Volume 47, Issue 1
July 1996, pages 1-98
pp 1-23 July 1996 Review
Quantum theory of continuous measurements and its applications in quantum optics
We present an overview of the quantum theory of continuous measurements and discuss some of its important applications in quantum optics. Quantum theory of continuous measurements is the appropriate generalization of the conventional formulation of quantum theory, which is adequate to deal with counting experiments where a detector monitors a system continuously over an interval of time and records the times of occurrence of a given type of event, such as the emission or arrival of a particle.
We first discuss the classical theory of counting processes and indicate how one arrives at the celebrated photon counting formula of Mandel for classical optical fields. We then discuss the inadequacies of the so called quantum Mandel formula. We explain how the unphysical results that arise from the quantum Mandel formula are due to the fact that the formula is obtained on the basis of an erroneous identification of the coincidence probability densities associated with a continuous measurement situation. We then summarize the basic framework of the quantum theory of continuous measurements as developed by Davies. We explain how a complete characterization of the counting process can be achieved by specifying merely the measurement transformation associated with the change in the state of the system when a single event is observed in an infinitesimal interval of time.
In order to illustrate the applications of the quantum theory of continuoius measurements in quantum optics, we first derive the photon counting probabilities of a single-mode free field and also of a single-mode field in interaction with an external source. We then discuss the general quantum counting formula of Chmara for a multi-mode electromagnetic field coupled to an external source. We explain how the Chmara counting formula is indeed the appropriate quantum generalization of the classical Mandel formula. To illustrate the fact that the quantum theory of continuous measurements has other diverse applications in quantum optics, besides the theory of photodetection, we summarize the theory of ‘quantum jumps’ developed by Zoller, Marte and Walls and Barchielli, where the continuous measurements framework is employed to evaluate the statistics of photon emission events in the resonance fluorescence of an atomic system.
pp 25-31 July 1996 Research Articles
Magnetized cylindrically symmetric universe in general relativity
A magnetized cylindrically symmetric universe with two degrees of freedom in which the free gravitational field is Petrov type I degenerate, is obtained. The magnetic field is due to an electric current produced along the x-axis. The distribution consists of an electrically neutral perfect fluid with an infinite electrical conductivity. The behaviour of the model when magnetic field tends to zero and other physical aspects of the model are also discussed.
pp 33-39 July 1996 Research Articles
Stationary rotating string world models with a magnetic field
Following the techniques used by Letelier and Stachel some new physically relevant stationary solutions of string cosmology with magnetic field are presented. In these solutions, the flow vector of matter has non-zero rotation and the cosmological constant is taken to be non-zero. Previously known solutions are derived as particular cases from our class of solutions. Some string models with vanishing cosmological constant are also discussed.
pp 41-55 July 1996 Research Articles
A model of the universe with decaying vacuum energy
The consequences of taking the total active gravitational mass of the universe phasewise constant together with a decaying vacuum energy in the background of Robertson-Walker space-time are investigated. The model so determined admits a contracted Ricci-collineation along the fluid flow vectorν^{i}. It is geometrically closed but ever-expanding and does not possess the initial singularity, horizon, entropy, monopole or cosmological constant problems of the standard big bang cosmology. Estimates of the present matter; radiation and vacuum energy densities, the age of the universe and the present values of the deceleration parameter and the scale factor are also obtained.
pp 57-63 July 1996 Research Articles
Cross sections and other parameters ofe^{−} − H_{2}O scattering (E_{i}⩾50 eV)
K N Joshipura Minaxi Vinodkumar
Our previous theoretical work one^{−} − H_{2}O scattering has been modified and extended to intermediate and high energiesE_{i}. Using the Bethe plot, we compare the present inelastic cross-sections with the experimental ionization cross sections. Total cross-sections are analytically represented asQ_{TOT}(cm^{2})=a.(E_{i}eV)^{−b} and the parameters ‘a’ and ‘b’ are discussed for molecules H_{2}O, NH_{3} and CH_{4} in the rangeE_{i}=100–1000eV.
pp 65-77 July 1996 Research Articles
New method for the evaluation of the RKR potential-integrals for diatomic molecules
Suresh Chandra A K Sharma Z H Khan
We present a new method for the evaluation of the RKR potential-integrals for diatomic molecules. This method is straightforward and fast, and the calculations can be performed to an accuracy better than any other method.
pp 79-85 July 1996 Research Articles
(e, 2e) triple differential cross section for ionization-excitation of helium
Simultaneous ionization and excitation of helium by electron impact is considered in an improved second Born approximation. The wave function of the low energy ejected electron is obtained in the field of residual He^{+} ion in 2s-state. The calculation has been done for the processe^{−}+He→e^{−}+He^{+}(2s)+e^{−} in the coplanar asymmetric geometry with Hartree-Fock wave function of Byron and Joachain for the helium ground state and the results are compared with the absolute experimental data of Dupreet al [J. Phys.B25, 259 (1992)] at ∼ 5.5 keV incident energy. Our results are found to increase the ratio of the recoil peak to binary peak intensity by about 30% over the first Born results and thus to bring it closer to the experimental data.
pp 87-98 July 1996 Research Articles
Positron scattering from alkaline-earth elements
The total (elastic + inelastic) cross sections fore^{+} impact on alkaline-earth elements from Be to Ra are calculated by employing a complex spherical optical potential. This potential has static, polarization and absorption components. The positron energy range is from a few eV to several thousand eV. We have compared our elastic cross sections for Mg and Ca with the other available results and the agreement is good for energies above 100eV. We have also compared our absorption cross sections withe^{−} ionization cross sections at high energies where our absorption cross sections are in good accord. We have made Bethe plots fore^{+} scattering on these elements.
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