Electrons exchanging phonon

It is generally known that limits for speed-up of digital circuits, especially microprocessors, are determined by thermal problems. There are several analogues between the electrical Gp and the thermal Gp conductance of a nanostructure. However, an analysis of thermal conductance is more complex than electrical conductance because of contribution either phonons or electrons in heat exchange. Quantized thermal conductance in one-dimensional systems was predicted theoretically by Greiner [4] and Rego [5] for ballistic transport of electrons and phonons. Quantized thermal conductance Gp and its quantum (unit)... 

Frohlich (10) showed how second order perturbation theory could be applied to derive an effective interaction between electrons from the direct electron-ion interactions. The physical idea is that as one electron scatters from a nuclear center it distorts the lattice, this distortion is felt by another electron, and thus the electrons experience an indirect interaction. The result is that we can think of the electrons as exchanging phonon momentum q in an electron-electron scattering process shown in Figure 2. The effective potential of interaction between the electrons for a scattering involving a change in momentum q is (11),... 

The first two terms denote the reactant and the metal, the last term affects electron exchange between the metal and the reactant c denotes a creation and c an annihilation operator. Just like in Marcus (and polaron) theory, the solvent modes are divided into a fast part, which is supposed to follow the electron transfer instantly, and a slow part. The latter is modeled as a phonon bath after transformation to a single, normalized reaction coordinate q, with corresponding momentum p, the corresponding part of the Hamiltonian is... 

Several types of spin-lattice relaxation processes have been described in the literature [31]. Here a brief overview of some of the most important ones is given. The simplest spin-lattice process is the direct process in which a spin transition is accompanied by the creation or annihilation of a single phonon such that the electronic spin transition energy, A, is exchanged by the phonon energy, hcoq. Using the Debye model for the phonon spectrum, one finds for k T A that... 

While, in the BCS theory, such attractive force for electron Cooper pair is provided by phonons, for dense quark matter, where phonons are absent, the gluon exchange interaction provides the attraction, as one-gluon exchange interaction is attractive in the color anti-triplet channel1 One therefore expects that color anti-triplet Cooper pairs will form and quark matter is color superconducting, which is indeed shown more than 20 years ago [13, 14],... 

The localized-electron model or the ligand-field approach is essentially the same as the Heitler-London theory for the hydrogen molecule. The model assumes that a crystal is composed of an assembly of independent ions fixed at their lattice sites and that overlap of atomic orbitals is small. When interatomic interactions are weak, intraatomic exchange (Hund s rule splitting) and electron-phonon interactions favour the localized behaviour of electrons. This increases the relaxation time of a charge carrier from about 10 s in an ordinary metal to 10 s, which is the order of time required for a lattice vibration in a polar crystal. 

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