A targeted reweighting method for accelerating the exploration of highdimensional configuration space

Time scales available to biomolecular simulations are limited by barriers among states in a high-dimensional configuration space. If equilibrium averages are to be computed, methods that accelerate barrier passage can be carried out by non-Boltzmann sampling. Barriers can be reduced by modifying the potential-energy function and running dynamics on the modified surface. The Boltzmann average can be restored by reweighting each point along the trajectory. We introduce a targeted reweighting scheme where some barriers are reduced, while others are not modified. If only equilibrium properties are desired, trajectories in configuration space can be generated by Langevin dynamics. Once past a transient time, these trajectories guarantee equilibrium sampling when reweighted. A relatively high-order stochastic integration method can be used to generate trajectories. The targeted reweighting scheme is illustrated by a series of double-well models with varying degrees of freedom and shown to be a very efficient method to provide the correct equilibrium distributions, in comparison with analytic results. The scheme is applied to a protein model consisting of a chain of connected beads characterized by dihedral angles and the van der Waals interactions among the beads. We investigate the sampling of configuration space for a model of a helix-turn-helix motif. The targeted reweighting is found to be essential to permit the original all-helical conformation to bend and generate turn structures while still maintaining the alpha-helical segments.Institutos Nacionales de Salud de Estados Unidos GM47274Ministerio de Educación y Ciencia de España BFM2002-0382

Controlling low-temperature tunneling dynamics with external fields

The tunneling of a particle between two states, as influenced by coupling the particle to an external field, is investigated. A spin-boson Hamiltonian is used to describe the tunnel system and its interaction with a medium and is augmented by a term coupling the dipole moment of the particle to the external field. A projection operator method is introduced that provides equations of motion for the particle's density matrix and permits discussion of external field effects on tunneling even at very low temperatures. These equations of motion can exhibit solutions characterized by population relaxation with a rate constant that is an average over the period of the external field. As an application of this theory, the modification by an external field of the tunneling rate of a defect in a metal, where the system-medium interaction is characterized by an Ohmic spectrum, is evaluated. At sufficiently low temperatures, for experimentally relevant parameter values, suitably chosen (constant and/or sinusoidal), external fields can greatly suppress or enhance the tunneling rate relative to the field-independent value

External-field effects on molecular electronic transitions in charge-transfer systems

We investigate strong-external-field effects on optical transitions between electronic states of charge-transfer systems in condensed media. We will use as a model a two-level system coupled to a dissipative medium driven by a strong, time-dependent external field. The external field induces transitions between the levels, and the dissipation, represented by a stochastic process, induces relaxation. The power absorbed by the system is characterized by spectral densities that not only depend on the detuning from resonance and the strength of the dissipation, as found for line shapes in linear spectroscopy, but also on the strength of the external field. Our treatment is nonperturbative in the strength of the external field, and leads to the conclusion that spectral line shapes can be manipulated by the application of sufficiently strong external fields.Dirección General de Investigaciones Científicas y Técnicas PB95-053

Expansion for the moments of a nonlinear stochastic model

We present a procedure to systematically evaluate all the moments of the Fokker-Planck equation by expanding them in a power series in a given function of t. The expansion coefficients are easily determined in terms of algebraic recursion relations. Applications to a linear Fokker-Planck equation, as well as to a truly nonlinear mean-field model, whose drift coefficient exhibits a functional dependence on the distribution function, show this formalism to be advantageous over the standard time series expansion of the moments which is shown to be rather impractical.Dirección General de Investigación Científica y Técnica (España) PB92-068

Path Integral Solution of the Kramers Problem

An iterative method to generate a discrete path integral solution of the Kramers problem is presented. It is based on a straightforward derivation of the functional formalism from the underlying Langevin equations. The method is rather simple and systematic and allows us to analytically evaluate the short time propagator up to and including terms of fourth order in a time increment τ. This means a significant reduction of the number of time steps N that are necessary to obtain convergent results for a given net increment t=Nτ.Dirección General de Investigación Científica y Técnica (España) PB95-053

Strong external field effects on electronic dephasing of molecular transitions in condensed media

We discuss the effects of a strong external field on the optical transition between two electronic states of a solute immersed in a medium. The solute states may be weakly or quite strongly coupled to the medium. The electronic dephasing process is characterized via the power absorbed by the solute. The average absorbed power P¯(t) for resonant, strong fields exhibits an oscillatory decay in time, reflecting the finite change in the population difference of the electronic states, and the dephasing arising from the coupling to the medium. The coefficients of P¯(t) depend on the detuning from resonance as well as the coupling strength between the external field and the solute’s transition dipole. Our method is nonperturbative in the external field strength and shows that the spectral line shapes can be systematically altered by the application of a strong external field. We also show that for strong but off-resonance fields, P¯(t) returns to the linear response regime.Center for Fundamental Materials Research at Michigan State UniversityDirección General de Enseñanza Superior de España PB95-0536Junta de Andalucí

Dynamics of single and multiple Zener transitions

The probability of remaning in a given state is evaluated for a two-level system that can cross repeatedly and periodically as a function of a control parameter. The possibility of multiple Zener transitions between the surfaces introduces the issue of the appropriate initial conditions for each successive transition. We devise a simple model, which is readily analyzed numerically, to evaluate the consequences of an initially nondiaganol density matrix on the subsequent evolution through the crossing region. The initial state strongly affects the outcome of the transition. Thus successive transitions are, in general, not independent of each other. Consequently, we find that the probability oscillates in time. This contrasts with the result of convergence at long times to a constant state occupation which would be predicted based solely on probabilities of single transitions. We also analyze the role that inelastic transitions play in modifying the nondissipative multiple-Zener-transition model. This model finds application to small tunnel junctions, where the control parameter is a current and the output is a voltage. Here, we show that the average dc voltage is nonzero when inelastic transitions are included, in contrast to the zero average voltage obtained in the absence of inelastic transitions, or when their rate is very large.Dirección General de Investigación Científica y Técnica PS89-0123OTAN CRG 89046

Noise-induced forced synchronization of global variables in coupled bistable systems

We analyze the noise-induced synchronization between a collective variable characterizing a complex system with a finite number of interacting bistable units and time-periodic driving forces. A random phase process associated to the collective stochastic variable is defined. Its average phase frequency and average phase diffusion are used to characterize the phenomenon. Our analysis is based on numerical solutions of the corresponding set of Langevin equations.Ministerio de Educación y Ciencia FIS2005-0288

System Size Synchronization

In this paper we bring out the existence of a kind of synchronization associated with the size of a complex system. A dichotomic random jump process associated with the dynamics of an externally driven stochastic system with N coupled units is constructed. We define an output frequency and phase diffusion coefficient. System size synchronization occurs when the average output frequency is locked to the external one and the average phase diffusion coefficient shows a very deep minimum for a range of system sizes. Analytical and numerical procedures are introduced to study the phenomenon, and the results describe successfully the existence of system size synchronization.Ministerio de Economía y Competitividad FIS2017-86478-PJunta de Andalucia P20_0061

Solvation in binary mixtures of dipolar hard sphere solvents: Theory and simulations

The structure of mixtures of dipolar hard sphere fluids with components of equal size but different dipole moments around a single ion is studied. The solvation energy and the polarization around the ion is obtained in the framework of the mean spherical approximation (MSA). Our theoretical results and the results of other workers are compared with simulation data obtained from Monte Carlo simulations. An interpretation of the meaning of preferential solvation is given in terms of the contrasting behaviors of partial polarization in the bulk and near the ion.Dirección General de Enseñanza Superior de España PB98-0423 y PB98-1120Junta de Andalucí