Time-domain ab initio simulation of electron and hole relaxation dynamics in a single-wall semiconducting carbon nanotube

The electron and hole relaxation in the (7, 0) zigzag carbon nanotube is simulated in time domain using a surface-hopping Kohn-Sham density functional theory. Following a photoexcitation between the second van Hove singularities, the electrons and holes decay to the Fermi level on characteristic subpicosecond time scales. Surprisingly, despite a lower density of states, the electrons relax faster than the holes. The relaxation is primarily mediated by the high-frequency longitudinal optical (LO) phonons. Hole dynamics are more complex than the electron dynamics: in addition to the LO phonons, holes couple to lower frequency breathing modes and decay over multiple time scales.     

Non-equilibrium relaxation and tumbling times of polymers in semidilute solution

The end-over-end tumbling dynamics of individual polymers in dilute and semidilute solutions is studied under shear flow by large-scale mesoscale hydrodynamic simulations. End-to-end vector relaxation times are determined along the flow, gradient, and vorticity directions. Along the flow and gradient directions, the correlation functions decay exponentially with sinusoidal modulations at short times. In dilute solution, the decay times of the various directions are very similar. However, in semidilute solutions, the relaxation behaviors are rather different along the various directions, with the longest relaxation time in the vorticity direction and the shortest time in the flow direction. The various relaxation times exhibit a power-law shear-rate dependence with the exponent -?2/3 at high shear rates. Quantitatively, the relaxation times are equal to the tumbling times extracted from cross-correlation functions of fluctuations of radius-of-gyration components along the flow and gradient direction.     

Anomalous power law decay in solvation dynamics of DNA: a mode coupling theory analysis of ion contribution

Several time dependent fluorescence Stokes shift (TDFSS) experiments have reported a slow power law decay in the hydration dynamics of a DNA molecule. Such a power law has neither been observed in computer simulations nor in some other TDFSS experiments. Here we observe that a slow decay may originate from collective ion contribution because in experiments DNA is immersed in a buffer solution, and also from groove bound water and lastly from DNA dynamics itself. In this work we first express the solvation time correlation function in terms of dynamic structure factors of the solution. We use mode coupling theory to calculate analytically the time dependence of collective ionic contribution. A power law decay in seen to originate from an interplay between long-range probe–ion direct correlation function and ion–ion dynamic structure factor. Although the power law decay is reminiscent of Debye–Falkenhagen effect, yet solvation dynamics is dominated by ion atmosphere relaxation times at longer length scales (small wave number) than in electrolyte friction. We further discuss why this power law may not originate from water motions which have been computed by molecular dynamics simulations. Finally, we propose several experiments to check the prediction of the present theoretical work.     

Manifestations of Slow Site Exchange Processes in Solution NMR: A Continuous Gaussian Exchange Model

The effects of site exchange due to slow conformational changes in rapidly rotating molecules in solution are examined in detail. Significant gaps in the currently available theory are filled. The effects of site exchange on the lineshape, decay of a simple spin-echo, decay of the even echoes in a Carr-Purcell-Meiboom-Gill (CPMG) pulse-sequence, and decay of the transverse magnetization in a resonant spin-locking field are investigated. Both trajectory and stochastic operator approaches are formulated and shown to be completely equivalent whenever the dynamics of population transfers among the inequivalent sites is governed by either a stationary or a nonstationary Markov process. A nonstationary Markov process may result from Brownian dynamics (a stationary Markov process) in a larger conformational space that contains the subspace of inequivalent sites. A continuous Gaussian exchange model is formulated in which a nucleus undergoes continuous one-dimensional motion in a harmonic potential well that is located in a linear chemical shift gradient. The effects of this Gaussian exchange model on the lineshape, simple spin-echo decay, and decay of the even echoes of a CPMG pulse train are treated rigorously via the trajectory approach. Compact analytical expressions are obtained for the relevant correlation functions in each case. The relevant decays are found to be exponential in the very short time and long time limits, which are not necessarily experimentally significant in any given case. In the fast exchange limit the relevant decays are exponential at all times, and explicit formulas are given for their decay rates. In the long time limit, all discrete multisite models with the same intrinsic Ro2 at every site are shown to be completely equivalent to a continuous Gaussian model with appropriate relaxation time and variance of the Larmor frequency. The effects of this Gaussian exchange model on the decay of the transverse magnetization in a resonant spin-locking field are treated heuristically by a trajectory approach. The intrinsic contribution (Ro1rho) of rapid rotations and dipole-dipole interactions to relax the transverse magnetizations of two nuclei of the same kind in the presence of a (nearly) resonant spin-locking field is also derived and found to be practically the same as the intrinsic contribution, Ro2, of those same rotations to the simple and CPMG spin-echo decay rates and linewidth. Literature data for the linewidth, decay rate of the CPMG even spin-echoes, and R(1rho) decay rate for the A9-H2 protons of adenines at the central TpA step in the sequence, 5'-GCAGGTTTAAACCTCG-3', are analyzed using the Gaussian exchange model to assess the time-scale and variance of the site exchange process as well as the intrinsic Ro2 rate. Although a single Gaussian exchange process with appropriate parameters can fit these three A9-H2 data rather well, this particular "solution" cannot be reconciled with NMR relaxation data on other protons in the same DNA molecule. Rather good agreement with all of the observations is obtained by using a model of two concurrent Gaussian exchange processes, whose relaxation times, tau = 7 and 460 micros, differ in time-scale by a factor of 65. The insensitivity of R1rho in the presence of a fast site exchange process to much slower concurrent site exchange processes is explicitly demonstrated. Protocols for detecting and characterizing a second slow site exchange process are suggested.     

