561 research outputs found
Computing heights via limits of Hodge structures
We consider the problem of explicitly computing BeilinsonâBloch heights of homologically trivial cycles on varieties defined over number fields. Recent results have established a congruence, up to the rational span of logarithms of primes, between the height of certain limit mixed Hodge structures and certain BeilinsonâBloch heights obtained from odd-dimensional hypersurfaces with a node. This congruence suggests a new method to compute BeilinsonâBloch heights. Here we explain how to compute the relevant limit mixed Hodge structures in practice, then apply our computational method to a nodal quartic curve and a nodal cubic threefold. In both cases we explain the nature of the primes occurring in the congruence.Number theory, Algebra and Geometr
Asymptotically exact dispersion relations for collective modes in a confined charged Fermi liquid
Using general local conservations laws we derive dispersion relations for
edge modes in a slab of electron liquid confined by a symmetric potential. The
dispersion relations are exact up to , where is a wave
vector and is an effective screening length. For a harmonic external
potential the dispersion relations are expressed in terms of the {\em exact}
static pressure and dynamic shear modulus of a homogeneous liquid with the
density taken at the slab core. We also derive a simple expression for the
frequency shift of the dipole (Kohn) modes in nearly parabolic quantum dots in
a magnetic field.Comment: RevTeX4, 4 pages. Revised version with new results on quantum qots
and wires. Published in Phys.Rev.
Path Integral Approach to the Nonextensive Canonical Density Matrix
Feynman's path integral is herein generalized to the nonextensive canonical
density matrix based on Tsallis entropy. This generalization is done in two
ways by using unnormalized and normalized constraints. Firstly, we consider the
path integral formulation with unnormalized constraints, and this
generalization is worked out through two different ways, which are shown to be
equivalent. These formulations with unnormalized constraints are solutions to
two generalized Bloch equations proposed in this work. The first form of the
generalized Bloch equation is linear, but with a temperature-dependent
effective Hamiltonian; the second form is nonlinear and resembles the anomalous
correlated diffusion equation (porous medium equation). Furthermore, we can
extend these results to the prescription of field theory using integral
representations. The second development is dedicated to analyzing the path
integral formulation with normalized constraints.
To illustrate the methods introduced here, we analyze the free particle case
and a non-interacting scalar field. The results herein obtained are expected to
be useful in the discussion of generic nonextensive contexts.Comment: (Univ. Est. de Maringa, PR- Brazil),17 pages, Late
Adiabatic response for Lindblad dynamics
We study the adiabatic response of open systems governed by Lindblad
evolutions. In such systems, there is an ambiguity in the assignment of
observables to fluxes (rates) such as velocities and currents. For the
appropriate notion of flux, the formulas for the transport coefficients are
simple and explicit and are governed by the parallel transport on the manifold
of instantaneous stationary states. Among our results we show that the response
coefficients of open systems, whose stationary states are projections, is given
by the adiabatic curvature.Comment: 33 pages, 4 figures, accepted versio
Quantum Dynamics in Non-equilibrium Strongly Correlated Environments
We consider a quantum point contact between two Luttinger liquids coupled to
a mechanical system (oscillator). For non-vanishing bias, we find an effective
oscillator temperature that depends on the Luttinger parameter. A generalized
fluctuation-dissipation relation connects the decoherence and dissipation of
the oscillator to the current-voltage characteristics of the device. Via a
spectral representation, this result is generalized to arbitrary leads in a
weak tunneling regime.Comment: 4 pages, 1 figur
A kinetic approach to eta' production from a CP-odd phase
The production of (eta,eta')- mesons during the decay of a CP-odd phase is
studied within an evolution operator approach. We derive a quantum kinetic
equation starting from the Witten-DiVecchia-Veneziano Lagrangian for
pseudoscalar mesons containing a U_A(1) symmetry breaking term. The non-linear
vacuum mean field for the flavour singlet pseudoscalar meson is treated as a
classical, self-interacting background field with fluctuations assumed to be
small. The numerical solution provides the time evolution of momentum
distribution function of produced eta'- mesons after a quench at the
deconfinement phase transition. We show that the time evolution of the momentum
distribution of the produced mesons depend strongly on the shape of the
effective potential at the end of the quench, exhibiting either parametric or
tachyonic resonances. Quantum statistical effects are essential and lead to a
pronounced Bose enhancement of the low momentum states.Comment: 10 pages, latex, epsfig, 6 figure
Prediction of Extreme Ultraviolet Variability Experiment (EVE)/Extreme Ultraviolet Spectro-Photometer (ESP) Irradiance from Solar Dynamics Observatory (SDO)/Atmospheric Imaging Assembly (AIA) Images Using Fuzzy Image Processing and Machine Learning
YesThe cadence and resolution of solar images have been increasing dramatically with the launch of new spacecraft such as STEREO and SDO. This increase in data volume provides new opportunities for solar researchers, but the efficient processing and analysis of these data create new challenges. We introduce a fuzzy-based solar feature-detection system in this article. The proposed system processes SDO/AIA images using fuzzy rules to detect coronal holes and active regions. This system is fast and it can handle different size images. It is tested on six months of solar data (1 October 2010 to 31 March 2011) to generate filling factors (ratio of area of solar feature to area of rest of the solar disc) for active regions and coronal holes. These filling factors are then compared to SDO/EVE/ESP irradiance measurements. The correlation between active-region filling factors and irradiance measurements is found to be very high, which has encouraged us to design a time-series prediction system using Radial Basis Function Networks to predict ESP irradiance measurements from our generated filling factors
-Strands
A -strand is a map for a Lie
group that follows from Hamilton's principle for a certain class of
-invariant Lagrangians. The SO(3)-strand is the -strand version of the
rigid body equation and it may be regarded physically as a continuous spin
chain. Here, -strand dynamics for ellipsoidal rotations is derived as
an Euler-Poincar\'e system for a certain class of variations and recast as a
Lie-Poisson system for coadjoint flow with the same Hamiltonian structure as
for a perfect complex fluid. For a special Hamiltonian, the -strand is
mapped into a completely integrable generalization of the classical chiral
model for the SO(3)-strand. Analogous results are obtained for the
-strand. The -strand is the -strand version of the
Bloch-Iserles ordinary differential equation, whose solutions exhibit dynamical
sorting. Numerical solutions show nonlinear interactions of coherent wave-like
solutions in both cases. -strand equations on the
diffeomorphism group are also introduced and shown
to admit solutions with singular support (e.g., peakons).Comment: 35 pages, 5 figures, 3rd version. To appear in J Nonlin Sc
Coherent matter wave inertial sensors for precision measurements in space
We analyze the advantages of using ultra-cold coherent sources of atoms for
matter-wave interferometry in space. We present a proof-of-principle experiment
that is based on an analysis of the results previously published in [Richard et
al., Phys. Rev. Lett., 91, 010405 (2003)] from which we extract the ratio h/m
for 87Rb. This measurement shows that a limitation in accuracy arises due to
atomic interactions within the Bose-Einstein condensate
Closed-Time Path Integral Formalism and Medium Effects of Non-Equilibrium QCD Matter
We apply the closed-time path integral formalism to study the medium effects
of non-equilibrium gluon matter. We derive the medium modified resummed gluon
propagator to the one loop level in non-equilibrium in the covariant gauge. The
gluon propagator we derive can be used to remove the infrared divergences in
the secondary parton collisions to study thermalization of minijet parton
plasma at RHIC and LHC.Comment: Final version, To appear in Physical Review D, Minor modification,
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