25,301 research outputs found

### Linear Form of Canonical Gravity

Recent work in the literature has shown that general relativity can be
formulated in terms of a jet bundle which, in local coordinates, has five
entries: local coordinates on Lorentzian space-time, tetrads, connection
one-forms, multivelocities corresponding to the tetrads and multivelocities
corresponding to the connection one-forms. The derivatives of the Lagrangian
with respect to the latter class of multivelocities give rise to a set of
multimomenta which naturally occur in the constraint equations. Interestingly,
all the constraint equations of general relativity are linear in terms of this
class of multimomenta. This construction has been then extended to complex
general relativity, where Lorentzian space-time is replaced by a
four-complex-dimensional complex-Riemannian manifold. One then finds a
holomorphic theory where the familiar constraint equations are replaced by a
set of equations linear in the holomorphic multimomenta, providing such
multimomenta vanish on a family of two-complex-dimensional surfaces. In quantum
gravity, the problem arises to quantize a real or a holomorphic theory on the
extended space where the multimomenta can be defined.Comment: 5 pages, plain-te

### Essential self-adjointness in one-loop quantum cosmology

The quantization of closed cosmologies makes it necessary to study squared
Dirac operators on closed intervals and the corresponding quantum amplitudes.
This paper proves self-adjointness of these second-order elliptic operators.Comment: 14 pages, plain Tex. An Erratum has been added to the end, which
corrects section

### The genesis of the quantum theory of the chemical bond

An historical overview is given of the relevant steps that allowed the
genesis of the quantum theory of the chemical bond, starting from the
appearance of the new quantum mechanics and following later developments till
approximately 1931. General ideas and some important details are discussed
concerning molecular spectroscopy, as well as quantum computations for simple
molecular systems performed within perturbative and variational approaches, for
which the Born-Oppenheimer method provided a quantitative theory accounting for
rotational, vibrational and electronic states. The novel concepts introduced by
the Heitler-London theory, complemented by those underlying the method of the
molecular orbitals, are critically analyzed along with some of their relevant
applications. Further improvements in the understanding of the nature of the
chemical bond are also considered, including the ideas of one-electron and
three-electron bonds introduced by Pauling, as well as the generalizations of
the Heitler-London theory firstly performed by Majorana, which allowed the
presence of ionic structures into homopolar compounds and provided the
theoretical proof of the stability of the helium molecular ion. The study of
intermolecular interactions, as developed by London, is finally examined.Comment: amsart, 34 pages, 2 figure

### Majorana solution of the Thomas-Fermi equation

We report on an original method, due to Majorana, leading to a
semi-analytical series solution of the Thomas-Fermi equation, with appropriate
boundary conditions, in terms of only one quadrature. We also deduce a general
formula for such a solution which avoids numerical integration, but is
expressed in terms of the roots of a given polynomial equation.Comment: RevTex, 5 pages, 1 figur

### Following Weyl on Quantum Mechanics: the contribution of Ettore Majorana

After a quick historical account of the introduction of the group-theoretical
description of Quantum Mechanics in terms of symmetries, as proposed by Weyl,
we examine some unpublished papers by Ettore Majorana. Remarkable results
achieved by him in frontier research topics as well as in physics teaching
point out that the Italian physicist can be well considered as a follower of
Weyl in his reformulation of Quantum Mechanics.Comment: LaTeX, 15 pages, 1 ps figur

### Ettore Majorana's course on Theoretical Physics: a recent discovery

We analyze in some detail the course of Theoretical Physics held by Ettore
Majorana at the University of Naples in 1938, just before his mysterious
disappearance. In particular we present the recently discovered "Moreno Paper",
where all the lecture notes are reported. Six of these lectures are not present
in the collection of the original manuscripts conserved at the Domus Galilaeana
in Pisa, consisting of only ten lectures.Comment: AMS-latex, 16 pages, 2 figure

### PASSATA - Object oriented numerical simulation software for adaptive optics

We present the last version of the PyrAmid Simulator Software for Adaptive
opTics Arcetri (PASSATA), an IDL and CUDA based object oriented software
developed in the Adaptive Optics group of the Arcetri observatory for
Monte-Carlo end-to-end adaptive optics simulations. The original aim of this
software was to evaluate the performance of a single conjugate adaptive optics
system for ground based telescope with a pyramid wavefront sensor. After some
years of development, the current version of PASSATA is able to simulate
several adaptive optics systems: single conjugate, multi conjugate and ground
layer, with Shack Hartmann and Pyramid wavefront sensors. It can simulate from
8m to 40m class telescopes, with diffraction limited and resolved sources at
finite or infinite distance from the pupil. The main advantages of this
software are the versatility given by the object oriented approach and the
speed given by the CUDA implementation of the most computational demanding
routines. We describe the software with its last developments and present some
examples of application.Comment: 9 pages, 2 figures, 3 tables. SPIE conference Astronomical Telescopes
and Instrumentation, 26 June - 01 July 2016, Edinburgh, Scotland, United
Kingdo

### Tightening the uncertainty principle for stochastic currents

We connect two recent advances in the stochastic analysis of nonequilibrium
systems: the (loose) uncertainty principle for the currents, which states that
statistical errors are bounded by thermodynamic dissipation; and the analysis
of thermodynamic consistency of the currents in the light of symmetries.
Employing the large deviation techniques presented in [Gingrich et al., Phys.
Rev. Lett. 2016] and [Pietzonka et al., Phys. Rev. E 2016], we provide a short
proof of the loose uncertainty principle, and prove a tighter uncertainty
relation for a class of thermodynamically consistent currents $J$. Our bound
involves a measure of partial entropy production, that we interpret as the
least amount of entropy that a system sustaining current $J$ can possibly
produce, at a given steady state. We provide a complete mathematical discussion
of quadratic bounds which allows to determine which are optimal, and finally we
argue that the relationship for the Fano factor of the entropy production rate
$\mathrm{var}\, \sigma / \mathrm{mean}\, \sigma \geq 2$ is the most significant
realization of the loose bound. We base our analysis both on the formalism of
diffusions, and of Markov jump processes in the light of Schnakenberg's cycle
analysis.Comment: 13 pages, 4 figure

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