231 research outputs found
Lagrangian Description of the Variational Equations
A variant of the usual Lagrangian scheme is developed which describes both
the equations of motion and the variational equations of a system. The required
(prolonged) Lagrangian is defined in an extended configuration space comprising
both the original configurations of the system and all the virtual
displacements joining any two integral curves. Our main result establishes that
both the Euler-Lagrange equations and the corresponding variational equations
of the original system can be viewed as the Lagrangian vector field associated
with the first prolongation of the original LagrangianAfter discussing certain
features of the formulation, we introduce the so-called inherited constants of
the motion and relate them to the Noether constants of the extended system
Limitations on the superposition principle: superselection rules in non-relativistic quantum mechanics
The superposition principle is a very basic ingredient of quantum theory.
What may come as a surprise to many students, and even to many practitioners of
the quantum craft, is tha superposition has limitations imposed by certain
requirements of the theory. The discussion of such limitations arising from the
so-called superselection rules is the main purpose of this paper. Some of their
principal consequences are also discussed. The univalence, mass and particle
number superselection rules of non-relativistic quantum mechanics are also
derived using rather simple methods.Comment: 22 pages, no figure
Effects of experimental warming on peroxidase, nitrate reductase and glutamine synthetase activities in wheat
ArticleGiven the effects of climate change and its significant consequences on plant productivity, it is necessary to evaluate the enzymatic responses of the most important crops such as wheat (Triticum durum L.). We examined the response of foliar peroxidase activity, nitrate reductase, and glutamine synthetase to experimental increments of temperature (+2 °C) under field conditions following conventional agricultural practices. Foliar samples, in both control and warming treatments were taken during growth, tillering and flowering phenophases to test the peroxidase activity. Similarly, nitrate reductase, glutamine synthetase activities, and glutamine content were measured during the heading phenophase. Due to the effects of experimental warming, peroxidase activity significantly increased. The nitrate reductase activity was also higher in the warming treatment, suggesting a high nitrogen metabolism efficiency. Whereas, the increase observed in the glutamine synthetase activity, and consequently the glutamine content, evidenced a biochemical signal of an early senescence due to the effect of warming
Recurrence relation for relativistic atomic matrix elements
Recurrence formulae for arbitrary hydrogenic radial matrix elements are
obtained in the Dirac form of relativistic quantum mechanics. Our approach is
inspired on the relativistic extension of the second hypervirial method that
has been succesfully employed to deduce an analogous relationship in non
relativistic quantum mechanics. We obtain first the relativistic extension of
the second hypervirial and then the relativistic recurrence relation.
Furthermore, we use such relation to deduce relativistic versions of the
Pasternack-Sternheimer rule and of the virial theorem.Comment: 10 pages, no figure
New non-unitary representations in a Dirac hydrogen atom
New non-unitary representations of the SU(2) algebra are introduced for the
case of the Dirac equation with a Coulomb potential; an extra phase, needed to
close the algebra, is also introduced. The new representations does not require
integer or half integer labels. The set of operators defined are used to span
the complete space of bound state eigenstates of the problem thus solving it in
an essentially algebraic way
Relativistically extended Blanchard recurrence relation for hydrogenic matrix elements
General recurrence relations for arbitrary non-diagonal, radial hydrogenic
matrix elements are derived in Dirac relativistic quantum mechanics. Our
approach is based on a generalization of the second hypervirial method
previously employed in the non-relativistic Schr\"odinger case. A relativistic
version of the Pasternack-Sternheimer relation is thence obtained in the
diagonal (i.e. total angular momentum and parity the same) case, from such
relation an expression for the relativistic virial theorem is deduced. To
contribute to the utility of the relations, explicit expressions for the radial
matrix elements of functions of the form and
---where is a Dirac matrix--- are presented.Comment: 21 pages, to be published in J. Phys. B: At. Mol. Opt. Phys. in Apri
Statistical Scattering of Waves in Disordered Waveguides: from Microscopic Potentials to Limiting Macroscopic Statistics
We study the statistical properties of wave scattering in a disordered
waveguide. The statistical properties of a "building block" of length (delta)L
are derived from a potential model and used to find the evolution with length
of the expectation value of physical quantities. In the potential model the
scattering units consist of thin potential slices, idealized as delta slices,
perpendicular to the longitudinal direction of the waveguide; the variation of
the potential in the transverse direction may be arbitrary. The sets of
parameters defining a given slice are taken to be statistically independent
from those of any other slice and identically distributed. In the
dense-weak-scattering limit, in which the potential slices are very weak and
their linear density is very large, so that the resulting mean free paths are
fixed, the corresponding statistical properties of the full waveguide depend
only on the mean free paths and on no other property of the slice distribution.
The universality that arises demonstrates the existence of a generalized
central-limit theorem.
Our final result is a diffusion equation in the space of transfer matrices of
our system, which describes the evolution with the length L of the disordered
waveguide of the transport properties of interest. In contrast to earlier
publications, in the present analysis the energy of the incident particle is
fully taken into account.Comment: 75 pages, 10 figures, submitted to Phys. Rev
- …