Semiclassical dynamics of electron transfer at metal surfaces

In this Letter, we demonstrate that nonadiabatic dynamics of molecular scattering from metal surfaces can be efficiently simulated by semiclassical Gaussian wave packet propagation on a local complex potential. The method relies on the wideband limit decoupling of the nuclear equations of motion on different electronic states. If the continuum diabatic potential surfaces are assumed to be parallel, the number of Gaussian wave packets spawned scales at most linearly with propagation time, allowing efficient propagation of nuclear dynamics.     

Structure and mobility of defects formed from collision cascades in MgO

We study radiation-damage events in MgO on experimental time scales by augmenting molecular dynamics cascade simulations with temperature accelerated dynamics, molecular statics, and density functional theory. At 400 eV, vacancies and mono- and di-interstitials form, but often annihilate within milliseconds. At 2 and 5 keV, larger clusters can form and persist. While vacancies are immobile, interstitials aggregate into clusters (In) with surprising properties; e.g., an I4 is immobile, but an impinging I2 can create a metastable I6 that diffuses on the nanosecond time scale but is stable for years.     

The G-Scheme: A framework for multi-scale adaptive model reduction

The numerical solution of mathematical models for reaction systems in general, and reacting flows in particular, is a challenging task because of the simultaneous contribution of a wide range of time scales to the system dynamics. However, the dynamics can develop very-slow and very-fast time scales separated by a range of active time scales. An opportunity to reduce the complexity of the problem arises when the fast/active and slow/active time scales gaps becomes large. We propose a numerical technique consisting of an algorithmic framework, named the G-Scheme, to achieve multi-scale adaptive model reduction along-with the integration of the differential equations (DEs). The method is directly applicable to initial-value ODEs and (by using the method of lines) PDEs. We assume that the dynamics is decomposed into active, slow, fast, and when applicable, invariant subspaces. The G-Scheme introduces locally a curvilinear frame of reference, defined by a set of orthonormal basis vectors with corresponding coordinates, attached to this decomposition. The evolution of the curvilinear coordinates associated with the active subspace is described by non-stiff DEs, whereas that associated with the slow and fast subspaces is accounted for by applying algebraic corrections derived from asymptotics of the original problem. Adjusting the active DEs dynamically during the time integration is the most significant feature of the G-Scheme, since the numerical integration is accomplished by solving a number of DEs typically much smaller than the dimension of the original problem, with corresponding saving in computational work. To demonstrate the effectiveness of the G-Scheme, we present results from illustrative as well as from relevant problems.     

Diagnostics of many-particle electronic states: Non-stationary currents and residual charge dynamics

We propose the method for identifying many particle electronic states in the system of coupled quantum dots (impurities) with Coulomb correlations. We demonstrate that different electronic states can be distinguished by the complex analysis of localized charge dynamics and non-stationary characteristics. We show that localized charge time evolution strongly depends on the properties of initial state and analyze different time scales in charge kinetics for initially prepared singlet and triplet states. We reveal the conditions for existence of charge trapping effects governed by the selection rules for electron transitions between the states with different occupation numbers.     

Ionization dynamics of dense matter generated by intense ultrashort X‐ray pulses

We investigate a pump‐probe X‐ray Thomson scattering (XRTS) experiment that might be carried out at a free electron laser facility to study warm‐to‐hot states of dense matter. Ultrashort and intense X‐ray pulses with different energies (1,560–1,830 eV) heat a 1 µm thick Al target isochorically and create homogeneous and uncompressed warm‐to‐hot states of dense matter. A second pulse with variable delay probes this heated state via XRTS. The X‐ray laser–target interaction is modelled within radiation‐hydrodynamic simulations applying the HELIOS‐CR code. The HELIOS‐CR results qualitatively agree with Monte‐Carlo simulations, where the laser pulse absorption is simulated based on a uniform random sequence of events. The electron feature in the simultaneously observed X‐ray scattering spectrum is a function of the degree of ionization and the target temperature. Therefore, the temporal evolution of the plasmon peak measures the ionization dynamics on ultra‐short time scales. The XRTS spectrum is calculated based on the Chihara formula utilizing the Born‐Mermin approximation for the free electron dynamic structure factor. The proposed experiment will reveal important details of the ionization dynamics on ultra‐short time scales as well as of the relaxation on ps time scales.     

Minimal curvature trajectories: Riemannian geometry concepts for slow manifold computation in chemical kinetics

In dissipative ordinary differential equation systems different time scales cause anisotropic phase volume contraction along solution trajectories. Model reduction methods exploit this for simplifying chemical kinetics via a time scale separation into fast and slow modes. The aim is to approximate the system dynamics with a dimension-reduced model after eliminating the fast modes by enslaving them to the slow ones via computation of a slow attracting manifold. We present a novel method for computing approximations of such manifolds using trajectory-based optimization. We discuss Riemannian geometry concepts as a basis for suitable optimization criteria characterizing trajectories near slow attracting manifolds and thus provide insight into fundamental geometric properties of multiple time scale chemical kinetics. The optimization criteria correspond to a suitable mathematical formulation of “minimal relaxation” of chemical forces along reaction trajectories under given constraints. We present various geometrically motivated criteria and the results of their application to four test case reaction mechanisms serving as examples. We demonstrate that accurate numerical approximations of slow invariant manifolds can be obtained.     