Friction tensor for a pair of Brownian particles: Spurious finite-size effects and molecular dynamics estimates

In this work, we show thatin any finite system, the binary friction tensor for two Brownian particlescannot be directly estimated from an evaluation of the microscopic Green-Kubo formula, involving the time integral of force-force autocorrelation functions. This pitfall is associated with a subtle inversion of the thermodynamic and long-time limits and leads to spurious results for the estimates of the friction matrix based on molecular dynamics simulations. Starting from a careful analysis of the coupled Langevin equations for two interacting Brownian particles, we derive a method to circumvent these effects and extract the binary friction tensor from the correlation function matrix of the instantaneous forces exerted by the bath particles on the fixed Brownian particles, and from the relaxation of the total momentum of the bath in afinite system. The general methodology is applied to the case of two hard or soft Brownian spheres in a bath of light particles. Numerical estimates of the relevant correlation functions and of the resulting self and mutual components of the matrix of friction tensors are obtained by molecular dynamics simulations for various spacings between the Brownian particles. This paper is dedicated to B. Jancovici on the occassion of his 65th birthday.     

Conformational fluctuations of a tethered polymer in uniform flow

The decay of correlations in the conformational fluctuations of a tethered polymer subjected to a uniform flow is analyzed in terms of relaxation times and associated normal modes. These quantities are calculated numerically from Brownian dynamics simulations of several bead spring polymer models. In this way, the influence of different effects like a finite extensibility of the springs and excluded-volume as well as hydrodynamic interactions between the beads on the decay of fluctuations is identified. Moreover, by comparison of the simulation results to analytically tractable blob models with corresponding assumptions, the capability of the tensile-blob picture to predict relaxation times and modes is assessed. For excluded-volume and hydrodynamic interactions a crossover to Rouse-like behavior occurs when the flow velocity and hence the polymer deformation exceeds a certain value. For finitely extensible springs, in contrast, the relaxation times decrease monotonically with increasing polymer deformation. This latter behavior differs from assumptions often used in rheological modeling by dumbbells and is not captured by the blob model.Received: 4 April 2003, Published online: 12 August 2003PACS: 83.80.Rs Polymer solutions - 83.10.Mj Molecular dynamics, Brownian dynamics - 36.20.Ey Conformation (statistics and dynamics) - 47.50. + d Non-Newtonian fluid flows     

Dynamics of a polymer chain confined in a membrane

We present a Brownian dynamics theory with full hydrodynamics (Stokesian dynamics) for a Gaussian polymer chain embedded in a liquid membrane which is surrounded by bulk solvent and walls. The mobility tensors are derived in Fourier space for the two geometries, namely, a free membrane embedded in a bulk fluid, and a membrane sandwiched by the two walls. Within the preaveraging approximation, a new expression for the diffusion coefficient of the polymer is obtained for the free-membrane geometry. We also carry out a Rouse normal mode analysis to obtain the relaxation time and the dynamical structure factor. For large polymer size, both quantities show Zimm-like behavior in the free-membrane case, whereas they are Rouse-like for the sandwiched membrane geometry. We use the scaling argument to discuss the effect of excluded-volume interactions on the polymer relaxation time.     

