Dressed propagator

The link between the simple propagator, g ° and the dressed propagator, g, is provided by the self-energy, Z, which is complex and energy-dependent and acts as a generalization of the ordinary potential energy in the conventional Schrodinger equation. 

Figure 2.58 presents Green s two-point connected functions up to the third order. The sum of all the terms of this series is called a total (or dressed) propagator and is denoted by (Ryder, 1985)... 

Fig. 2. These diagrams represent (a) Dyson equation for diffusion propagator, (b) interaction vertex dressed by impurity and intergranular scattering, (c) Screened Coulomb interaction.

The form of (2.105) suggests the use of the approximation of Migdal,52 which consists in dressing the free-exciton propagator with itself in (2.100). The self-consistent equation to solve, in diagrammatic form, is... 

The optical response of a monomolecular layer consists of scattered waves at the frequency of the incident wave. Since the surface model is a perfect infinite layer, the scattered waves are reflected and transmitted plane waves. In the case of a 3D crystal, we have defined (Section I.B.2) a dielectric permittivity tensor providing a complete description of the optical response of the 3D crystal. This approach, which embodies the concept of propagation of dressed photons in the 3D matter space, cannot be applied in the 2D matter system, since the photons continue propagating in the 3D space. Therefore, the problem of the 2D exciton must be tackled directly from the general theory of the matter-radiation interaction presented in Section I. 

Fig. 1 (a) Self-energy in diagrammatic representation, (b) Expansion series for the vertex E up to g. Thick solid, thick dashed, and thin dashed lines indicate, respectively, the electron Green s function, the dressed phonon, and the bare phonon propagators... 

Fig. 15. The inclusion of the vacuum polarization potential into the Dirac equation results in an electron propagator dressed by vacuum polarization oops.

This dependence of the H+ KE on the XUV-IR delay in this case of the longer, 35 fs FWHM, IR pulse can be understood in terms of the adiabatic-ity of the Floquet dynamics underlying the dissociation processes, and the way that the IR intensity affects both the preparation and the propagation of the Floquet components of the wavepackets. More precisely, the IR probe pulse projects the various vibrational components of the wavepacket onto Floquet resonances, whose widths vary with the intensity of the IR pulse. We recall that these resonances are of two types Shape resonances supported by the lower adiabatic potential defined at the one-photon crossing between the dressed (g, n), (u, n ) channels and leading to efficient dissociation through the BS mechanism, or Feshbach resonances, vibrationally trapped in the upper adiabatic potential well. 

M. Fleischhauer, A.S. Manka, Propagation of laser pulses and coherent population transfer in dissipative three-level systems An adiabatic dressed-state picture, Phys. Rev. A 54 (1996) 794. 

It is productive to calculate the sp propagator from a Schrddinger-like equation. This is accomplished by relating the propagation of the dressed particle to propagation in a simple potential well in terms of the Dyson equation. 

Nanophotonics, proposed by the author in 1993 [1-3], is a novel optical technology that utilizes the optical near-field. The optical near-field is the dressed photons that mediate the interaction between nanometric particles located in close proximity to each other. Nanophotonics allows the realization of qualitative innovations in photonic devices, fabrication techniques, and systems by utilizing novel functions and phenomena enabled by optical near-field interactions that would otherwise be impossible if only conventional propagating light were used. In this sense, the principles and concepts of nanophotonics are completely different from those of conventional wave-optical technology, encompassing photonic crystals, plasmon-ics, metamaterials, and silicon photonics. This review describes these differences and shows examples of such qualitative innovations. 

In this subsection, we will study the propagation dynamics of a probe pulse incident upon a sample of ultracold Rb atoms dressed by a time-modulated SW coupling, and pay special attention to the stationary light generation during the process where the two coupling components are switched on and off as in Fig. 13. In Fig. 14, we focus on and together with... 

We first consider an analysis of physical systems in periodic external fields using the Floquet theorem [134, 168]. As we shall see below, the theorem provides theoretical basis for the existence of field-dressed quasi-stationary state which expand the propagator. Earlier application of the Floquet theorem or related ideas to physical problems includes Refs. [224, 370], whereas the progress in this field is recently reviewed in Ref. [90]. Although it will later be extended to allow small non-periodic modulations, discussions in this section assumes perfect periodicity. The Schrodinger equation is given as... 

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