Dissipative quantum Church-Turing theorem

We show that the time evolution of an open quantum system, described by a possibly time dependent Liouvillian, can be simulated by a unitary quantum circuit of a size scaling polynomially in the simulation time and the size of the system. An immediate consequence is that dissipative quantum computing is no more powerful than the unitary circuit model. Our result can be seen as a dissipative Church-Turing theorem, since it implies that under natural assumptions, such as weak coupling to an environment, the dynamics of an open quantum system can be simulated efficiently on a quantum computer. Formally, we introduce a Trotter decomposition for Liouvillian dynamics and give explicit error bounds. This constitutes a practical tool for numerical simulations, e.g., using matrix-product operators. We also demonstrate that most quantum states cannot be prepared efficiently.     

Chaotic itinerancy, temporal segmentation and spatio-temporal combinatorial codes

We study a deterministic dynamics with two time scales in a continuous state attractor network. To the usual (fast) relaxation dynamics towards point attractors (“patterns”) we add a slow coupling dynamics that makes the visited patterns lose stability, leading to an itinerant behavior in the form of punctuated equilibria. One finds that the transition frequency matrix for transitions between patterns shows non-trivial statistical properties in the chaotic itinerant regime. We show that mixture input patterns can be temporally segmented by the itinerant dynamics. The viability of a combinatorial spatio-temporal neural code is also demonstrated.     

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.     

A new method for studying sub‐pulse dynamics at synchrotron sources

The possibility of studying dynamics at time scales on the order of the pulse duration at synchrotron X‐ray sources with present avalanche photodiode point detection technology is investigated, without adopting pump–probe techniques. It is found that sample dynamics can be characterized by counting single and double photon events and an analytical approach is developed to estimate the time required for a statistically significant measurement to be made. The amount of scattering required to make such a measurement possible presently within a few days is indicated and it is shown that at next‐generation synchrotron sources this time will be reduced dramatically, i.e. by more than three orders of magnitude. The analytical results are confirmed with simulations in the frame of Gaussian statistics. In the future, this approach could be extended to even shorter time scales with the implementation of ultrafast streak cameras.     

Multiscale entropy analysis of complex physiologic time series

There has been considerable interest in quantifying the complexity of physiologic time series, such as heart rate. However, traditional algorithms indicate higher complexity for certain pathologic processes associated with random outputs than for healthy dynamics exhibiting long-range correlations. This paradox may be due to the fact that conventional algorithms fail to account for the multiple time scales inherent in healthy physiologic dynamics. We introduce a method to calculate multiscale entropy (MSE) for complex time series. We find that MSE robustly separates healthy and pathologic groups and consistently yields higher values for simulated long-range correlated noise compared to uncorrelated noise.     

Time scale bridging in atomistic simulation of slow dynamics: viscous relaxation and defect activation

Atomistic simulation methods are known for timescale limitations in resolving slow dynamical processes. Two well-known scenarios of slow dynamics are viscous relaxation in supercooled liquids and creep deformation in stressed solids. In both phenomena the challenge to theory and simulation is to sample the transition state pathways efficiently and follow the dynamical processes on long timescales. We present a perspective based on the biased molecular simulation methods such as metadynamics, autonomous basin climbing (ABC), strain-boost and adaptive boost simulations. Such algorithms can enable an atomic-level explanation of the temperature variation of the shear viscosity of glassy liquids, and the relaxation behavior in solids undergoing creep deformation. By discussing the dynamics of slow relaxation in two quite different areas of condensed matter science, we hope to draw attention to other complex problems where anthropological or geological-scale time behavior can be simulated at atomic resolution and understood in terms of micro-scale processes of molecular rearrangements and collective interactions. As examples of a class of phenomena that can be broadly classified as materials ageing, we point to stress corrosion cracking and cement setting as opportunities for atomistic modeling and simulations.     

Modelling the air transport with complex networks: A short review

Air transport is a key infrastructure of modern societies. In this paper we review some recent approaches to air transport, which make extensive use of theory of complex networks. We discuss possible networks that can be defined for the air transport and we focus our attention to networks of airports connected by flights. We review several papers investigating the topology of these networks and their dynamics for time scales ranging from years to intraday intervals, and consider also the resilience properties of air networks to extreme events. Finally we discuss the results of some recent papers investigating the dynamics on air transport network, with emphasis on passengers traveling in the network and epidemic spreading.     

