Phonon multi

G. Herzberg, Molecular Spectra and Molecular Structure, Vol. II - Infrared and Raman Spectra of Polyatomic Molecules, Van Nostrand Reinhold, New York, 1945 In the crystalline state, it is more convenient to speak about multi-phonon processes since the modes from the whole dispersion range of the first Brillouin zone are allowed to contribute according to the conservation of energy and momentum of the phonons involved in the process... 

Lorenc M, Moisan N, Servol M, Cailleau H, Koshihara S, Maesato M, Shao X, Nakano Y, Yamochi H, Saito G, Collet E (2009) Multi-phonon dynamics of the ultra-fast photoinduced transition of (EDO-TTF)2SbF6. J Phys Conf Ser 148 012001/1-4... 

A further generalization is to write down a multi-dimensional GLE, in which the system is described in terms of a finite munber of degrees of freedom, each of which feels a frictional and random force. For example, an atom diffusing on a surface, moves in three degrees of freedom, two in the plane of the surface and a third which is perpendicular to the siuface. Each of these degrees of Ifeedom feels a phonon friction. Multi-dimensional generalizations and considerations may be foimd in Refs. 72-82. 

In this paper, we investigate our two-band model for the explanation the multi-gap superconductivity of MgB2. We apply the model to an electron-phonon mechanism for the traditional BCS method, an electron-electron interaction mechanism for high- Tc superconductivity, and a cooperative mechanism in relation to multi-band superconductivity. 

Conventional Theory of Multi-Phonon Electron Transitions... 

Calculation of Multi-Phonon Transition Probability in Unit of Time. 18... 

The nuclear wave functions h/v)- corresponding to different electronic terms, i.e. for different /u are not orthogonal with each other, (Xnjln ) 0 at ji v for any ns and. It is this non-orthogonality that is the principal reason for the population change in many modes of the vibration system (multi-phonon transition), as it was first noticed by Frenkel [3]. 

The goal of the theory of multi-phonon transitions is to calculate the rate constant (9) and to determine its dependence on the energy defect AE and the temperature T. This problem was resolved for the first time in the works described in Refs. [1, 2] for the case of Einstein s crystal, i.e. all phonons participating in the electron transition have the same frequency co. It took into account only the shift of the equilibrium positions, and the result was obtained by straight calculation of the number of distributions of the energy AE on the phonon modes. 

As stated above, expression (9) for the rate constant of transition in Einstein s crystal was first calculated analytically by the method of the straight search in the pioneer works of Pekar [1] and Kun and Rhys [2]. Their analytic expression remains till now the unique exact expression for multi-phonon transition probability in the time unit. Then, there appeared different methods that permit to derive the integral expressions for the rate constant in the general case of the phonon frequencies dispersion the operator calculation method [5], the method of generating polynomial [6], and the method of density matrix [7]. The detailed consideration of these methods was made in the Perlin s review [9],... 

The theory of multi-phonon electron transitions due to non-adiabatic interaction between the electron terms is expounded in this chapter. The participation of the large number of the vibration degrees of freedom in the transition is caused by the non-orthogonality of the oscillator wave function in the initial and final states. This non-orthogonality may be connected with the following factors the shift of the equilibrium positions of the oscillations, the change of the frequencies in the transition, and the change of the set of normal coordinates of the vibration system. 

Some important problems of the theory of multi-phonon electron transition were not touched upon in this chapter. These are, first, the calculation of the expression for the electron matrix element at the tunneling transfer, second, the influence of medium on the electron matrix element, and, finally, the investigation of the applicability of Born-Oppenheimer approach in the electron tunneling transfer. These issues will be considered in the next chapter. 

Why is the electron transition a multi-phonon transition Name the main reason. 

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