Search results for "Formalism"

An alternative formulation of Classical Mechanics based on an analogy with Thermodynamics

2013

We study new Legendre transforms in classical mechanics and investigate some of their general properties. The behaviour of the new functions is analyzed under coordinate transformations.When invariance under different kinds of transformations are considered, the new formulation is found to be completly equivalent to the usual Lagrangian formulation, recovering well established results like the conservation of the angular momentum. Furthermore, a natural generalization of the Poisson Bracket is found to be inherent to the formalism introduced. On the other hand, we find that with a convenient redefinition of the Lagrangian, $\mathcal{L}^{\prime}=-\mathcal{L}$, it is possible to establish an …

Random polarisations of the dipoles

2012

We extend the dipole formalism for massless and massive partons to random polarisations of the external partons. The dipole formalism was originally formulated for spin-summed matrix elements and later extended to individual helicity eigenstates. For efficiency reasons one wants to replace the spin sum by a smooth integration over additional variables. This requires the extension of the dipole formalism to random polarisations. In this paper we derive the modified subtraction terms. We only modify the real subtraction terms, the integrated subtraction terms do not require any modifications.

The Maximum Entropy Formalism.

1980

S-matrix formulation of mesoscopic systems and evanescent modes.

2009

The Landauer-Butikker formalism is an important formalism to study mesoscopic systems. Its validity for linear transport is well established theoretically as well as experimentally. Akkermans et al [Phys. Rev. Lett. {\bf 66}, 76 (1991)] had shown that the formalism can be extended to study thermodynamic properties like persistent currents. It was earlier verified for simple one dimensional systems. We study this formula very carefully and conclude that it requires reinterpretation in quasi one dimension. This is essentially because of the presence of evanescent modes in quasi one dimension.

Generalized bloch equations for optical interactions in confined geometries

2005

By combining the field-susceptibility technique with the optical Bloch equations, a general formalism is developed for the investigation of molecular photophysical phenomena triggered by nanometer scale optical fields in the presence of complex environments. This formalism illustrate the influence of the illumination regime on the fluorescence signal emitted by a single molecule in a complex environment. In the saturated case, this signal is proportional to the optical local density of states, while it is proportional to the near-field intensity in the non-saturated case. (C) 2005 Elsevier B.V. All rights reserved.

Long-Range interaction of temporal incoherent solitons

2014

Contrary to conventional solitons, temporal incoherent solitons are sustained by a defocusing nonlinearity with anomalous dispersion and exhibit a non-mutual attractive-repulsive interaction. We explain these results by a long-range Vlasov formalism.

Asymptotic normalization coefficients and halo radii of12B in the excited states

2017

We present the results of measurements and analysis of the differential cross sections of the 11 B(d, p )12 B reaction leading to formation of the 1+ ground state and the 0.953-MeV 2+ , 1.674-MeV 2− , 2.621-MeV 1− , 2.723-MeV 0+ , 3.389-MeV 3− excited states of 12 B at Ed = 21.5 MeV. The analysis of the data was carried out within the coupled-reaction-channels method for the direct neutron transfer and the Hauser-Feshbach formalism of the statistical compound-nucleus model. We deduced the spectroscopic factors, asymptotic normalization coefficients, and rms radii of the last neutron in all states studied. The existence of the neutron halos in the 1.674-MeV 2− and 2.621-MeV 1− states was fou…

Two-Quasiparticle Mixing in Odd-Odd Nuclei

2007

In Chap. 16 the residual Hamiltonian was used to mix proton-proton and neutron—neutron two-quasiparticle configurations. The resulting wave functions described states in even-even open-shell nuclei. In this chapter we develop a corresponding formalism, the proton-neutron QTDA, for mixing proton-neutron two-quasiparticle configurations. This mixing produces wave functions that describe states in odd-odd open-shell nuclei. The quasiparticles are obtained from a BCS calculation for an even-even reference nucleus next to the odd-odd nucleus of interest.

Weak Lensing Observables in the Halo Model

2011

The halo model (HM) describes the inhomogeneous universe as a collection of halos. The full nonlinear power spectrum of the universe is well approximated by the HM, whose prediction can be easily computed without lengthy numerical simulations. This makes the HM a useful tool in cosmology. Here we explore the lensing properties of the HM by use of the stochastic gravitational lensing (sGL) method. We obtain for the case of point sources exact and simple integral expressions for the expected value and variance of the lensing convergence, which encode detailed information about the internal halo properties. In particular a wide array of observational biases can be easily incorporated and the d…

Relativistic second-order perturbations of the Einstein-de Sitter universe

1998

We consider the evolution of relativistic perturbations in the Einstein-de Sitter cosmological model, including second-order effects. The perturbations are considered in two different settings: the widely used synchronous gauge and the Poisson (generalized longitudinal) one. Since, in general, perturbations are gauge dependent, we start by considering gauge transformations at second order. Next, we give the evolution of perturbations in the synchronous gauge, taking into account both scalar and tensor modes in the initial conditions. Using the second-order gauge transformation previously defined, we are then able to transform these perturbations to the Poisson gauge. The most important feat…