arXiv subjects

Aldo H. Romero

Publications and source records attributed to Aldo H. Romero.

57 records · Page 4Linked to original sources

arXiv1998

Exact weak-coupling radius of the Holstein polaron in one, two, and three dimensions

We apply weak-coupling perturbation theory to the Holstein molecular crystal model in order to compute an electron-phonon correlation function characterizing the shape and size of the polaron lattice distortion in one, two, and three dimensions. This correlation function is computed exactly to leading order in the electron-phonon coupling constant, permitting a complete description of correlations in any dimension for both isotropic and arbitrarily anisotropic cases. Using this exact result, the width of the polaron is characterized along arbitrary directions. The width of the polaron thus determined disagrees in every dimension with some well-known characterizations of polarons, signalling in particular the breakdown of the adiabatic approximation and the characterizations of self-trapping associated with it.

cond-mat.str-el↗

arXiv1998

Solving the Holstein molecular crystal model

We present selected results for the Holstein molecular crystal model in one space dimension as determined by the Global-Local variational method, including complete polaron energy bands, ground state energies, and effective masses. We juxtapose our results with specific comparable results of numerous other methodologies of current interest, including quantum Monte Carlo, cluster diagonalization, dynamical mean field theory, density matrix renormalization group, semiclassical analysis, weak-coupling perturbation theory, and strong-coupling perturbation theory. This comparison confirms the Global-Local variational method as being highly accurate over a wide range of the polaron parameter space, from the non-adiabatic limit to the extremes of high adiabaticity, from weak coupling through intermediate coupling to strong coupling.

cond-mat↗

arXiv1998

The Kramers Problem in the Energy-Diffusion Limited Regime

The Kramers problem in the energy-diffusion limited regime of very low friction is difficult to deal with analytically becasue of the repeated recrossings of the barrier that typically occur before an asymptotic rate constant is achieved. Thus, the transmission coefficient of particles over the potential barrier undergoes oscillatory behavior in time before settling into a steady state. Recently Kohen and Tannor (JCP Vol. 103, Pg. 6013, 1995) developed a method based on the phase space distribution function to calculate the transmission coefficient as a function of time in the high-friction regime. Here we formulate a parallel method for the low-friction regime. We find analytic results for the full time and temperature dependence of the rate coefficient in this regime. Our low-friction result at long times reproduces the equilibrium result of Kramers at very low friction and extends it to higher friction and lower temperatures below the turn-over region. Our results indicate that the single most important quantity in determining the entire time evolution of the transmission coefficient is the rate of energy loss of a particle that starts above the barrier. We test our resutls, as well as those of Kohen and Tannor for the Kramers problem, against detailed numerical simulations.

cond-mat.stat-mech↗