Phonon cloud

Fig. 2 shows that if V < cs, the survival probability first decreases and then approaches the constant value of about 0.85, almost independent on V. This behavior reveals the physical reason for the short-time non exponential decay the initial conditions Eq. (2) imply that, initially, the impurity atom is surrounded by no virtual phonons, while in the steady state, the impurity atom must be surrounded by a cloud of virtual phonons (cf. the polaronic effect for electrons in a crystal, [Isihara 1971]). Thus the non-exponential stage of the decay is associated with the formation of such a phonon cloud. 

The faster the impurity atom moves, the weaker its coupling to the phonon cloud is. Therefore the decrease of ujs corresponds to the vanishing of nonexponential decay effects as V increases. This behavior is displayed in Fig. 3 by the numerically calculated [from Eq. (8)] decay rate 7 and frequency shift... 

In the 2-level limit a perturbative approach has been used in two famous problems the Marcus model in chemistry and the small polaron model in physics. Both models describe hopping of an electron that drags the polarization cloud that it is formed because of its electrostatic coupling to the enviromnent. This enviromnent is the solvent in the Marcus model and the crystal vibrations (phonons) in the small polaron problem. The details of the coupling and of the polarization are different in these problems, but the Hamiltonian formulation is very similar. ... 

Plasmon-phonon coupling represents mixing of two quasi-particles. The coupling of three quasi-particles has also been observed. The term plasmariton was used by Alfano 45) for a coupled state of a TO phonon and a dressed photon , namely, a photon surrounded by an electron cloud (a coupled state of a plasmon and a photon). The quasi-particle dressed photon is also called a transverse plasmon. Because the coupled state of a photon and a TO phonon has been termed polariton, a plasmariton can also be regarded as coupled state of a plasmon and a polariton. Earlier the term plasmariton was used in a more restricted sense, namely, when a partly transverse character of the plasmon is induced by an external magnetic field. 

The cause of this kind of decoherence is evidently thermal because of the alteration of the deBroglie wavelength of the wave packet associated with the quantum particle. Dissipation, on the other hand, arises from the exchange of energy between the system, which, in this case, comprise the tunneling particle and the environment of the electron cloud, or, for that matter, phonons that get excited because of the elastic distortion created by the particle (which are called interstitial sites). In either case, the coupling with the environment can be modeled as... 

It means that for electrons which satisfy condition of extreme nonadiabaticity (antiadiabaticity with respect to interacting phonon mode r in particular direction of reciprocal lattice where the gap in one-electron spectrum has been opened), the electron (nonadiabatic polaron)-renormalized phonon interaction energy equals zero. Expressed explicitly, in the presence of external electric potential, dissipation-less motion of relevant valence band electrons (holes) on the lattice scale can be induced at the Fermi level (electric resistance p = 0). At the same time, the motion of nuclei remains bound to circumferential revolution over distorted, energetically equivalent, configurations. The electrons move in a form of itinerant-mobile bipolarons, i.e. as a polarized cloud of inter-site charge density distribution- sequence b, d, e, f, b, d, e, f. in Fig. 27.6. For temperature increase, thermal excitations of valence band electrons to conduction band induce sudden transition from the antiadiabatic state to adiabatic state at T — 7, i.e. < AEd Rd) holds and the system is... 

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