22,441 research outputs found
A simple and surprisingly accurate approach to the chemical bond obtained from dimensional scaling
We present a new dimensional scaling transformation of the Schrodinger
equation for the two electron bond. This yields, for the first time, a good
description of the two electron bond via D-scaling. There also emerges, in the
large-D limit, an intuitively appealing semiclassical picture, akin to a
molecular model proposed by Niels Bohr in 1913. In this limit, the electrons
are confined to specific orbits in the scaled space, yet the uncertainty
principle is maintained because the scaling leaves invariant the
position-momentum commutator. A first-order perturbation correction,
proportional to 1/D, substantially improves the agreement with the exact ground
state potential energy curve. The present treatment is very simple
mathematically, yet provides a strikingly accurate description of the potential
energy curves for the lowest singlet, triplet and excited states of H_2. We
find the modified D-scaling method also gives good results for other molecules.
It can be combined advantageously with Hartree-Fock and other conventional
methods.Comment: 4 pages, 5 figures, to appear in Phys. Rev. Letter
Spectral fluctuations and 1/f noise in the order-chaos transition regime
Level fluctuations in quantum system have been used to characterize quantum
chaos using random matrix models. Recently time series methods were used to
relate level fluctuations to the classical dynamics in the regular and chaotic
limit. In this we show that the spectrum of the system undergoing order to
chaos transition displays a characteristic noise and is
correlated with the classical chaos in the system. We demonstrate this using a
smooth potential and a time-dependent system modeled by Gaussian and circular
ensembles respectively of random matrix theory. We show the effect of short
periodic orbits on these fluctuation measures.Comment: 4 pages, 5 figures. Modified version. To appear in Phys. Rev. Let
Collisions with ice-volatile objects: Geological implications
The collision of the Earth with extra-terrestrial ice-volatile bodies is proposed as a mechanism to produce rapid changes in the geologic record. These bodies would be analogs of the ice satellites found for the Jovian planets and suspected for comets and certain low density bodies in the Asteroid belt. Five generic end-members are postulated: (1) water ice; (2) dry ice: carbon-carbon dioxide rich, (3) oceanic (chloride) ice; (4) sulfur-rich ice; (5) ammonia hydrate-rich ice; and (6) clathrate: methane-rich ice. Due to the volatile nature of these bodies, evidence for their impact with the Earth would be subtle and probably best reflected geochemically or in the fossil record. Actual boloids impacting the Earth may have a variable composition, generally some admixture with water ice. However for discussion purposes, only the effects of a dominant component will be treated. The general geological effects of such collisions, as a function of the dominant component would be: (1) rapid sea level rise unrelated to deglaciation, (2) decreased oceanic pH and rapid climatic warming or deglaciation; (3) increased paleosalinities; (4) increased acid rain; (5) increased oceanic pH and rapid carbonate deposition; and (6) rapid climatic warming or deglaciation
Can apparent superluminal neutrino speeds be explained as a quantum weak measurement?
Probably not.Comment: 10 pages, 1 figur
Hierarchical ResNeXt Models for Breast Cancer Histology Image Classification
Microscopic histology image analysis is a cornerstone in early detection of
breast cancer. However these images are very large and manual analysis is error
prone and very time consuming. Thus automating this process is in high demand.
We proposed a hierarchical system of convolutional neural networks (CNN) that
classifies automatically patches of these images into four pathologies: normal,
benign, in situ carcinoma and invasive carcinoma. We evaluated our system on
the BACH challenge dataset of image-wise classification and a small dataset
that we used to extend it. Using a train/test split of 75%/25%, we achieved an
accuracy rate of 0.99 on the test split for the BACH dataset and 0.96 on that
of the extension. On the test of the BACH challenge, we've reached an accuracy
of 0.81 which rank us to the 8th out of 51 teams
Nonclassical Degrees of Freedom in the Riemann Hamiltonian
The Hilbert-Polya conjecture states that the imaginary parts of the zeros of
the Riemann zeta function are eigenvalues of a quantum hamiltonian. If so,
conjectures by Katz and Sarnak put this hamiltonian in Altland and Zirnbauer's
universality class C. This implies that the system must have a nonclassical
two-valued degree of freedom. In such a system, the dominant primitive periodic
orbits contribute to the density of states with a phase factor of -1. This
resolves a previously mysterious sign problem with the oscillatory
contributions to the density of the Riemann zeros.Comment: 4 pages, no figures; v3-6 have minor corrections to v2, v2 has a more
complete solution of the sign problem than v
The genetic characterisation of adult plant resistance (APR) to yellow rust in the winter wheat cultivar Claire
The genetic characterisation of adult plant resistance (APR) to yellow rust in the winter wheat cultivar Claire
A generalized Pancharatnam geometric phase formula for three level systems
We describe a generalisation of the well known Pancharatnam geometric phase
formula for two level systems, to evolution of a three-level system along a
geodesic triangle in state space. This is achieved by using a recently
developed generalisation of the Poincare sphere method, to represent pure
states of a three-level quantum system in a convenient geometrical manner. The
construction depends on the properties of the group SU(3)\/ and its
generators in the defining representation, and uses geometrical objects and
operations in an eight dimensional real Euclidean space. Implications for an
n-level system are also discussed.Comment: 12 pages, Revtex, one figure, epsf used for figure insertio
Geometrical Optics of Beams with Vortices: Berry Phase and Orbital Angular Momentum Hall Effect
We consider propagation of a paraxial beam carrying the spin angular momentum
(polarization) and intrinsic orbital angular momentum (IOAM) in a smoothly
inhomogeneous isotropic medium. It is shown that the presence of IOAM can
dramatically enhance and rearrange the topological phenomena that previously
were considered solely in connection to the polarization of transverse waves.
In particular, the appearance of a new-type Berry phase that describes the
parallel transport of the beam structure along a curved ray is predicted. We
derive the ray equations demonstrating the splitting of beams with different
values of IOAM. This is the orbital angular momentum Hall effect, which
resembles Magnus effect for optical vortices. Unlike the recently discovered
spin Hall effect of photons, it can be much larger in magnitude and is inherent
to waves of any nature. Experimental means to detect the phenomena is
discussed.Comment: 5 pages, 2 figure
- …