Dynamical screening and ionic conductivity in water from ab initio simulations

We present a method to calculate ionic conductivities of complex fluids from ab initio simulations. This is achieved by combining density functional theory molecular dynamics simulations with polarization theory. Conductivities are then obtained via a Green-Kubo formula using time-dependent effective charges of electronically screened ions. The method is applied to two different phases of warm dense water. We observe large fluctuations in the effective charges; protons can transport effective charges greater than +e for ultrashort time scales. Furthermore, we compare our results with a simpler model of ionic conductivity in water that is based on diffusion coefficients. Our approach can be directly applied to study ionic conductivities of electronically insulating materials of arbitrary composition, e.g., complex molecular mixtures under such extreme conditions that occur deep inside giant planets.     

Efficient and accurate Car-Parrinello-like approach to Born-Oppenheimer molecular dynamics

We present a new method which combines Car-Parrinello and Born-Oppenheimer molecular dynamics in order to accelerate density functional theory based ab initio simulations. Depending on the system a gain in efficiency of 1 to 2 orders of magnitude has been observed, which allows ab initio molecular dynamics of much larger time and length scales than previously thought feasible. It will be demonstrated that the dynamics is correctly reproduced and that high accuracy can be maintained throughout for systems ranging from insulators to semiconductors and even to metals in condensed phases. This development considerably extends the scope of ab initio simulations.     

Suppression of dynamics and frequency synchronization in coupled slow and fast dynamical systems

We present our study on the emergent states of two interacting nonlinear systems withdiffering dynamical time scales. We find that the inability of the interacting systems tofall in step leads to difference in phase as well as change in amplitude. If the mismatchis small, the systems settle to a frequency synchronized state with constant phasedifference. But as mismatch in time scale increases, the systems have to compromise to astate of no oscillations. We illustrate this for standard nonlinear systems and identifythe regions of quenched dynamics in the parameter plane. The transition curves to thisstate are studied analytically and confirmed by direct numerical simulations. As animportant special case, we revisit the well-known model of coupled ocean-atmosphere systemused in climate studies for the interactive dynamics of a fast oscillating atmosphere andslowly changing ocean. Our study in this context indicates occurrence of multi stableperiodic states and steady states of convection coexisting in the system, with a complexbasin structure.     

Simulation of a critical state without critical slowing down by a renormalization group multi-grid method

We have implemented and tested a method to eliminate critical slowing down from Monte Carlo (and possibly other) simulations of very large systems, even for a “critical” state, where the correlation length of fluctuations is the size of the sample. Static correlation functions on all length scales (down to microscopic!) may thus be obtained with an amount of work asymptotically growing with size only as in conventional simulations of nearly uncorrelated states. In the simulation we use a finite but large set of approximated renormalized coupling constants, which describe very closely the coarse grained variable interactions of the simulated model. As a test bed, the 2D Ising model has been used. The method has the advantage that critical states of other types of systems can be simulated along the same line.     

Dynamic fluctuations in optical bistability

We present results on the time correlation function of a system undergoing absorptive optical bistability. We first use the Zwanzig-Mori formalism to calculate time correlation functions both near marginal stability points and in the coexistence region. Near marginal stability the theory predicts large deviations from a single exponential form of the correlation function. The truncated continued fraction expansion is shown to become inapplicable close to the coexistence point. The difficulties are due to the presence of long time scales, viz. the very large mean first passage times between the two metastable steady states. When these scales are important we show that the memory kernel relaxation is no longer faster than that of a field fluctuation. An increase in the size of the system increases the disparity of the time scales and thus exacerbates the problems of the projection operator formalism as used here following reference [14].We next present an ansatz for the correlation function incorporating the four major time scales important near coexistence, the two single branch relaxation times and the two mean first passage times for transitions between the stable states. This form of the correlation function avoids the difficulties cited in connection with the use of the projection operator method.     

Understanding the enhanced synchronization of delay-coupled networks with fluctuating topology

We study the dynamics of networks with coupling delay, from which the connectivity changes over time. The synchronization properties are shown to depend on the interplay of three time scales: the internal time scale of the dynamics, the coupling delay along the network links and time scale at which the topology changes. Concentrating on a linearized model, we develop an analytical theory for the stability of a synchronized solution. In two limit cases, the system can be reduced to an “effective” topology: in the fast switching approximation, when the network fluctuations are much faster than the internal time scale and the coupling delay, the effective network topology is the arithmetic mean over the different topologies. In the slow network limit, when the network fluctuation time scale is equal to the coupling delay, the effective adjacency matrix is the geometric mean over the adjacency matrices of the different topologies. In the intermediate regime, the system shows a sensitive dependence on the ratio of time scales, and on the specific topologies, reproduced as well by numerical simulations. Our results are shown to describe the synchronization properties of fluctuating networks of delay-coupled chaotic maps.     

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.