Tagged-particle motion in glassy systems under shear: Comparison of mode coupling theory and Brownian dynamics simulations

We study the dynamics of a tagged particle in a glassy system under shear. The recently developed integration through transients approach, based on mode coupling theory, is continued to arrive at the equations for the tagged-particle correlators and the mean squared displacements. The equations are solved numerically for a two-dimensional system, including a nonlinear stability analysis of the glass solution, the so called β-analysis. We perform Brownian Dynamics simulations in 2D and compare with theory. After switch on, transient glassy correlation functions show strong fingerprints of the stress overshoot scenario, including, additionally to previously studied superexponential decay, a shoulder-like slowing down after the overshoot. We also find a new type of Taylor dispersion in glassy states which has intriguing similarity to the known low-density case. The theory qualitatively captures most features of the simulations with quantitative deviations concerning the shear-induced time scales. We attribute these deviations to an underestimation of the overshoot scenario in the theory.     

Dynamics of driven Brownian inverted oscillator

In this paper, we derive the quantum Langevin equation for a driven Brownian inverted oscillator in the framework of the Heisenberg picture for the Caldeira-Leggett model. We describe the influence of an arbitrary time-dependent force on an open inverted oscillator dynamics. We take into account environment through the integral operator of relaxation and the force correlation function. The resulting behavior of the system is represented as a combination the time evolution of the position expectation and the variance, being induced simultaneously by spreading the wave packet and the chaotic Brownian motion. We discuss the possibility of stabilization of an open inverted oscillator, when applying external alternating force.     

Rotational Relaxation of Linear π-Systems with Flexible Side Chains in Solution

The classical hydrodynamic theory for Brownian rotational motion is applied to model compounds of conjugated polymers with alkoxy side chains of variable length. Theory predicts two rotational relaxation times for these types of molecules with the dipole transition moment parallel to the longest axis whereas experiments reveal only one. The rotational relaxation times and their relative amplitudes were calculated for a wide span of axial ratios of a general ellipsoid. In this way, the range in the axial ratios is obtained such that there is a chance to detect both rates experimentally. Rotational relaxation times of five particular molecules were measured in liquid n-butane. Theoretical calculations using ellipsoid parameters obtained from molecular dynamics calculations compare well with experimental results. Calculation of the rotational relaxation times from the autocorrelation function of the transition dipole moment vector requires significantly greater computational effort.     

Are long time tails observable

An experiment is proposed to detect the long time tail of the velocity correlation function for a molecular sized Brownian particle. This decay is predicted by recent hydrodynamical models, in contradistinction to the exponential behavior predicted by classical theory.     

Thermal undulations of lipid bilayers relax by intermonolayer friction at submicrometer length scales

The time correlation functions of the thermal undulations of a lipid membrane have been studied by molecular dynamics simulations of a coarse-grained bilayer model. We observe a double-exponential decay, with relaxation rates in good agreement with the theory by Seifert and Langer, [Europhys. Lett. 23, 71 (1993)]. Intermonolayer friction resulting from local velocity differences between the two monolayers is shown to be the dominant dissipative mechanism for fluctuations with wave lengths below approximately -0.1 microm.     

The sphericalp-spin interaction spin-glass model

The relaxational dynamics for local spin autocorrelations of the sphericalp-spin interaction spin-glass model is studied in the mean field limit. In the high temperature and high external field regime, the dynamics is ergodic and similar to the behaviour in known liquid-glass transition models. In the static limit, we recover the replica symmetric solution for the long time correlation. This phase becomes unstable on a critical line in the (T, h) plane, where critical slowing down is observed with a cross-over to power law decay of the correlation function ∝t ^?ν, with an exponent ν varying along the critical line. For low temperatures and low fields, ergodicity in phase space is broken. For small fields the transition is discontinuous, and approaching this transition from above, two long time scales are seen to emerge. This dynamical transition lies at a somewhat higher temperature than the one obtained within replica theory. For larger fields the transition becomes continuous at some tricritical point. The low temperature phase with broken ergodicity is studied within a modified equilibrium theory and alternatively for adiabatic cooling across the transition line. This latter scheme yields rather detailed insight into the formation and structure of the ergodic components.     

