Pub Date : 2008-06-01DOI: 10.2478/V10155-010-0090-Z
B. Shore
The internal structure of a particle – an atom or other quantum system in which the excitation energies are discrete – undergoes change when exposed to pulses of near-resonant laser light. This tutorial review presents basic concepts of quantum states, of laser radiation and of the Hilbert-space statevector that provides the theoretical portrait of probability amplitudes – the tools for quantifying quantum properties not only of individual atoms and molecules but also of artificial atoms and other quantum systems. It discusses the equations of motion that describe the laser-induced changes (coherent excitation), and gives examples of laserpulse effects, with particular emphasis on two-state and three-state adiabatic time evolution within the rotating-wave approximation. It provides pictorial descriptions of excitation based on the Bloch equations that allow visualization of two-state excitation as motion of a threedimensional vector (the Bloch vector). Other visualization techniques allow portrayal of more elaborate systems, particularly the Hilbert-space motion of adiabatic states subject to various pulse sequences. Various more general multilevel systems receive treatment that includes degeneracies, chains and loop linkages. The concluding sections discuss techniques for creating arbitrary pre-assigned quantum states, for manipulating them into alternative coherent superpositions and for analyzing an unknown superposition. Appendices review some basic mathematical concepts and provide further details of the theoretical formalism, including photons, pulse propagation, statistical averages, analytic solutions to the equations of motion, exact solutions of periodic Hamiltonians, and population-trapping “dark” states.
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Pub Date : 2008-02-01DOI: 10.2478/V10155-010-0088-6
P. Povinec, B. Mária, A. Jull, P. Vojtyla
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Pub Date : 2007-04-01DOI: 10.2478/V10155-010-0084-X
P. Moczo, J. Kristek, M. Galis, P. Pazak, M. Balazovjech
Numerical modeling of seismic wave propagation and earthquake motion is an irreplaceable tool in investigation of the Earth’s structure, processes in the Earth, and particularly earthquake phenomena. Among various numerical methods, the finite-difference method is the dominant method in the modeling of earthquake motion. Moreover, it is becoming more important in the seismic exploration and structural modeling. At the same time we are convinced that the best time of the finite-difference method in seismology is in the future. This monograph provides tutorial and detailed introduction to the application of the finitedifference (FD), finite-element (FE), and hybrid FD-FE methods to the modeling of seismic wave propagation and earthquake motion. The text does not cover all topics and aspects of the methods. We focus on those to which we have contributed. We present alternative formulations of equation of motion for a smooth elastic continuum. We then develop alternative formulations for a canonical problem with a welded material interface and free surface. We continue with a model of an earthquake source. We complete the general theoretical introduction by a chapter on the constitutive laws for elastic and viscoelastic media, and brief review of strong formulations of the equation of motion. What follows is a block of chapters on the finite-difference and finite-element methods. We develop FD targets for the free surface and welded material interface. We then present various FD schemes for a smooth continuum, free surface, and welded interface. We focus on the staggered-grid and mainly optimally-accurate FD schemes. We also present alternative formulations of the FE method. We include the FD and FE implementations of the traction-at-split-nodes method for simulation of dynamic rupture propagation. The FD modeling is applied to the model of the deep sedimentary Grenoble basin, France. The FD and FE methods are combined in the hybrid FD-FE method. The hybrid method is then applied to two earthquake scenarios for the Grenoble basin. Except chapters 1, 3, 5, and 12, all chapters include new, previously unpublished material and results.
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