380 research outputs found
On the Precision of a Length Measurement
We show that quantum mechanics and general relativity imply the existence of
a minimal length. To be more precise, we show that no operational device
subject to quantum mechanics, general relativity and causality could exclude
the discreteness of spacetime on lengths shorter than the Planck length. We
then consider the fundamental limit coming from quantum mechanics, general
relativity and causality on the precision of the measurement of a length.Comment: 5 pages, to appear in the proceedings of the 2006 International
School of Subnuclear Physics in Erice and in ''Young Scientists'' online-only
supplement of the European Physical Journal C-Direct (Springer
Extensive alternative splicing within the amino-propeptide coding domain of α2(XI) procollagen mRNAs: Expression of transcripts encoding truncated pro-α chains
Heterogeneity in type XI procollagen structure is extensive because all three α(XI) collagen genes undergo complex alternative splicing within the amino-propeptide coding domain. Exon 7 of the human and exons 6-8 of the mouse α2(XI) collagen genes, encoding part of the amino-propeptide variable region, have recently been shown to be alternatively spliced. We show that exon 6-containing mRNAs for human α2(XI) procollagen are expressed at 28 weeks in fetal tendon and cartilage but not at 38-44 days or 11 weeks. In the mouse, exon 6 is expressed in chondrocytes from 13.5 days onward. We recently identified conserved sequences within intron 6 of the human and mouse α2(XI) collagen genes, containing additional consensus splice acceptor and donor sites that potentially increase the size of exon 7, dividing it into three parts, designated 7A, 7B, and 7C. We show by reverse transcription polymerase chain reaction and in situ hybridization that these potential splice sites are used to yield additional α2(XI) procollagen mRNA splice variants that are expressed in fetal tissues. In human, expression of exon 7B-containing transcripts may be developmental stage-specific. Interestingly, inclusion of exon 7A or exon 7B in human and mouse α2(XI) procollagen mRNAs, respectively, would result in the insertion of an in-frame termination codon, suggesting that some of the additional splice variants encode a truncated pro-α2(XI) chain
Time Uncertainty in Quantum Gravitational Systems
It is generally argued that the combined effect of Heisenberg principle and
general relativity leads to a minimum time uncertainty. Most of the analyses
supporting this conclusion are based on a perturbative approach to
quantization. We consider a simple family of gravitational models, including
the Einstein-Rosen waves, in which the (non-linearized) inclusion of gravity
changes the normalization of time translations by a monotonic energy-dependent
factor. In these circumstances, it is shown that a maximum time resolution
emerges non-perturbatively only if the total energy is bounded. Perturbatively,
however, there always exists a minimum uncertainty in the physical time.Comment: (4 pages, no figures) Accepted for publication in Physical Review
Measurement of the space-time interval between two events using the retarded and advanced times of each event with respect to a time-like world-line
Several recent studies have been devoted to investigating the limitations
that ordinary quantum mechanics and/or quantum gravity might impose on the
measurability of space-time observables. These analyses are often confined to
the simplified context of two-dimensional flat space-time and rely on a simple
procedure for the measurement of space-like distances based on the exchange of
light signals. We present a generalization of this measurement procedure
applicable to all three types of space-time intervals between two events in
space-times of any number of dimensions. We also present some preliminary
observations on an alternative measurement procedure that can be applied taking
into account the gravitational field of the measuring apparatus, and briefly
discuss quantum limitations of measurability in this context.Comment: 17 page
Quantized adiabatic charge pumping and resonant transmission
Adiabatically pumped charge, carried by non-interacting electrons through a
quantum dot in a turnstile geometry, is studied as function of the strength of
the two modulating potentials (related to the conductances of the two
point-contacts to the leads) and of the phase shift between them. It is shown
that the magnitude and sign of the pumped charge are determined by the relative
position and orientation of the closed contour traversed by the system in the
parameter plane, and the transmission peaks (or resonances) in that plane.
Integer values (in units of the electronic charge ) of the pumped charge
(per modulation period) are achieved when a transmission peak falls inside the
pumping contour. The integer value is given by the winding number of the
pumping contour: double winding in the same direction gives a charge of 2,
while winding around two opposite branches of the transmission peaks or winding
in opposite directions can give a charge close to zero.Comment: 7 pages, 12 figure
Analytic theory of ground-state properties of a three-dimensional electron gas at varying spin polarization
We present an analytic theory of the spin-resolved pair distribution
functions and the ground-state energy of an electron gas
with an arbitrary degree of spin polarization. We first use the Hohenberg-Kohn
variational principle and the von Weizs\"{a}cker-Herring ideal kinetic energy
functional to derive a zero-energy scattering Schr\"{o}dinger equation for
. The solution of this equation is implemented
within a Fermi-hypernetted-chain approximation which embodies the Hartree-Fock
limit and is shown to satisfy an important set of sum rules. We present
numerical results for the ground-state energy at selected values of the spin
polarization and for in both a paramagnetic and a fully
spin-polarized electron gas, in comparison with the available data from Quantum
Monte Carlo studies over a wide range of electron density.Comment: 13 pages, 8 figures, submitted to Phys. Rev.
Statistical anisotropy of magnetohydrodynamic turbulence
Direct numerical simulations of decaying and forced magnetohydrodynamic (MHD)
turbulence without and with mean magnetic field are analyzed by higher-order
two-point statistics. The turbulence exhibits statistical anisotropy with
respect to the direction of the local magnetic field even in the case of global
isotropy. A mean magnetic field reduces the parallel-field dynamics while in
the perpendicular direction a gradual transition towards two-dimensional MHD
turbulence is observed with inertial-range scaling of the
perpendicular energy spectrum. An intermittency model based on the Log-Poisson
approach, , is able to describe the observed
structure function scalings.Comment: 4 pages, 3 figures. To appear in Phys.Rev.
Polynomial-Time Amoeba Neighborhood Membership and Faster Localized Solving
We derive efficient algorithms for coarse approximation of algebraic
hypersurfaces, useful for estimating the distance between an input polynomial
zero set and a given query point. Our methods work best on sparse polynomials
of high degree (in any number of variables) but are nevertheless completely
general. The underlying ideas, which we take the time to describe in an
elementary way, come from tropical geometry. We thus reduce a hard algebraic
problem to high-precision linear optimization, proving new upper and lower
complexity estimates along the way.Comment: 15 pages, 9 figures. Submitted to a conference proceeding
Hawking Temperature in Taub-NUT (A)dS spaces via the Generalized Uncertainty Principle
Using the extended forms of the Heisenberg uncertainty principle from string
theory and the quantum gravity theory, we drived Hawking temperature of a
Taub-Nut-(A)dS black hole. In spite of their distinctive natures such as
asymptotically locally flat and breakdown of the area theorem of the horizon
for the black holes, we show that the corrections to Hawking temperature by the
generalized versions of the the Heisenberg uncertainty principle increases like
the Schwarzschild-(A)dS black hole and give the reason why the Taub-Nut-(A)dS
metric may have AdS/CFT dual picture.Comment: version published in General Relativity and Gravitatio
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