267,086 research outputs found
Zooming in on Quantum Trajectories
We propose to use the effect of measurements instead of their number to study
the time evolution of quantum systems under monitoring. This time redefinition
acts like a microscope which blows up the inner details of seemingly
instantaneous transitions like quantum jumps. In the simple example of a
continuously monitored qubit coupled to a heat bath, we show that this
procedure provides well defined and simple evolution equations in an otherwise
singular strong monitoring limit. We show that there exists anomalous
observable localised on sharp transitions which can only be resolved with our
new effective time. We apply our simplified description to study the
competition between information extraction and dissipation in the evolution of
the linear entropy. Finally, we show that the evolution of the new time as a
function of the real time is closely related to a stable Levy process of index
1/2.Comment: 5 pages, 2 figure
Cosmological Information Contents on the Light-Cone
We develop a theoretical framework to describe the cosmological observables
on the past light cone such as the luminosity distance, weak lensing, galaxy
clustering, and the cosmic microwave background anisotropies. We consider that
all the cosmological observables include not only the background quantity, but
also the perturbation quantity, and they are subject to cosmic variance, which
sets the fundamental limits on the cosmological information that can be derived
from such observables, even in an idealized survey with an infinite number of
observations. To quantify the maximum cosmological information content, we
apply the Fisher information matrix formalism and spherical harmonic analysis
to cosmological observations, in which the angular and the radial positions of
the observables on the light cone carry different information. We discuss the
maximum cosmological information that can be derived from five different
observables: (1) type Ia supernovae, (2) cosmic microwave background
anisotropies, (3) weak gravitational lensing, (4) local baryon density, and (5)
galaxy clustering. We compare our results with the cosmic variance obtained in
the standard approaches, which treat the light cone volume as a cubic box of
simultaneity. We discuss implications of our formalism and ways to overcome the
fundamental limit.Comment: 39 pages, no figures, submitted to JCA
A random walk description of the heterogeneous glassy dynamics of attracting colloids
We study the heterogeneous dynamics of attractive colloidal particles close
to the gel transition using confocal microscopy experiments combined with a
theoretical statistical analysis. We focus on single particle dynamics and show
that the self part of the van Hove distribution function is not the Gaussian
expected for a Fickian process, but that it reflects instead the existence, at
any given time, of colloids with widely different mobilities. Our confocal
microscopy measurements can be described well by a simple analytical model
based on a conventional continuous time random walk picture, as already found
in several other glassy materials. In particular, the theory successfully
accounts for the presence of broad tails in the van Hove distributions that
exhibit exponential, rather than Gaussian, decay at large distance.Comment: 13 pages, 5 figs. Submitted to special issue "Classical and Quantum
Glasses" of J. Phys.: Condens. Matter; v2: response to refere
On the nature of continuous physical quantities in classical and quantum mechanics
Within the traditional Hilbert space formalism of quantum mechanics, it is
not possible to describe a particle as possessing, simultaneously, a sharp
position value and a sharp momentum value. Is it possible, though, to describe
a particle as possessing just a sharp position value (or just a sharp momentum
value)? Some, such as Teller (Journal of Philosophy, 1979), have thought that
the answer to this question is No -- that the status of individual continuous
quantities is very different in quantum mechanics than in classical mechanics.
On the contrary, I shall show that the same subtle issues arise with respect to
continuous quantities in classical and quantum mechanics; and that it is, after
all, possible to describe a particle as possessing a sharp position value
without altering the standard formalism of quantum mechanics.Comment: 26 pages, LaTe
Light and Motion in SDSS Stripe 82: The Catalogues
We present a new public archive of light-motion curves in Sloan Digital Sky
Survey (SDSS) Stripe 82, covering 99 deg in right ascension from RA = 20.7 h to
3.3 h and spanning 2.52 deg in declination from Dec = -1.26 to 1.26 deg, for a
total sky area of ~249 sq deg. Stripe 82 has been repeatedly monitored in the
u, g, r, i and z bands over a seven-year baseline. Objects are cross-matched
between runs, taking into account the effects of any proper motion. The
resulting catalogue contains almost 4 million light-motion curves of stellar
objects and galaxies. The photometry are recalibrated to correct for varying
photometric zeropoints, achieving ~20 mmag and ~30 mmag root-mean-square (RMS)
accuracy down to 18 mag in the g, r, i and z bands for point sources and
extended sources, respectively. The astrometry are recalibrated to correct for
inherent systematic errors in the SDSS astrometric solutions, achieving ~32 mas
and ~35 mas RMS accuracy down to 18 mag for point sources and extended sources,
respectively.
For each light-motion curve, 229 photometric and astrometric quantities are
derived and stored in a higher-level catalogue. On the photometric side, these
include mean exponential and PSF magnitudes along with uncertainties, RMS
scatter, chi^2 per degree of freedom, various magnitude distribution
percentiles, object type (stellar or galaxy), and eclipse, Stetson and Vidrih
variability indices. On the astrometric side, these quantities include mean
positions, proper motions as well as their uncertainties and chi^2 per degree
of freedom. The here presented light-motion curve catalogue is complete down to
r~21.5 and is at present the deepest large-area photometric and astrometric
variability catalogue available.Comment: MNRAS accepte
About Lorentz invariance in a discrete quantum setting
A common misconception is that Lorentz invariance is inconsistent with a
discrete spacetime structure and a minimal length: under Lorentz contraction, a
Planck length ruler would be seen as smaller by a boosted observer. We argue
that in the context of quantum gravity, the distance between two points becomes
an operator and show through a toy model, inspired by Loop Quantum Gravity,
that the notion of a quantum of geometry and of discrete spectra of geometric
operators, is not inconsistent with Lorentz invariance. The main feature of the
model is that a state of definite length for a given observer turns into a
superposition of eigenstates of the length operator when seen by a boosted
observer. More generally, we discuss the issue of actually measuring distances
taking into account the limitations imposed by quantum gravity considerations
and we analyze the notion of distance and the phenomenon of Lorentz contraction
in the framework of ``deformed (or doubly) special relativity'' (DSR), which
tentatively provides an effective description of quantum gravity around a flat
background. In order to do this we study the Hilbert space structure of DSR,
and study various quantum geometric operators acting on it and analyze their
spectral properties. We also discuss the notion of spacetime point in DSR in
terms of coherent states. We show how the way Lorentz invariance is preserved
in this context is analogous to that in the toy model.Comment: 25 pages, RevTe
Position Measurements Obeying Momentum Conservation
We present a hitherto unknown fundamental limitation to a basic measurement:
that of the position of a quantum object when the total momentum of the object
and apparatus is conserved. This result extends the famous Wigner-Araki-Yanase
(WAY) theorem, and shows that accurate position measurements are only
practically feasible if there is a large momentum uncertainty in the apparatus
- …