2,141 research outputs found
Wigner transform and pseudodifferential operators on symmetric spaces of non-compact type
We obtain a general expression for a Wigner transform (Wigner function) on
symmetric spaces of non-compact type and study the Weyl calculus of
pseudodifferential operators on them
Topological Insulators and Superconductors from String Theory
Topological insulators and superconductors in different spatial dimensions
and with different discrete symmetries have been fully classified recently,
revealing a periodic structure for the pattern of possible types of topological
insulators and supercondutors, both in terms of spatial dimensions and in terms
of symmetry classes. It was proposed that K-theory is behind the periodicity.
On the other hand, D-branes, a solitonic object in string theory, are also
known to be classified by K-theory. In this paper, by inspecting low-energy
effective field theories realized by two parallel D-branes, we establish a
one-to-one correspondence between the K-theory classification of topological
insulators/superconductors and D-brane charges. In addition, the string theory
realization of topological insulators and superconductors comes naturally with
gauge interactions, and the Wess-Zumino term of the D-branes gives rise to a
gauge field theory of topological nature, such as ones with the Chern-Simons
term or the -term in various dimensions. This sheds light on
topological insulators and superconductors beyond non-interacting systems, and
the underlying topological field theory description thereof. In particular, our
string theory realization includes the honeycomb lattice Kitaev model in two
spatial dimensions, and its higher-dimensional extensions. Increasing the
number of D-branes naturally leads to a realization of topological insulators
and superconductors in terms of holography (AdS/CFT).Comment: 13 pages, 3 figures;references update
Searching for a trail of evidence in a maze
Consider a graph with a set of vertices and oriented edges connecting pairs
of vertices. Each vertex is associated with a random variable and these are
assumed to be independent. In this setting, suppose we wish to solve the
following hypothesis testing problem: under the null, the random variables have
common distribution N(0,1) while under the alternative, there is an unknown
path along which random variables have distribution , , and
distribution N(0,1) away from it. For which values of the mean shift can
one reliably detect and for which values is this impossible? Consider, for
example, the usual regular lattice with vertices of the form and oriented edges , where . We show that for paths of length starting at
the origin, the hypotheses become distinguishable (in a minimax sense) if
, while they are not if . We derive
equivalent results in a Bayesian setting where one assumes that all paths are
equally likely; there, the asymptotic threshold is . We
obtain corresponding results for trees (where the threshold is of order 1 and
independent of the size of the tree), for distributions other than the Gaussian
and for other graphs. The concept of the predictability profile, first
introduced by Benjamini, Pemantle and Peres, plays a crucial role in our
analysis.Comment: Published in at http://dx.doi.org/10.1214/07-AOS526 the Annals of
Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical
Statistics (http://www.imstat.org
On the Solvability of the Transvection group of Extrinsic Symplectic Symmetric Spaces
Let be a symplectic symmetric space, and let be an
extrinsic symplectic symmetric immersion, i.e., is a symplectic
vector space and is an injective symplectic immersion such that for
each point , the geodesic symmetry in is compatible with the
reflection in the affine normal space at . We show that the
existence of such an immersion implies that the transvection group of is
solvable.Comment: 15 page
Lightlike simultaneity, comoving observers and distances in general relativity
We state a condition for an observer to be comoving with another observer in
general relativity, based on the concept of lightlike simultaneity. Taking into
account this condition, we study relative velocities, Doppler effect and light
aberration. We obtain that comoving observers observe the same light ray with
the same frequency and direction, and so gravitational redshift effect is a
particular case of Doppler effect. We also define a distance between an
observer and the events that it observes, that coincides with the known affine
distance. We show that affine distance is a particular case of radar distance
in the Minkowski space-time and generalizes the proper radial distance in the
