Semiclassical theory

Miller W H 1998 Quantum and semiclassical theory of chemical reaction rates Faraday Disc. Chem. Soc. 110 1... 

Miller W H 1970 Semiclassical theory of atom-diatom collisions path integrals and the classical S matrix J. Chem. Phys. 53 1949-59... 

Marcus R A 1973 Semiclassical theory for collisions involving complexes (compound state resonances) and for bound state systems Faraday Discuss. Chem. Soc. 55 34—44... 

This chapter deals with qnantal and semiclassical theory of heavy-particle and electron-atom collisions. Basic and nsefnl fonnnlae for cross sections, rates and associated quantities are presented. A consistent description of the mathematics and vocabnlary of scattering is provided. Topics covered inclnde collisions, rate coefficients, qnantal transition rates and cross sections. Bom cross sections, qnantal potential scattering, collisions between identical particles, qnantal inelastic heavy-particle collisions, electron-atom inelastic collisions, semiclassical inelastic scattering and long-range interactions. 

Sun X, Wang H B and Miller W H 1998 Semiclassical theory of electronically nonadiabatic dynamics Results of a linearized approximation to the initial value representation J. Chem. Phys. 109 7064... 

Stenholm S 1986 The semiclassical theory of laser cooling Rev.Mod.Phys. 58 699-739... 

Gordon R. G. Semiclassical theory of spectra and relaxation in molecular gases, J. Chem. Phys. 45, 1649-55 (1966). 

Strekalov M. L. Semiclassical theory of rotational energy relaxation in diffusion approximation, Khim. Fiz. 7, 1182-92 (1988). 

Smith E. W., Giraud M., Cooper J. A semiclassical theory for spectral line broadening in molecules, J. Chem. Phys. 65, 1256-67 (1976). 

Eagles T. E., McClung R. E. D. Rotational diffusion of spherical top molecules in liquids and gases. IV. Semiclassical theory and applications to the v3 and v4 band shapes of methane in high pressure gas mixtures, J. Chem. Phys. 61, 4070-82 (1974). 

To obtain single photon pulses, one can use the emission by a single dipole as shown below in section 21.3.1. The experiment was performed in 1977 by Kimble, Dagenais and Mandel (Kimble et al., 1977). They showed that single atoms from an atomic beam emitted light which, at small time scales, exhibited a zero correlation function. This result can not be explained through a semiclassical theory and requests a quantum description of light. 

March NH (1996) Semiclassical Theory of Atoms and Ions in Intense External Fields. 86 63-96... 

In this section we estimate the magnitude of these quantum mixing effects. Even though the strictly semiclassical theory agrees well with experiment as is, making such estimates that go beyond it is useful for two distinct reasons. First, we must check to what extent the semiclassical picture, tacitly assumed earher, is a consistent zeroth order approximation to a more complete treatment. 

Second, it is important to ask whether the expected corrections to the strict semiclassical theory lead to observable consequences. In what follows, we provide approximate arguments that indeed such corrections are discernible and may even potentially answer some longstanding puzzles in this field. 

We have carrried out an analysis of the multilevel structure of the tunneling centers that goes beyond a semiclassical picture of the formation of those centers at the glass transition, which was primarily employed in this chapter. These effects exhibit themselves in a deviation of the heat capacity and conductivity from the nearly linear and quadratic laws, respectively, that are predicted by the semiclassical theory. 

The semiclassical theory introduced above can be extended to low vibrationally excited states [32]. The multidimensionality effects are more crucial in this case. As was found before [62, 70], the energy splitting may oscillate or even decrease against vibrational excitation. This cannot be explained at all by the effective ID theory. 

A multitude of semiempirical and semiclassical theories have been developed to calculate electron impact ionization cross sections of atoms and atomic ions, with relatively few for the more complicated case of molecular electron impact ionization cross sections. One of the earlier treatments of molecular targets was that of Jain and Khare.38 Two of the more successful recent approaches are the method proposed by Deutsch and Mark and coworkers12-14 and the binary-encounter Bethe method developed by Kim and Rudd.15,16 The observation of a strong correlation between the maximum in the ionization efficiency curve and the polarizability of the target resulted in the semiempirical polarizability model which depends only on the polarizability, ionization potential, and maximum electron impact ionization cross section of the target molecule.39,40 These and other methods will be considered in detail below. 

Another important contribution came in the form of a solution to an old problem, that of the semiclassical theory of Helium (G.S. Ezra, et.al., 1991). Besides demonstrating the necessity to include contributions from unstable dynamics in computing the energies, the work also showed that doubly excited resonances (corresponding to strongly... 

Keywords Quantum chaos, Scar theory, Semiclassical theories, Excited vibrational states, Vibrational spectroscopy... 

K. Richter, Semiclassical Theory of Mesoscopic Quantum Systems. Springer, Berlin... 

Chemical and electrochemical reactions in condensed phases are generally quite complex processes only outer-sphere electron-transfer reactions are sufficiently simple that we have reached a fair understanding of them in terms of microscopic concepts. In this chapter we give a simple derivation of a semiclassical theory of outer-sphere electron-transfer reactions, which was first systematically developed by Marcus [1] and Hush [2] in a series of papers. A more advanced treatment will be presented in Chapter 19. 

Berry, M. V. (1985), Semiclassical Theory of Spectral Rigidity, Proc. Roy. Soc. Lond. A400, 229. 

Harter, W. G. (1986), SU(2) Coordinate Geometry for Semiclassical Theory of Rotors and Oscillators, 7. Chem. Phys. 85, 5560. 

Percival, I. C. (1977), Semiclassical Theory of Bound States, Adv. Chem. Phys. 36,1. 

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