Simple Hopping Model Research Articles

Loss of ergodicity in a quantum hopping model of a dense many body system with repulsive interactions

In this work we report on a loss of ergodicity in a simple hopping model, motivated by the Hubbard Hamiltonian, of a many body quantum system at zero temperature, quantized in Euclidean time. We show that this quantum system may lose ergodicity at high densities on a large lattice, as a result of both Pauli exclusion and strong Coulomb repulsion. In particular we study particle hopping susceptibilities and the tendency towards particle localization. It is found that the appearance and existence of quantum phase transitions in this model, in the case of high density and strong Coulomb repulsion, depends on the starting configuration of particle trajectories in the numerical simulation. We argue that this breakdown may be the Euclidean time version of a breakdown of the eigenstate thermalization hypothesis in real time quantization.

Dielectric Relaxation and Non‐Overlapping Small Polaron Tunneling Model Conduction Studies of Ag2‐xNaxZnP2O7 (x = 0, 1, and 2) Materials

AbstractThe Ag2−xNaxZnP2O7 (x = 0, 1, and 2) materials are prepared using the solid–solid method followed by heat treatment. The investigated samples are characterized by combining X‐ray powder diffraction and electrical impedance spectroscopy techniques. The Rietveld refinement of the X‐ray diffraction (XRD) pattern revealed that these Ag2ZnP2O7, AgNaZnP2O7, and Na2ZnP2O7 compounds are indexed in the tetragonal system with the P42/n space group. Their dielectric properties are measured in the frequency and temperature ranges of 200–107 Hz and 419–518 K, respectively. In these compounds, the dielectric relaxation can be described by a Cole–Cole model. The frequency dependence of the conductivity is interpreted in terms of Jonscher's law. For the three compounds, the activation energy for conduction has a different value compared to the activation energy for the relaxation process. This indicates that the conduction in the compound is not predicted by the simple hopping model. Then, the temperature dependence of the power‐law exponent(s) suggests that the non‐overlapping small polaron tunneling model is the dominant transport process in these materials. Moreover, the values of defect states N(EF) and the tunnel distance RW show the electrical performance of the Ag2ZnP2O7 compound.

Concerted Control of Stance and Balance Locomotor Subfunctions—Leg Force as a Conductor

In human locomotion, the complex structure of the human body is controlled such that conceptual models (e.g., the spring-loaded-inverted-pendulum model) can describe the significant features. This suggests that the interplay of the complex control and musculoskeletal systems projects into a low-dimensional space to perform different movements. Such simplification can involve splitting the task into different modular control subproblems (locomotor subfunctions) that can be solved individually. Here, we asked how two locomotor subfunctions, namely stance and balance, could be coordinated to generate repeatable and robust motor commands. We developed a simple neuromechanical hopping model, based on decoupling axial and perpendicular leg forces. For this, bouncing behaviors and trunk posture control can be addressed by a knee extensor muscle and biarticular thigh muscles, respectively. We suggest utilizing the leg force feedback as interplay among environment, body mechanics, and sensory control to synchronize the decoupled subfunctions. We evaluated this approach in push recovery, attenuating ground drop perturbations and by investigating its sensitivity to the reflex gain as the control parameter. Leg force feedback can improve robustness of hopping by generating rhythmic hopping patterns. Such a parsimony model-based control concept could simplify controlling assistive devices, such as exoskeletons and prostheses.

Simple diffusion hopping model with convection.

We present results from a new variant of a diffusion hopping model, the convective diffusive lattice model, to describe the behavior of a particulate flux around bluff obstacles. Particle interactions are constrained to an underlying square lattice where particles are subject to excluded volume conditions. In an extension to previous models, we impose a real continuous velocity field upon the lattice such that particles have an associated velocity vector. We use this velocity field to mediate the position update of the particles through the use of a convective update after which particles also undergo diffusion. We demonstrate the emergence of an expected wake behind a square obstacle which increases in size with increasing object size. For larger objects we observe the presence of recirculation zones marked by the presence of symmetric vortices in qualitative agreement with experiment and previous simulations.

Superexchange Charge Transport in Loaded Metal Organic Frameworks.

In the past, nanoporous metal-organic frameworks (MOFs) have been mostly studied for their huge potential with regard to gas storage and separation. More recently, the discovery that the electrical conductivity of a widely studied, highly insulating MOF, HKUST-1, improves dramatically when loaded with guest molecules has triggered a huge interest in the charge carrier transport properties of MOFs. The observed high conductivity, however, is difficult to reconcile with conventional transport mechanisms: neither simple hopping nor band transport models are consistent with the available experimental data. Here, we combine theoretical results and new experimental data to demonstrate that the observed conductivity can be explained by an extended hopping transport model including virtual hops through localized MOF states or molecular superexchange. Predictions of this model agree well with precise conductivity measurements, where experimental artifacts and the influence of defects are largely avoided by using well-defined samples and the Hg-drop junction approach.

