20,464 research outputs found
Semiparametric Bayesian models for human brain mapping
Functional magnetic resonance imaging (fMRI) has led to enormous progress in human brain mapping. Adequate analysis of the massive spatiotemporal data sets generated by this imaging technique, combining parametric and non-parametric components, imposes challenging problems in statistical modelling. Complex hierarchical Bayesian models in combination with computer-intensive Markov chain Monte Carlo inference are promising tools.The purpose of this paper is twofold. First, it provides a review of general semiparametric Bayesian models for the analysis of fMRI data. Most approaches focus on important but separate temporal or spatial aspects of the overall problem, or they proceed by stepwise procedures. Therefore, as a second aim, we suggest a complete spatiotemporal model for analysing fMRI data within a unified semiparametric Bayesian framework. An application to data from a visual stimulation experiment illustrates our approach and demonstrates its computational feasibility
Quantum critical behaviour of the plateau-insulator transition in the quantum Hall regime
High-field magnetotransport experiments provide an excellent tool to
investigate the plateau-insulator phase transition in the integral quantum Hall
effect. Here we review recent low-temperature high-field magnetotransport
studies carried out on several InGaAs/InP heterostructures and an InGaAs/GaAs
quantum well. We find that the longitudinal resistivity near the
critical filling factor ~ 0.5 follows the universal scaling law
, where . The critical exponent equals ,
which indicates that the plateau-insulator transition falls in a non-Fermi
liquid universality class.Comment: 8 pages, accepted for publication in Proceedings of the Yamada
Conference LX on Research in High Magnetic Fields (August 16-19, 2006,
Sendai
Binary neutron star mergers: a jet engine for short gamma-ray bursts
We perform magnetohydrodynamic simulations in full general relativity (GRMHD)
of quasi-circular, equal-mass, binary neutron stars that undergo merger. The
initial stars are irrotational, polytropes and are magnetized. We explore
two types of magnetic-field geometries: one where each star is endowed with a
dipole magnetic field extending from the interior into the exterior, as in a
pulsar, and the other where the dipole field is initially confined to the
interior. In both cases the adopted magnetic fields are initially dynamically
unimportant. The merger outcome is a hypermassive neutron star that undergoes
delayed collapse to a black hole (spin parameter )
immersed in a magnetized accretion disk. About ms following merger, the region above the black hole poles
becomes strongly magnetized, and a collimated, mildly relativistic outflow ---
an incipient jet --- is launched. The lifetime of the accretion disk, which
likely equals the lifetime of the jet, is s. In contrast to black hole--neutron star mergers, we find
that incipient jets are launched even when the initial magnetic field is
confined to the interior of the stars.Comment: 6 pages, 3 figures, 1 table, matches published versio
Localizing coalescing massive black hole binaries with gravitational waves
Massive black hole binary coalescences are prime targets for space-based
gravitational wave (GW) observatories such as {\it LISA}. GW measurements can
localize the position of a coalescing binary on the sky to an ellipse with a
major axis of a few tens of arcminutes to a few degrees, depending on source
redshift, and a minor axis which is times smaller. Neglecting weak
gravitational lensing, the GWs would also determine the source's luminosity
distance to better than percent accuracy for close sources, degrading to
several percent for more distant sources. Weak lensing cannot, in fact, be
neglected and is expected to limit the accuracy with which distances can be
fixed to errors no less than a few percent. Assuming a well-measured cosmology,
the source's redshift could be inferred with similar accuracy. GWs alone can
thus pinpoint a binary to a three-dimensional ``pixel'' which can help guide
searches for the hosts of these events. We examine the time evolution of this
pixel, studying it at merger and at several intervals before merger. One day
before merger, the major axis of the error ellipse is typically larger than its
final value by a factor of . The minor axis is larger by a factor
of , and, neglecting lensing, the error in the luminosity distance is
larger by a factor of . This large change over a short period of
time is due to spin-induced precession, which is strongest in the final days
before merger. The evolution is slower as we go back further in time. For , we find that GWs will localize a coalescing binary to within $\sim 10\
\mathrm{deg}^2$ as early as a month prior to merger and determine distance (and
hence redshift) to several percent.Comment: 30 pages, 10 figures, 5 tables. Version published in Ap
First excited state calculation using different phonon bases for the two-site Holstein model
The single-electron energy and static charge-lattice deformation correlations
have been calculated for the first excited state of a two-site Holstein model
within perturbative expansions using different standard phonon bases obtained
through Lang-Firsov (LF) transformation, LF with squeezed phonon states,
modified LF, modified LF transformation with squeezed phonon states, and also
within weak-coupling perturbation approach. Comparisons of the convergence of
