5,488 research outputs found
Lie algebra cohomology and group structure of gauge theories
We explicitly construct the adjoint operator of coboundary operator and
obtain the Hodge decomposition theorem and the Poincar\'e duality for the Lie
algebra cohomology of the infinite-dimensional gauge transformation group. We
show that the adjoint of the coboundary operator can be identified with the
BRST adjoint generator for the Lie algebra cohomology induced by
BRST generator . We also point out an interesting duality relation -
Poincar\'e duality - with respect to gauge anomalies and Wess-Zumino-Witten
topological terms. We consider the consistent embedding of the BRST adjoint
generator into the relativistic phase space and identify the
noncovariant symmetry recently discovered in QED with the BRST adjoint N\"other
charge .Comment: 24 pages, RevTex, Revised version submitted to J. Math. Phy
Cauchy problem for the Boltzmann-BGK model near a global Maxwellian
In this paper, we are interested in the Cauchy problem for the Boltzmann-BGK
model for a general class of collision frequencies. We prove that the
Boltzmann-BGK model linearized around a global Maxwellian admits a unique
global smooth solution if the initial perturbation is sufficiently small in a
high order energy norm. We also establish an asymptotic decay estimate and
uniform -stability for nonlinear perturbations.Comment: 26 page
Measurement of statistical evidence on an absolute scale following thermodynamic principles
Statistical analysis is used throughout biomedical research and elsewhere to
assess strength of evidence. We have previously argued that typical outcome
statistics (including p-values and maximum likelihood ratios) have poor
measure-theoretic properties: they can erroneously indicate decreasing evidence
as data supporting an hypothesis accumulate; and they are not amenable to
calibration, necessary for meaningful comparison of evidence across different
study designs, data types, and levels of analysis. We have also previously
proposed that thermodynamic theory, which allowed for the first time derivation
of an absolute measurement scale for temperature (T), could be used to derive
an absolute scale for evidence (E). Here we present a novel
thermodynamically-based framework in which measurement of E on an absolute
scale, for which "one degree" always means the same thing, becomes possible for
the first time. The new framework invites us to think about statistical
analyses in terms of the flow of (evidential) information, placing this work in
the context of a growing literature on connections among physics, information
theory, and statistics.Comment: Final version of manuscript as published in Theory in Biosciences
(2013
Emergent modular neural control drives coordinated motor actions.
A remarkable feature of motor control is the ability to coordinate movements across distinct body parts into a consistent, skilled action. To reach and grasp an object, 'gross' arm and 'fine' dexterous movements must be coordinated as a single action. How the nervous system achieves this coordination is currently unknown. One possibility is that, with training, gross and fine movements are co-optimized to produce a coordinated action; alternatively, gross and fine movements may be modularly refined to function together. To address this question, we recorded neural activity in the primary motor cortex and dorsolateral striatum during reach-to-grasp skill learning in rats. During learning, the refinement of fine and gross movements was behaviorally and neurally dissociable. Furthermore, inactivation of the primary motor cortex and dorsolateral striatum had distinct effects on skilled fine and gross movements. Our results indicate that skilled movement coordination is achieved through emergent modular neural control
Growth control of oxygen stoichiometry in homoepitaxial SrTiO3 films by pulsed laser epitaxy in high vacuum
In many transition metal oxides (TMOs), oxygen stoichiometry is one of the
most critical parameters that plays a key role in determining the structural,
physical, optical, and electrochemical properties of the material. However,
controlling the growth to obtain high quality single crystal films having the
right oxygen stoichiometry, especially in a high vacuum environment, has been
viewed as a challenge. In this work, we show that through proper control of the
plume kinetic energy, stoichiometric crystalline films can be synthesized
without generating oxygen defects, even in high vacuum. We use a model
homoepitaxial system of SrTiO3 (STO) thin films on single crystal STO
substrates. Physical property measurements indicate that oxygen vacancy
generation in high vacuum is strongly influenced by the energetics of the laser
plume, and it can be controlled by proper laser beam delivery. Therefore, our
finding not only provides essential insight into oxygen stoichiometry control
in high vacuum for understanding the fundamental properties of STO-based thin
films and heterostructures, but expands the utility of pulsed laser epitaxy of
other materials as well
Optically mediated nonlinear quantum optomechanics
We consider theoretically the optomechanical interaction of several
mechanical modes with a single quantized cavity field mode for linear and
quadratic coupling. We focus specifically on situations where the optical
dissipation is the dominant source of damping, in which case the optical field
can be adiabatically eliminated, resulting in effective multimode interactions
between the mechanical modes. In the case of linear coupling, the coherent
contribution to the interaction can be exploited e.g. in quantum state swapping
protocols, while the incoherent part leads to significant modifications of cold
damping or amplification from the single-mode situation. Quadratic coupling can
result in a wealth of possible effective interactions including the analogs of
second-harmonic generation and four-wave mixing in nonlinear optics, with
specific forms depending sensitively on the sign of the coupling. The
cavity-mediated mechanical interaction of two modes is investigated in two
limiting cases, the resolved sideband and the Doppler regime. As an
illustrative application of the formal analysis we discuss in some detail a
two-mode system where a Bose-Einstein condensate is optomechanically linearly
coupled to the moving end mirror of a Fabry-P\'erot cavity.Comment: 11 pages, 8 figure
Emergent Geometry and Quantum Gravity
We explain how quantum gravity can be defined by quantizing spacetime itself.
A pinpoint is that the gravitational constant G = L_P^2 whose physical
dimension is of (length)^2 in natural unit introduces a symplectic structure of
spacetime which causes a noncommutative spacetime at the Planck scale L_P. The
symplectic structure of spacetime M leads to an isomorphism between symplectic
geometry (M, \omega) and Riemannian geometry (M, g) where the deformations of
symplectic structure \omega in terms of electromagnetic fields F=dA are
transformed into those of Riemannian metric g. This approach for quantum
gravity allows a background independent formulation where spacetime as well as
matter fields is equally emergent from a universal vacuum of quantum gravity
which is thus dubbed as the quantum equivalence principle.Comment: Invited Review for Mod. Phys. Lett. A, 17 page
Optical spectroscopic investigation on the coupling of electronic and magnetic structure in multiferroic hexagonal RMnO3 (R = Gd, Tb, Dy, and Ho) thin films
We investigated the effects of temperature and magnetic field on the
electronic structure of hexagonal RMnO3 (R = Gd, Tb, Dy, and Ho) thin films
using optical spectroscopy. As the magnetic ordering of the system was
disturbed, a systematic change in the electronic structure was commonly
identified in this series. The optical absorption peak near 1.7 eV showed an
unexpectedly large shift of more than 150 meV from 300 K to 15 K, accompanied
by an anomaly of the shift at the Neel temperature. The magnetic field
dependent measurement clearly revealed a sizable shift of the corresponding
peak when a high magnetic field was applied. Our findings indicated strong
coupling between the magnetic ordering and the electronic structure in the
multiferroic hexagonal RMnO3 compounds.Comment: 16 pages including 4 figure
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