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WORLD SCIENTIFIC eBooks

FORWARD-BACKWARD SEMICLASSICAL DYNAMICS

Nancy Makri

Published Jun 1, 2001• 3 citations
Publisher
DOI
10.1142/9789812811240_0002

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Quantum states can be described equivalently by density matrices, Wigner functions, or quantum tomograms. We analyze the accuracy and performance of three related semiclassical approaches to quantum dynamics, in particular with respect to their numerical implementation. As test cases, we consider the time evolution of Gaussian wave packets in different one-dimensional geometries, whereby tunneling, resonance, and anharmonicity effects are taken into account. The results and methods are benchmarked against an exact quantum mechanical treatment of the system, which is based on a highly efficient Chebyshev expansion technique of the time evolution operator.
A semiclassical model of nonstationary stimulated Raman scattering with account of forward and backward waves of different frequencies is proposed. Equations for the elements of a collective density matrix and electric-field amplitudes are obtained applying the averaging method. It is shown that forward waves are generated by a united polarization component, whereas each of the backward waves is formed by its own component. The description is based on the approximation of small scattering angles and assumes that the quantities considered do not depend on transverse coordinates. The emission dynamics of forward-backward Stokes pulses is investigated both for the linear case and under the strong depletion of pumping and level populations. The domain of applicability of the model of nonstationary forward stimulated Raman scattering is determined.