Ultrafast transport of laser-excited spin-polarized carriers in Au/Fe/MgO(001)

Hot carrier-induced spin dynamics is analyzed in epitaxial Au/Fe/MgO(001) by a time domain approach. We excite a spin current pulse in Fe by 35 fs laser pulses. The transient spin polarization, which is probed at the Au surface by optical second harmonic generation, changes its sign after a few hundred femtoseconds. This is explained by a competition of ballistic and diffusive propagation considering energy-dependent hot carrier relaxation rates. In addition, we observe the decay of the spin polarization within 1 ps, which is associated with the hot carrier spin relaxation time in Au.     

Equilibrium theory of molecular fluids: Structure and freezing transitions

In this article we review equilibrium theory of molecular fluids which includes structure and freezing transitions. The application of the theory to evaluate the pair correlation functions using Integral Equation methods and Computer Simulations have been discussed. Freezing of classical complex fluids based on the density functional approach is also discussed and compare a variety of its versions. Transitions discussed are sensitive to the value of direct correlation functions of the effective liquid which is required as an input information in the theory. Accurate evaluation of pair correlation functions is emphasized. Calculation of these correlation functions which pose problems in the case of ordered phases is discussed. The pair correlation functions of the ordered phase, which are supposed to be made up of two contributions, one that preserves the symmetry of the isotropic phase and a second that breaks it, are discussed. A new free-energy functional developed for an inhomogeneous system that contains both symmetry conserved and symmetry broken parts of the direct pair correlation function is discussed. The most useful three dimensional reference interaction site model (3D-RISM) and its extension done recently by many workers is discussed. Application of this theory to a large variety of complex systems in combination with the density functional theory method implemented in the Amsterdam density functional software package is discussed. Coupling of the 3D-RISM salvation theory with molecular dynamics in the Amber molecular dynamics package is also given.     

Scaling laws and memory effects in the dynamics of liquids and proteins

Recent progress in the numerical calculation of memory functions from molecular dynamics simulations allowed the gaining of deeper insight into the relaxation dynamics of liquids and proteins. The concept of memory functions goes back to the work of R. Zwanzig on the generalized Langevin equation, and it was the basis for the development of various dynamical models for liquids. In this article we present briefly a method for the numerical calculation of memory functions, which is then applied to study their scaling behavior in normal and fractional Brownian dynamics. It has been shown recently that the model of fractional Brownian dynamics constitutes effectively a link between protein dynamics on the nanosecond time scale, which is accessible to molecular dynamics simulations and thermal neutron scattering, and the much longer time scale of functional protein dynamics, which can be studied by fluorescence correlation spectroscopy. The text was submitted by the authors in English. Affiliated with the University of Orléans.     

Relaxation time distributions for an anomalously diffusing particle

As well known, the generalized Langevin equation with a memory kernel decreasing at large times as an inverse power law of time describes the motion of an anomalously diffusing particle. Here, we focus attention on some new aspects of the dynamics, successively considering the memory kernel, the particle’s mean velocity, and the scattering function. All these quantities are studied from a unique angle, namely, the discussion of the possible existence of a distribution of relaxation times characterizing their time decay. Although a very popular concept, a relaxation time distribution cannot be associated with any time-decreasing quantity (from a mathematical point of view, the decay has to be described by a completely monotonic function).Technically, we use a memory kernel decaying as a Mittag-Leffler function (the Mittag-Leffler functions interpolate between stretched or compressed exponential behaviour at short times and inverse power law behaviour at large times). We show that, in the case of a subdiffusive motion, relaxation time distributions can be defined for the memory kernel and for the scattering function, but not for the particle’s mean velocity. The situation is opposite in the superdiffusive case.     

Brownian dynamics simulation of electrostatically interacting proteins

Brownian dynamics simulation software has been developed to study the dynamics of proteins as a whole in solution. The proteins were modelled as spheres with point dipoles embedded in the centre of sphere. A set of Brownian dynamics simulations at different values of the dipole moments, protein concentration and translational diffusion coefficient was performed to investigate the influence of interprotein electrostatic interactions on dynamic protein behaviour in solution. It was shown that these interactions led to the slowing down of protein rotation and a complex non-exponential shape of the rotational correlation function. Analysis of the correlation functions was performed within the frame of the model of electrostatic interprotein interactions advanced earlier on the basis of NMR and dielectric spectroscopy data. This model assumes that, due to electrostatic interactions, protein Brownian rotation becomes anisotropic. The lifetime of this anisotropy is controlled mainly by translational diffusion of proteins. Thus, the correlation function can be decomposed into two components corresponding to anisotropic Brownian rotation and an isotropic motion of an external electric field vector produced by the surrounding proteins.