Deep nuclear resonant tunneling thermal rate constant calculations

A fast and robust time-independent method to calculate thermal rate constants in the deep resonant tunneling regime for scattering reactions is presented. The method is based on the calculation of the cumulative reaction probability which, once integrated, gives the thermal rate constant. We tested our method with both continuous (single and double Eckart barriers) and discontinuous first derivative potentials (single and double rectangular barriers). Our results show that the presented method is robust enough to deal with extreme resonating conditions such as multiple barrier potentials. Finally, the calculation of the thermal rate constant for double Eckart potentials with several quasi-bound states and the comparison with the time-independent log-derivative method are reported. An implementation of the method using the Mathematica Suite is included in the Supporting Information

An Infinite Swapping Approach to the Rare-Event Sampling Problem

We describe a new approach to the rare-event Monte Carlo sampling problem. This technique utilizes a symmetrization strategy to create probability distributions that are more highly connected and thus more easily sampled than their original, potentially sparse counterparts. After discussing the formal outline of the approach and devising techniques for its practical implementation, we illustrate the utility of the technique with a series of numerical applications to Lennard-Jones clusters of varying complexity and rare-event character.Comment: 24 pages, 16 figure

Discretization Dependence of Criticality in Model Fluids: a Hard-core Electrolyte

Grand canonical simulations at various levels, $\zeta=5$-20, of fine- lattice discretization are reported for the near-critical 1:1 hard-core electrolyte or RPM. With the aid of finite-size scaling analyses it is shown convincingly that, contrary to recent suggestions, the universal critical behavior is independent of $\zeta$ (\grtsim 4); thus the continuum $(\zeta\to\infty)$ RPM exhibits Ising-type (as against classical, SAW, XY, etc.) criticality. A general consideration of lattice discretization provides effective extrapolation of the {\em intrinsically} erratic $\zeta$-dependence, yielding (\Tc^ {\ast},\rhoc^{\ast})\simeq (0.0493_{3},0.075) for the $\zeta=\infty$ RPM.Comment: 4 pages including 4 figure

Monte Carlo simulations and field transformation: the scalar case

We describe a new method in lattice field theory to compute observables at various values of the parameters lambda_i in the action S[phi,lambda_i]. Firstly one performs a single simulation of a ``reference action'' S[phi^r, lambda_i^r] with fixed lambda_i^r. Then the phi^r-configurations are transformed into those of a field phi distributed according to S[phi,lambda_i], apart from a ``remainder action'' which enters as a \break weight. In this way we measure the observables at values of lambda_i different from lambda_i^r. We study the performance of the algorithm in the case of the simplest renormalizable model, namely the phi^4 scalar theory on a four dimensional lattice and compare the method with the ``histogram'' technique of which it is a generalization.Comment: Latex, 23 pgs, 8 eps-figures include

Low-energy quantum dynamics of atoms at defects. Interstitial oxygen in silicon

The problem of the low-energy highly-anharmonic quantum dynamics of isolated impurities in solids is addressed by using path-integral Monte Carlo simulations. Interstitial oxygen in silicon is studied as a prototypical example showing such a behavior. The assignment of a "geometry" to the defect is discussed. Depending on the potential (or on the impurity mass), there is a "classical" regime, where the maximum probability-density for the oxygen nucleus is at the potential minimum. There is another regime, associated to highly anharmonic potentials, where this is not the case. Both regimes are separated by a sharp transition. Also, the decoupling of the many-nuclei problem into a one-body Hamiltonian to describe the low-energy dynamics is studied. The adiabatic potential obtained from the relaxation of all the other degrees of freedom at each value of the coordinate associated to the low-energy motion, gives the best approximation to the full many-nuclei problem.Comment: RevTeX, 6 pages plus 4 figures (all the figures were not accesible before

A Multiscale Approach to Determination of Thermal Properties and Changes in Free Energy: Application to Reconstruction of Dislocations in Silicon

We introduce an approach to exploit the existence of multiple levels of description of a physical system to radically accelerate the determination of thermodynamic quantities. We first give a proof of principle of the method using two empirical interatomic potential functions. We then apply the technique to feed information from an interatomic potential into otherwise inaccessible quantum mechanical tight-binding calculations of the reconstruction of partial dislocations in silicon at finite temperature. With this approach, comprehensive ab initio studies at finite temperature will now be possible.Comment: 5 pages, 3 figure

Criticality in confined ionic fluids

A theory of a confined two dimensional electrolyte is presented. The positive and negative ions, interacting by a $1/r$ potential, are constrained to move on an interface separating two solvents with dielectric constants $\epsilon_1$ and $\epsilon_2$. It is shown that the Debye-H\"uckel type of theory predicts that the this 2d Coulomb fluid should undergo a phase separation into a coexisting liquid (high density) and gas (low density) phases. We argue, however, that the formation of polymer-like chains of alternating positive and negative ions can prevent this phase transition from taking place.Comment: RevTex, no figures, in press Phys. Rev.

Multiple Histogram Method for Quantum Monte Carlo

An extension to the multiple-histogram method (sometimes referred to as the Ferrenberg-Swendsen method) for use in quantum Monte Carlo simulations is presented. This method is shown to work well for the 2D repulsive Hubbard model, allowing measurements to be taken over a continuous region of parameters. The method also reduces the error bars over the range of parameter values due the overlapping of multiple histograms. A continuous sweep of parameters and reduced error bars allow one to make more difficult measurements, such as Maxwell constructions used to study phase separation. Possibilities also exist for this method to be used for other quantum systems.Comment: 4 pages, 5 figures, RevTeX, submitted to Phys. Rev. B Rapid Com

Temperature and density extrapolations in canonical ensemble Monte Carlo simulations

We show how to use the multiple histogram method to combine canonical ensemble Monte Carlo simulations made at different temperatures and densities. The method can be applied to study systems of particles with arbitrary interaction potential and to compute the thermodynamic properties over a range of temperatures and densities. The calculation of the Helmholtz free energy relative to some thermodynamic reference state enables us to study phase coexistence properties. We test the method on the Lennard-Jones fluids for which many results are available.Comment: 5 pages, 3 figure