971 research outputs found
A Farewell to Liouvillians
We examine the Liouvillian approach to the quantum Hall plateau transition,
as introduced recently by Sinova, Meden, and Girvin [Phys. Rev. B {\bf 62},
2008 (2000)] and developed by Moore, Sinova and Zee [Phys. Rev. Lett. {\bf 87},
046801 (2001)]. We show that, despite appearances to the contrary, the
Liouvillian approach is not specific to the quantum mechanics of particles
moving in a single Landau level: we formulate it for a general disordered
single-particle Hamiltonian. We next examine the relationship between
Liouvillian perturbation theory and conventional calculations of
disorder-averaged products of Green functions and show that each term in
Liouvillian perturbation theory corresponds to a specific contribution to the
two-particle Green function. As a consequence, any Liouvillian approximation
scheme may be re-expressed in the language of Green functions. We illustrate
these ideas by applying Liouvillian methods, including their extension to Liouvillian flavors, to random matrix ensembles, using numerical
calculations for small integer and an analytic analysis for large .
We find that behavior at is different in qualitative ways from that
at . In particular, the limit expressed using Green
functions generates a pathological approximation, in which two-particle
correlation functions fail to factorize correctly at large separations of their
energy, and exhibit spurious singularities inside the band of random matrix
energy levels. We also consider the large treatment of the quantum Hall
plateau transition, showing that the same undesirable features are present
there, too
Critical points in edge tunneling between generic FQH states
A general description of weak and strong tunneling fixed points is developed
in the chiral-Luttinger-liquid model of quantum Hall edge states. Tunneling
fixed points are a subset of `termination' fixed points, which describe
boundary conditions on a multicomponent edge. The requirement of unitary time
evolution at the boundary gives a nontrivial consistency condition for possible
low-energy boundary conditions. The effect of interactions and random hopping
on fixed points is studied through a perturbative RG approach which generalizes
the Giamarchi-Schulz RG for disordered Luttinger liquids to broken left-right
symmetry and multiple modes. The allowed termination points of a multicomponent
edge are classified by a B-matrix with rational matrix elements. We apply our
approach to a number of examples, such as tunneling between a quantum Hall edge
and a superconductor and tunneling between two quantum Hall edges in the
presence of interactions. Interactions are shown to induce a continuous
renormalization of effective tunneling charge for the integrable case of
tunneling between two Laughlin states. The correlation functions of
electronlike operators across a junction are found from the B matrix using a
simple image-charge description, along with the induced lattice of boundary
operators. Many of the results obtained are also relevant to ordinary Luttinger
liquids.Comment: 23 pages, 6 figures. Xiao-Gang Wen: http://dao.mit.edu/~we
Quantum and classical localisation, the spin quantum Hall effect and generalisations
We consider network models for localisation problems belonging to symmetry
class C. This symmetry class arises in a description of the dynamics of
quasiparticles for disordered spin-singlet superconductors which have a
Bogoliubov - de Gennes Hamiltonian that is invariant under spin rotations but
not under time-reversal. Our models include but also generalise the one studied
previously in the context of the spin quantum Hall effect. For these systems we
express the disorder-averaged conductance and density of states in terms of
sums over certain classical random walks, which are self-avoiding and have
attractive interactions. A transition between localised and extended phases of
the quantum system maps in this way to a similar transition for the classical
walks. In the case of the spin quantum Hall effect, the classical walks are the
hulls of percolation clusters, and our approach provides an alternative
derivation of a mapping first established by Gruzberg, Read and Ludwig, Phys.
Rev. Lett. 82, 4254 (1999).Comment: 11 pages, 5 figure
Beam instrumentation for the Tevatron Collider
The Tevatron in Collider Run II (2001-present) is operating with six times
more bunches and many times higher beam intensities and luminosities than in
Run I (1992-1995). Beam diagnostics were crucial for the machine start-up and
the never-ending luminosity upgrade campaign. We present the overall picture of
the Tevatron diagnostics development for Run II, outline machine needs for new
instrumentation, present several notable examples that led to Tevatron
performance improvements, and discuss the lessons for future colliders
Geometric effects on T-breaking in p+ip and d+id superconductors
Superconducting order parameters that change phase around the Fermi surface
modify Josephson tunneling behavior, as in the phase-sensitive measurements
that confirmed order in the cuprates. This paper studies Josephson coupling
when the individual grains break time-reversal symmetry; the specific cases
considered are and , which may appear in SrRuO and
NaCoO(HO) respectively. -breaking order parameters
lead to frustrating phases when not all grains have the same sign of
time-reversal symmetry breaking, and the effects of these frustrating phases
depend sensitively on geometry for 2D arrays of coupled grains. These systems
can show perfect superconducting order with or without macroscopic
-breaking. The honeycomb lattice of superconducting grains has a
superconducting phase with no spontaneous breaking of but instead power-law
correlations. The superconducting transition in this case is driven by binding
of fractional vortices, and the zero-temperature criticality realizes a
generalization of Baxter's three-color model.Comment: 8 page
Edge Dynamics in Quantum Hall Bilayers II: Exact Results with Disorder and Parallel Fields
We study edge dynamics in the presence of interlayer tunneling, parallel
magnetic field, and various types of disorder for two infinite sequences of
quantum Hall states in symmetric bilayers. These sequences begin with the 110
