Feynman diagrams, 0

Figure Al.6.5 Feynman diagram for die first-order proeess deseribed in the text.

Our first example of aP - signal is coherent anti-Stokes Raman spectroscopy, or CARS. Fomially, tire emission signal into direction k= - k + k. has 48 Feynman diagrams that contribute. Flowever, if the... 

Figure 14. Liouville space coupling schemes and their respective double-sided Feynman diagrams for three of the six pathways in Liouville space which contribute to p 2. The complex conjugates are not shown. All pathways proceed only via coherences, created by the interactions with the two fields shown as incoming arrows. Solid curves pertain to e( 11 and dashed curves to r/2T (Reproduced with permission from Ref. 47, Copyright 2005 American Institute of Physics.)...

Fig. 1. Second and third order antisymmetrized Feynman diagrams.

R. D. Mattuck, A Guide to Feynman Diagrams in the Many-Body Problem, 2nd ed., McGraw-Hill, New York, 1976. 

FIG. 1.2 Feynman diagrams describing (a) elastic scattering, (b) inelastic scattering. Source Feil (1975). 

In the first Bom approximation, the interaction between the photons and the scattering system is weak and no excited states are involved in the elastic scattering process. Furthermore, there is no rescattering of the scattered wave, that is, the single-scattering approximation is valid. In the Feynman diagrams (Fig. 1.2), there is only one point of interaction for first-Born-approximation processes. 

The two terms in Eq. (1.34a) include processes in which the initial photon k0 has been annihilated first, and those in which the final photon k has first been created. In the quantum-mechanical description of the first type of process, the photon k0 is absorbed and then, in a very small time interval, the photon k is emitted through a stimulated emission process. This process and three-beam multiple scattering are illustrated by the Feynman diagrams in Fig. 1.6. 

The two parts of this formula are derived from the same QED Feynman diagram for interaction of two electrons in the Coulomb gauge. The first term is the Coulomb potential and the second part, the Breit interaction, represents the mutual energy of the electron currents on the assumption that the virtual photon responsible for the interaction has a wavelength long compared with system dimensions. The DCB hamiltonian reduces to the complete standard Breit-Pauli Hamiltonian [9, 21.1], including all the relativistic and spin-dependent correction terms, when the electrons move nonrelativistically. 

Figure 1. Feynman diagrams corresponding to different channels of decay of the meso-atom (see text).

Fig. 1. Feynman diagrams for the interaction of a three-pulse sequence with a two-level system.

In this case the pulse sequence favours the generation of population and coherence ensembles in the excited state of the molecule according to the Feynman diagrams (a) and (b). The time evolution of the spectrum reflects the relaxation of those ensembles and can be used to determine the dynamics of molecules in the excited state. Some oscillations in the intensity of the echo spectrum versus population time are observed with several beat periods corresponding to the splitting of vibrational levels... 

By contrast, when the pump wavelength is longer than the probe, enhancement of the echo signal occurs on the blue side when scanning either the coherence time (fig. 2e, 2f and fig. 3e, 3f) or the population time (fig. 2d and fig. 3d). These results are interpreted as reflecting the dynamics of vibration in the electronic ground state (Feynman diagrams (c),(d)). 

VI. Kinetic Equations Feynman Diagrams and Correlation Diagrams. .. 21... 

VI. KINETIC EQUATIONS FEYNMAN DIAGRAMS AND CORRELATION DIAGRAMS... 

The most direct application of the Feynman diagrams is, of course, the... 

The important point is that dynamics has a double aspect the Feynman diagrams emphasize one of them, the correlation diagrams the other. 

In the response function formalism developed by Mukamel [1], all four wave-mixing spectroscopies are described by four response functions, R, ..., i 4, and their complex conjugates. Double-sided Feynman diagrams are shown in Fig. 12 representing these response functions. The response functions in turn are described by a single line shape function g t) given by... 

Figure 15. Feynman diagrams for r > 0 where rephasing is possible and r < 0 where rephasing is not possible. Note that for r > 0 the density matrix element during r and ( are complex conjugate of each other, but they have the same phase for r < 0.

The amplitude of the periodic orbits is therefore determined by the linear stability with respect to perturbations transverse to the orbit. In this sense, the leading term in expression (2.13), obtained by setting C = 0, treats the dynamics transverse to the orbit at the level of the harmonic approximation. The nonlinear stability properties appear thus as anharmonic corrections to the dynamics transverse to the orbit. These anharmonicities contribute to the trace formula by corrections given in terms of series in powers of the Planck constant involving the coefficients C , which can be obtained as Feynman diagrams [14, 31]. 

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