the perturbative expansions for different phonon bases reveal that modified LF
approach works much better than other approaches for major range of the
coupling strength.Comment: 11 pages (REVTEX), 4 postscript figure
Towards a quantum field theory of primitive string fields
We denote generating functions of massless even higher spin fields "primitive
string fields" (PSF's). In an introduction we present the necessary definitions
and derive propagators and currents of these PDF's on flat space. Their
off-shell cubic interaction can be derived after all off-shell cubic
interactions of triplets of higher spin fields have become known [2],[3]. Then
we discuss four-point functions of any quartet of PSF's. In subsequent sections
we exploit the fact that higher spin field theories in are
determined by AdS/CFT correspondence from universality classes of critical
systems in dimensional flat spaces. The O(N) invariant sectors of the O(N)
vector models for play for us the role of "standard
models", for varying , they contain e.g. the Ising model for N=1 and the
spherical model for . A formula for the masses squared that break
gauge symmetry for these O(N) classes is presented for d = 3. For the PSF on
space it is shown that it can be derived by lifting the PSF on flat space
by a simple kernel which contains the sum over all spins. Finally we use an
algorithm to derive all symmetric tensor higher spin fields. They arise from
monomials of scalar fields by derivation and selection of conformal
(quasiprimary) fields. Typically one monomial produces a multiplet of spin
conformal higher spin fields for all , they are distinguished by
their anomalous dimensions (in ) or by their mass (in ). We sum
over these multiplets and the spins to obtain "string type fields", one for
each such monomial.Comment: 16 pages,Late
Thermodynamic properties of Holstein polarons and the effects of disorder
The ground state and finite temperature properties of polarons are studied
considering a two-site and a four-site Holstein model by exact diagonalization
of the Hamiltonian. The kinetic energy, Drude weight, correlation functions
involving charge and lattice deformations, and the specific heat have been
evaluated as a function of electron-phonon (e-ph) coupling strength and
temperature. The effects of site diagonal disorder on the above properties have
been investigated. The disorder is found to suppress the kinetic energy and the
Drude weight, reduces the spatial extension of the polaron, and makes the
large-to-small polaron crossover smoother. Increasing temperature also plays
similar role. For strong coupling the kinetic energy arises mainly from the
incoherent hopping processes owing to the motion of electrons within the
polaron and is almost independent of the disorder strength. From the coherent
and incoherent contributions to the kinetic energy, the temperature above which
the incoherent part dominates is determined as a function of e-ph coupling
strength.Comment: 17 pages. 17 figure
Momentum average approximation for models with boson-modulated hopping: Role of closed loops in the dynamical generation of a finite quasiparticle mass
We generalize the momentum average approximation to study the properties of
single polarons in models with boson affected hopping, where the fermion-boson
scattering depends explicitly on both the fermion's and the boson's momentum.
As a specific example, we investigate the Edwards fermion-boson model in both
one and two dimensions. In one dimension, this allows us to compare our results
with exact diagonalization results, to validate the accuracy of our
approximation. The generalization to two-dimensional lattices allows us to
calculate the polaron's quasiparticle weight and dispersion throughout the
Brillouin zone and to demonstrate the importance of Trugman loops in generating
a finite effective mass even when the free fermion has an infinite mass.Comment: 15 pages, 14 figure
Phonon-affected steady-state transport through molecular quantum dots
We consider transport through a vibrating molecular quantum dot contacted to
macroscopic leads acting as charge reservoirs. In the equilibrium and
nonequilibrium regime, we study the formation of a polaron-like transient state
at the quantum dot for all ratios of the dot-lead coupling to the energy of the
local phonon mode. We show that the polaronic renormalization of the dot-lead
coupling is a possible mechanism for negative differential conductance.
Moreover, the effective dot level follows one of the lead chemical potentials
to enhance resonant transport, causing novel features in the inelastic
tunneling signal. In the linear response regime, we investigate the impact of
the electron-phonon interaction on the thermoelectrical properties of the
quantum dot device.Comment: 11 pages, 7 figures, FQMT11 Proceeding
On Quantum Groups in the Hubbard Model with Phonons
The correct Hamiltonian for an extended Hubbard model with quantum group
symmetry as introduced by A. Montorsi and M. Rasetti is derived for a
D-dimensional lattice. It is shown that the superconducting SUq(2) holds as a
true quantum symmetry only for D = 1 and that terms of higher order in the
fermionic operators in addition to phonons are required for a quantum symmetric
hamiltonian. The condition for quantum symmetry is "half filling" and there is
no local electron-phonon coupling. A discussion of Quantum symmetries in
general is given in a formalism that should be readily accessible to non
Hopf-algebraists.Comment: latex, 17 page
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