and 331 Halperin states and include their fractional descendants at lower
filling factors; the former is easily realized experimentally while the latter
is a candidate for the experimentally observed quantum Hall state at a total
filling factor of 1/2 in bilayers. We discuss the experimentally interesting
observables that involve just one chiral edge of the sample and the correlation
functions needed for computing them. We present several methods for obtaining
exact results in the presence of interactions and disorder which rely on the
chiral character of the system. Of particular interest are our results on the
331 state which suggest that a time-resolved measurement at the edge can be
used to discriminate between the 331 and Pfaffian scenarios for the observed
quantum Hall state at filling factor 1/2 in realistic double-layer systems.Comment: revtex+epsf; two-up postscript at
http://www.sns.ias.edu/~leonid/ntwoup.p
Homologous Flares and Magnetic Field Topology in Active Region NOAA 10501 on 20 November 2003
We present and interpret observations of two morphologically homologous
flares that occurred in active region (AR) NOAA 10501 on 20 November 2003. Both
flares displayed four homologous H-alpha ribbons and were both accompanied by
coronal mass ejections (CMEs). The central flare ribbons were located at the
site of an emerging bipole in the center of the active region. The negative
polarity of this bipole fragmented in two main pieces, one rotating around the
positive polarity by ~ 110 deg within 32 hours. We model the coronal magnetic
field and compute its topology, using as boundary condition the magnetogram
closest in time to each flare. In particular, we calculate the location of
quasiseparatrix layers (QSLs) in order to understand the connectivity between
the flare ribbons. Though several polarities were present in AR 10501, the
global magnetic field topology corresponds to a quadrupolar magnetic field
distribution without magnetic null points. For both flares, the photospheric
traces of QSLs are similar and match well the locations of the four H-alpha
ribbons. This globally unchanged topology and the continuous shearing by the
rotating bipole are two key factors responsible for the flare homology.
However, our analyses also indicate that different magnetic connectivity
domains of the quadrupolar configuration become unstable during each flare, so
that magnetic reconnection proceeds differently in both events.Comment: 24 pages, 10 figures, Solar Physics (accepted
Fluctuations, dissipation and the dynamical Casimir effect
Vacuum fluctuations provide a fundamental source of dissipation for systems
coupled to quantum fields by radiation pressure. In the dynamical Casimir
effect, accelerating neutral bodies in free space give rise to the emission of
real photons while experiencing a damping force which plays the role of a
radiation reaction force. Analog models where non-stationary conditions for the
electromagnetic field simulate the presence of moving plates are currently
under experimental investigation. A dissipative force might also appear in the
case of uniform relative motion between two bodies, thus leading to a new kind
of friction mechanism without mechanical contact. In this paper, we review
recent advances on the dynamical Casimir and non-contact friction effects,
highlighting their common physical origin.Comment: 39 pages, 4 figures. Review paper to appear in Lecture Notes in
Physics, Volume on Casimir Physics, edited by Diego Dalvit, Peter Milonni,
David Roberts, and Felipe da Rosa. Minor changes, a reference adde
4pi Models of CMEs and ICMEs
Coronal mass ejections (CMEs), which dynamically connect the solar surface to
the far reaches of interplanetary space, represent a major anifestation of
solar activity. They are not only of principal interest but also play a pivotal
role in the context of space weather predictions. The steady improvement of
both numerical methods and computational resources during recent years has
allowed for the creation of increasingly realistic models of interplanetary
CMEs (ICMEs), which can now be compared to high-quality observational data from
various space-bound missions. This review discusses existing models of CMEs,
characterizing them by scientific aim and scope, CME initiation method, and
physical effects included, thereby stressing the importance of fully 3-D
('4pi') spatial coverage.Comment: 14 pages plus references. Comments welcome. Accepted for publication
in Solar Physics (SUN-360 topical issue
Origins of the Ambient Solar Wind: Implications for Space Weather
The Sun's outer atmosphere is heated to temperatures of millions of degrees,
and solar plasma flows out into interplanetary space at supersonic speeds. This
paper reviews our current understanding of these interrelated problems: coronal
heating and the acceleration of the ambient solar wind. We also discuss where
the community stands in its ability to forecast how variations in the solar
wind (i.e., fast and slow wind streams) impact the Earth. Although the last few
decades have seen significant progress in observations and modeling, we still
do not have a complete understanding of the relevant physical processes, nor do
we have a quantitatively precise census of which coronal structures contribute
to specific types of solar wind. Fast streams are known to be connected to the
central regions of large coronal holes. Slow streams, however, appear to come
from a wide range of sources, including streamers, pseudostreamers, coronal
loops, active regions, and coronal hole boundaries. Complicating our
understanding even more is the fact that processes such as turbulence,
stream-stream interactions, and Coulomb collisions can make it difficult to
unambiguously map a parcel measured at 1 AU back down to its coronal source. We
also review recent progress -- in theoretical modeling, observational data
analysis, and forecasting techniques that sit at the interface between data and
theory -- that gives us hope that the above problems are indeed solvable.Comment: Accepted for publication in Space Science Reviews. Special issue
connected with a 2016 ISSI workshop on "The Scientific Foundations of Space
Weather." 44 pages, 9 figure
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