Volume 35, Issue 3
September 1990, pages 205-348
pp 205-286 September 1990 Review
Some aspects of conformal field theories on the plane and higher genus Riemann surfaces
We review some aspects of conformal field theories on the plane as well as on higher genus Riemann surfaces.
pp 287-301 September 1990 Research Articles
Model equations from a chaotic time series
A K Agarwal D P Ahalpara P K Kaw H R Prabhakara A Sen
We present a method for obtaining a set of dynamical equations for a system that exhibits a chaotic time series. The time series data is first embedded in an appropriate phase space by using the improved time delay technique of Broomhead and King (1986). Next, assuming that the flow in this space is governed by a set of coupled first order nonlinear ordinary differential equations, a least squares fitting method is employed to derive values for the various unknown coefficients. The ability of the resulting model equations to reproduce global properties like the geometry of the attractor and Lyapunov exponents is demonstrated by treating the numerical solution of a single variable of the Lorenz and Rossler systems in the chaotic regime as the test time series. The equations are found to provide good short term prediction (a few cycle times) but display large errors over large prediction time. The source of this shortcoming and some possible improvements are discussed.
pp 303-315 September 1990 Research Articles
We investigate the question of local causality at the statistical level in Einstein-Podolsky-Rosen (EPR) type situations, taking into account the most general class of measurements envisaged in quantum theory. The condition for local causality at the statistical level used in this paper pertains to the invariance of statistics of measurements on one sub-system with respect to the choice and type of measurements on its correlated partner in the EPR-type examples. Our analysis is based on a criterion for measurements performed on one of the EPR sub-systems, which is more general than the criterion used in the earlier treatments. We discuss both non-absorptive measurements (where the system is available for further observation after the measurement is performed) as well as absorptive measurements (where the system is absorbed in the process of a particular outcome being realized). We show that in the case of arbitrary non-absorptive measurements characterized by operationvalued measures, the requirement of local causality at the statistical level is satisfied and in the process we identify the key inputs in such a proof. We also obtain the specific conditions under which an absorptive measurement satisfies local causality at the statistical level.
pp 317-323 September 1990 Research Articles
Mach’s principle and the notion of time
The role of time coordinate in the realization of March’s principle is highlighted. It is shown that Mach’s principle is linked to the definition of a ‘particle’. These results suggest a deep connection between quantum gravity and Mach’s principle.
pp 325-328 September 1990 Research Articles
Density of quarks in heavy spherical nuclei using NRQSM
A nonrelativistic quark shell model (NRQSM) is used to derive an expression for the density of quarks in heavy spherical nuclei. It is shown that quark density is related in a simple way with the probability of finding a nucleon in a nucleus. The quark density is used to determine the ratio of average distance between two quarks to the average distance between two nucleons.
pp 329-340 September 1990 Research Articles
Characterization of isomers of the nucleus^{154}Pm
Consideration of the expected two-quasiparticle structures and their estimated band head energies, and the selection rules for beta transition rates for the^{154}Nd →^{154}Pm →^{154}Sm decays are used to deduce the configurations for the isomers and the low-spin structures in the neutron rich doubly odd nucleus_{61}^{154}Pm_{93}. The 2.68 m high spin isomer and the 1.73 m low spin isomer are respectively assigned the spin-parity 4^{+} and 1^{+} with the configuration {p:5/2^{−} [532↑] +n:3/2^{−} [521↑]} with the 2.68 m isomer lying lower in energy, and thus forming the^{154}Pm ground state. Two-quasiparticle character of the beta-connected states in^{154}Nd decay and^{154}Pm decay is discussed.
pp 341-348 September 1990 Research Articles
Two-electron excitation in helium-like ions by electron impact
Calculation of cross-sections for the two-electron excitation in helium-like ions by electron impact employing Coulomb-Born-Oppenheimer (CBO) approximation is presented. Analytical expressions for the differential and total scattering cross-sections without using partial wave expansion of the wavefunction reported earlier have been used. The total and differential scattering cross-sections for each of the excitations 1s^{2}^{1}S* → 2s^{2}^{1}S^{e}, 2s2p^{1.3}P^{0}, 2p^{2}^{1}S^{e},^{3}P^{e},^{1}D^{e} in Be^{2+} and B^{3+} are computed. Results for Li^{+} reported earlier are also included for comparison.
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