Quantum lattice fluctuations

This model, which is sometimes referred to as the Fluctuating Gap Model (FGM) [42], has been used to study various aspects of quasi-one-dimensional systems. Examples arc the thermodynamic properties of quasi-one-dimensional organic compounds (NMP-TCNQ, TTF-TCNQ) [271, the effect of disorder on the Peierls transition [43, 44, and the effect of quantum lattice fluctuations on the optical spectrum of Peierls materials [41, 45, 46]. 

For long (infinite) /am.v-polyacclylene chains, the treatment of quantum lattice fluctuations is very complicated, because many lattice degrees of freedom couple in a non-linear way to the lowest electronic transitions. We have recently shown that for chains of up to 70 CH units, the amount of relevant lattice degrees of freedom reduces to only one or two, which makes it possible to calculate the low-energy part of the absorption spectrum in an essentially exact way [681. It remains a challenge to study models in which both disorder and the lattice quantum dynamics are considered. 

In this chapter we will review recent developments in the simulation of lattice (and continuum) models by classical and quantum Monte Carlo simulations. Unbiased numerical methods are required to obtain reliable results for classical and quantum lattice model when interactions or fluctuations are strong, especially in the vicinity of phase transitions, in frustrated models and in systems where quantum effects are important. For classical systems, molecular dynamics or the Monte Carlo method are the methods of choice since they can treat large systems. 

In conclusion, we present herein a rather compelling model for the short-time dynamics of the excited states in DNA chains that incorporates both charge-transfer and excitonic transfer. It is certainly not a complete model and parametric refinements are warranted before quantitative predictions can be established. For certain, there are various potentially important contributions we have left out disorder in the system, the fluctuations and vibrations of the lattice, polarization of the media, dissipation, quantum decoherence. We hope that this work serves as a starting point for including these physical interactions into a more comprehensive description of this system. 

It is obviously ideally suited to measuring the effect of the electron quantum fluctuations on the phonon frequency. What one immediately learns from Eq. (26) is that the propagator is quasistatic that is, the >m = 0 component dominates for T > co /2tt. This comes from the definition of the Matsubara frequencies for bosons [under Eq. (8)]. As far as the electrons are concerned, the atoms move very slowly (the adiabatic limit). If 2g2 gi> - g3 (see Fig. 5), the electrons are able to screen the slow lattice motion and thus soften the interactions. We are obviously interested in the 2kF phonons, which will be screened most effectively by the dominant 2kF charge response of the one-dimensional electron gas. 

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