Schwarzschild space-time. Finally, we show that affine distance gives us a new
concept of distance in Robertson-Walker space-times, according to Hubble law.Comment: 17 pages, 5 figures. Since "lightlike distance" is in fact the known
"affine distance", the notation has been change
Large-N Solution of the Heterotic CP(N-1) Model with Twisted Masses
We address a number of unanswered questions in the N=(0,2)-deformed CP(N-1)
model with twisted masses. In particular, we complete the program of solving
CP(N-1) model with twisted masses in the large-N limit. In hep-th/0512153
nonsupersymmetric version of the model with the Z_N symmetric twisted masses
was analyzed in the framework of Witten's method. In arXiv:0803.0698 this
analysis was extended: the large-N solution of the heterotic N=(0,2) CP(N-1)
model with no twisted masses was found. Here we solve this model with the
twisted masses switched on. Dynamical scenarios at large and small m are
studied (m is the twisted mass scale). We found three distinct phases and two
phase transitions on the m plane. Two phases with the spontaneously broken
Z_N-symmetry are separated by a phase with unbroken Z_N. This latter phase is
characterized by a unique vacuum and confinement of all U(1) charged fields
("quarks"). In the broken phases (one of them is at strong coupling) there are
N degenerate vacua and no confinement, similarly to the situation in the
N=(2,2) model. Supersymmetry is spontaneously broken everywhere except a circle
|m|=\Lambda in the Z_N-unbroken phase. Related issues are considered. In
particular, we discuss the mirror representation for the heterotic model in a
certain limiting case.Comment: 69 pages, 14 figures; typos corrected, final version to appear in
PRD; v Jan. 2014 Erratum added on p. 50, two references added and two
references update
Reconstructing emission from pre-reionization sources with cosmic infrared background fluctuation measurements by the JWST
We present new methodology to use cosmic infrared background (CIB)
fluctuations to probe sources at 10<z<30 from a JWST/NIRCam configuration that
will isolate known galaxies to 28 AB mag at 0.5--5 micron. At present
significant mutually consistent source-subtracted CIB fluctuations have been
identified in the Spitzer and Akari data at 2--5 micron, but we demonstrate
internal inconsistencies at shorter wavelengths in the recent CIBER data. We
evaluate CIB contributions from remaining galaxies and show that the bulk of
the high-z sources will be in the confusion noise of the NIRCam beam, requiring
CIB studies. The accurate measurement of the angular spectrum of the
fluctuations and probing the dependence of its clustering component on the
remaining shot noise power would discriminate between the various currently
proposed models for their origin and probe the flux distribution of its
sources. We show that the contribution to CIB fluctuations from remaining
galaxies is large at visible wavelengths for the current instruments precluding
probing the putative Lyman-break of the CIB fluctuations. We demonstrate that
with the proposed JWST configuration such measurements will enable probing the
Lyman break. We develop a Lyman-break tomography method to use the NIRCam
wavelength coverage to identify or constrain, via the adjacent two-band
subtraction, the history of emissions over 10<z<30 as the Universe comes out of
the 'Dark Ages'. We apply the proposed tomography to the current Spitzer/IRAC
measurements at 3.6 and 4.5 micron, to find that it already leads to
interestingly low upper limit on emissions at z>30.Comment: ApJ, in press. Minor revisions/additions to match the version in
proof
Structure and magnetic properties of the cubic oxide fluoride BaFeO2F
Fluorination of the parent oxide, BaFeO3- δ, with polyvinylidine fluoride gives rise to a cubic compound with a = 4.0603(4) Å at 298K. 57Fe Mössbauer spectra confirmed that all the iron is present as Fe3+. Neutron diffraction data showed complete occupancy of the anion sites indicating a composition BaFeO2F, with a large displacement of the iron off-site. The magnetic ordering temperature was determined as TN = 645±5K. Neutron diffraction data at 4.2K established G-type antiferromagnetism with a magnetic moment per Fe3+ ion of 3.95μB. However, magnetisation measurements indicated the presence of a weak ferromagnetic moment which is assigned to the canting of the antiferromagnetic structure. 57Fe Mössbauer spectra in the temperature range 10 to 300K were fitted with a model of fluoride ion distribution that retains charge neutrality of the perovskite unit cel
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