The moments method was shown to be very useful for determining the linear response of very large harmonic systems. In the presence of anharmonicity or electron-phonon coupling, the phonon self-energy appears in the one-phonon propagator. The phonon frequency is then renormalized and the system is damped. In this paper, we show that it is possible to extend the moments method to compute the response of these damped systems. The method involves introducing a two-dimensional density functional that can be calculated by the moments techniques and which allows the computation of the response function. We illustrate these results via applications to several models: systems with constant damping, systems of coupled relaxation modes and oscillators, and systems with electron-phonon coupling.The moments method was shown to be very useful for determining the linear response of very large harmonic systems. In the presence of anharmonicity or electron-phonon coupling, the phonon self-energy appears in the one-phonon propagator. The phonon frequency is then renormalized and the system is damped. In this paper, we show that it is possible to extend the moments method to compute the response of these damped systems. The method involves introducing a two-dimensional density functional that can be calculated by the moments techniques and which allows the computation of the response function. We illustrate these results via applications to several models: systems with constant damping, systems of coupled relaxation modes and oscillators, and systems with electron-phonon coupling.

Journal of Physics Condensed MatterApr 25, 19949 citations

Electron and phonon correlations in systems of one-dimensional electrons coupled to phonons

Leiming Chen

Electron and phonon correlations in systems of one-dimensional electrons coupled to phonons are studied at low temperatures by emphasizing on the effect of electron-phonon backward scattering. It is found that the $2{k}_{F}$ -wave components of the electron density and phonon displacement field share the same correlations. Both correlations are quasi-long-ranged for a single conducting chain coupled to one-dimensional or three-dimensional phonons, and they are long-ranged for repulsive electron-electron interactions for a three-dimensional array of parallel one-dimensional conducting chains coupled to three-dimensional phonons.Electron and phonon correlations in systems of one-dimensional electrons coupled to phonons are studied at low temperatures by emphasizing on the effect of electron-phonon backward scattering. It is found that the $2{k}_{F}$-wave components of the electron density and phonon displacement field share the same correlations. Both correlations are quasi-long-ranged for a single conducting chain coupled to one-dimensional or three-dimensional phonons, and they are long-ranged for repulsive electron-electron interactions for a three-dimensional array of parallel one-dimensional conducting chains coupled to three-dimensional phonons.

arXiv:0806.0310Physical Review BNov 19, 20080 citations

Dynamics of one-dimensional electron-phonon systems at low temperatures

S. Brazovskiǐ, I. E. Dzyaloshinskiǐ

Journal of Experimental and Theoretical PhysicsDec 1, 19760 citations

RATE OF DECOHERENCE FOR AN ELECTRON WEAKLY COUPLED TO A PHONON GAS

Riccardo Adami, László Erdős

Abstract. We study the dynamics of an electron weakly coupled to a phonon gas. The initial state of the electron is the superposition of two spatially localized distant bumps moving towards each other, and the phonons are in a thermal state. We investigate the dynamics of the system in the kinetic regime and show that the time evolution makes the non-diagonal terms of the density matrix of the electron decay, destroying the interference between the two bumps. We show that such a damping effect is exponential in time, and the related decay rate is proportional to the total scattering cross section of the electron-phonon interaction. 1. Introduction andAbstract. We study the dynamics of an electron weakly coupled to a phonon gas. The initial state of the electron is the superposition of two spatially localized distant bumps moving towards each other, and the phonons are in a thermal state. We investigate the dynamics of the system in the kinetic regime and show that the time evolution makes the non-diagonal terms of the density matrix of the electron decay, destroying the interference between the two bumps. We show that such a damping effect is exponential in time, and the related decay rate is proportional to the total scattering cross section of the electron-phonon interaction. 1. Introduction and

Nov 20, 20125 citations

Dynamic electron -phonon interactions in one-dimensional models

Rahul P. Hardikar

Jan 1, 20070 citations

2{k}_{F}

-wave components of the electron density and phonon displacement field share the same correlations. Both correlations are quasi-long-ranged for a single conducting chain coupled to one-dimensional or three-dimensional phonons, and they are long-ranged for repulsive electron-electron interactions for a three-dimensional array of parallel one-dimensional conducting chains coupled to three-dimensional phonons.