 figures included, Revtex submitted to Physical Review
Random subcubes as a toy model for constraint satisfaction problems
We present an exactly solvable random-subcube model inspired by the structure
of hard constraint satisfaction and optimization problems. Our model reproduces
the structure of the solution space of the random k-satisfiability and
k-coloring problems, and undergoes the same phase transitions as these
problems. The comparison becomes quantitative in the large-k limit. Distance
properties, as well the x-satisfiability threshold, are studied. The model is
also generalized to define a continuous energy landscape useful for studying
several aspects of glassy dynamics.Comment: 21 pages, 4 figure
Diamagnetic Persistent Currents and Spontaneous Time-Reversal Symmetry Breaking in Mesoscopic Structures
Recently, new strongly interacting phases have been uncovered in mesoscopic
systems with chaotic scattering at the boundaries by two of the present authors
and R. Shankar. This analysis is reliable when the dimensionless conductance of
the system is large, and is nonperturbative in both disorder and interactions.
The new phases are the mesoscopic analogue of spontaneous distortions of the
Fermi surface induced by interactions in bulk systems and can occur in any
Fermi liquid channel with angular momentum . Here we show that the phase
with even has a diamagnetic persistent current (seen experimentally but
mysterious theoretically), while that with odd can be driven through a
transition which spontaneously breaks time-reversal symmetry by increasing the
coupling to dissipative leads.Comment: 4 pages, three eps figure
Elementary Excitations in Dimerized and Frustrated Heisenberg Chains
We present a detailed numerical analysis of the low energy excitation
spectrum of a frustrated and dimerized spin Heisenberg chain. In
particular, we show that in the commensurate spin--Peierls phase the ratio of
the singlet and triplet excitation gap is a universal function which depends on
the frustration parameter only. We identify the conditions for which a second
elementary triplet branch in the excitation spectrum splits from the continuum.
We compare our results with predictions from the continuum limit field theory .
We discuss the relevance of our data in connection with recent experiments on
, , and .Comment: Corrections to the text + 1 new figure, will appear in PRB (august
98
A Solvable Regime of Disorder and Interactions in Ballistic Nanostructures, Part I: Consequences for Coulomb Blockade
We provide a framework for analyzing the problem of interacting electrons in
a ballistic quantum dot with chaotic boundary conditions within an energy
(the Thouless energy) of the Fermi energy. Within this window we show that the
interactions can be characterized by Landau Fermi liquid parameters. When ,
the dimensionless conductance of the dot, is large, we find that the disordered
interacting problem can be solved in a saddle-point approximation which becomes
exact as (as in a large-N theory). The infinite theory shows a
transition to a strong-coupling phase characterized by the same order parameter
as in the Pomeranchuk transition in clean systems (a spontaneous
interaction-induced Fermi surface distortion), but smeared and pinned by
disorder. At finite , the two phases and critical point evolve into three
regimes in the plane -- weak- and strong-coupling regimes separated
by crossover lines from a quantum-critical regime controlled by the quantum
critical point. In the strong-coupling and quantum-critical regions, the
quasiparticle acquires a width of the same order as the level spacing
within a few 's of the Fermi energy due to coupling to collective
excitations. In the strong coupling regime if is odd, the dot will (if
isolated) cross over from the orthogonal to unitary ensemble for an
exponentially small external flux, or will (if strongly coupled to leads) break
time-reversal symmetry spontaneously.Comment: 33 pages, 14 figures. Very minor changes. We have clarified that we
are treating charge-channel instabilities in spinful systems, leaving
spin-channel instabilities for future work. No substantive results are
change
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