RESUMO
The Holstein model describes the interaction between fermions and a collection of local (dispersionless) phonon modes. In the dilute limit, the phonon degrees of freedom dress the fermions, giving rise to polaron and bipolaron formation. At higher densities, the phonons mediate collective superconducting (SC) and charge-density wave (CDW) phases. Quantum Monte Carlo (QMC) simulations have considered both these limits but have not yet focused on the physics of more general phonon spectra. Here we report QMC studies of the role of phonon dispersion on SC and CDW order in such models. We quantify the effect of finite phonon bandwidth and curvature on the critical temperature T_{cdw} for CDW order and also uncover several novel features of diagonal long-range order in the phase diagram, including a competition between charge patterns at momenta q=(π,π) and q=(0,π) which lends insight into the relationship between Fermi surface nesting and the wave vector at which charge order occurs. We also demonstrate SC order at half filling in situations where a nonzero bandwidth sufficiently suppresses T_{cdw}.
RESUMO
We study numerically the roughness exponent zeta of an in-plane fracture front slowly propagating along a heterogeneous interface embedded in an elastic body, using a model based on the evolution of a process zone rather than a fracture line. We find zeta=0.60+/-0.05. For the first time, simulation results are in close agreement with experimental results. We then show that the roughness exponent is related to the correlation length exponent nu of a stress-weighted percolation problem through zeta=nu/(1+nu). A numerical study of the stress-weighted percolation problem yields nu=1.54 giving zeta=0.61 in close agreement with our numerical results and with experimental observations.
RESUMO
We present a simple criterion based on the Einstein relation for determining whether diffusion in systems governed by a generalized Langevin equation with long-range memory is normal, superdiffusive, or subdiffusive. We support our analysis with numerical simulations.