Calculation of Carrier Mobility in Copper Phthalocyanine by Simple Hopping Model

The Monte Carlo approach is used to calculate carrier mobility in molecular copper phthalocyanine (CuPc) with applied electric field in the range of 0.5 to 20 × 103 kV/cm. Density functional theory (DFT) is employed to derive the molecular interaction between neighboring molecules with various applied electric fields. The result of DFT calculation to evaluate transfer integral that used to calculate hopping rate in the range of applied electric fields. The charge transfer rate between adjacent molecules can be estimated by using the Marcus–Levich–Jortner (MLJ) formalism. The charge is assumed to be localized on the donor and then transferred to the acceptor. Tunneling is modeled by including selected vibration modes at the quantum mechanical level. The result of hopping rate is in ordered of 1015 s-1 for hole hopping in direction of applied electric field on the contrary hopping rate in ordered of 1014 s-1. The result of mobility can be calculated in range of 0.44 - 10.0 cm2/Vs decrease as a function of applied electric field that calculated by simple hopping model.

Influence of Interparticle Structure on the Steady-State and Transient Current within Arrays of Thiocyanate-Treated PbS Nanocubes

This paper describes the dependence of the DC conductivity, film charging dynamics, and transient photocurrent dynamics of quasi-two-dimensional arrays of thiocyanate-capped PbS nanocubes (NCs) on the edge length of the NC. Arrays were prepared monolayer-by-monolayer using self-assembly at a liquid–air interface. Across-film conductivity increases with NC size with a dependence consistent with a simple diffusional hopping model. Upon application of a constant source-drain bias, the measured dark current decays exponentially to a nonzero steady-state value as immobile hole traps fill. Illumination with 532-nm light produces a repeatable photoresponse, which also fits to an exponential function. The lifetimes associated with decay of the dark current and growth of the photocurrent both increase with increasing NC size. Comparison of the electrical data with electron microscopy images reveals that this trend is related to the connectivity of the percolation networks within the film, which depends on the inte...

Two-dimensional NMR measurement and point dipole model prediction of paramagnetic shift tensors in solids.

A new two-dimensional Nuclear Magnetic Resonance (NMR) experiment to separate and correlate the first-order quadrupolar and chemical/paramagnetic shift interactions is described. This experiment, which we call the shifting-d echo experiment, allows a more precise determination of tensor principal components values and their relative orientation. It is designed using the recently introduced symmetry pathway concept. A comparison of the shifting-d experiment with earlier proposed methods is presented and experimentally illustrated in the case of (2)H (I = 1) paramagnetic shift and quadrupolar tensors of CuCl2⋅2D2O. The benefits of the shifting-d echo experiment over other methods are a factor of two improvement in sensitivity and the suppression of major artifacts. From the 2D lineshape analysis of the shifting-d spectrum, the (2)H quadrupolar coupling parameters are 〈Cq〉 = 118.1 kHz and 〈ηq〉 = 0.88, and the (2)H paramagnetic shift tensor anisotropy parameters are 〈ζP〉 = - 152.5 ppm and 〈ηP〉 = 0.91. The orientation of the quadrupolar coupling principal axis system (PAS) relative to the paramagnetic shift anisotropy principal axis system is given by (α,β,γ)=(π2,π2,0). Using a simple ligand hopping model, the tensor parameters in the absence of exchange are estimated. On the basis of this analysis, the instantaneous principal components and orientation of the quadrupolar coupling are found to be in excellent agreement with previous measurements. A new point dipole model for predicting the paramagnetic shift tensor is proposed yielding significantly better agreement than previously used models. In the new model, the dipoles are displaced from nuclei at positions associated with high electron density in the singly occupied molecular orbital predicted from ligand field theory.

Isolated large π systems in pyrene–fluorene derivatives for intramolecular through-space interaction in organic semiconductors

In order to give an insight of the special spectra of isolated π systems, a series of pyrene–fluorene derivatives, with conjugated or non-conjugated pyrene groups, were systematically studied. Besides absorption of non-conjugated pyrene itself and main conjugation chain, all the pyrene-non-conjugated large conjugated materials show a characteristic sharp absorption peak at ∼352nm. Through systematical investigation, this special absorption peak was attributed to the intramolecular through-space interaction between the two isolated large π systems. Such interaction could also be defined as π – π hyperconjugation. And from quantum calculation, this intramolecular interaction does shorten the length of single bond. Through systematical research, the condition of this intramolecular through-space interaction is proved to be that the non-conjugated pyrene must have projection on fluorene plane. And then this effect is applied to explain the improved injection ability of the materials by bringing out one simple hopping model.

First-principles study of chlorine atom diffusion on Si(1 1 1)–5 × 5 reconstructed surfaces

Diffusion mechanisms of Cl atom adsorbed on Si(111)–(5×5) reconstructed surfaces are investigated by means of the first-principles density functional calculations. We compare two diffusion models for Cl diffusion; one is simple atom hopping model and the other is SiCl complex diffusion one, which is originally proposed to explain the diffusion process for another halogen, F. The energy barrier for the former model is calculated to be 1.73eV, while that of the latter is 1.34eV. This means that the complex diffusion model is preferred for Cl diffusion, similarly to the F case. It is expected that the enhancement of the diffusion frequency by the additional deposition of Si atoms found for F diffusion would be found even for Cl diffusion.

Herding Effect in Coupled Pedestrian-Pedestrian Interacting Dynamics

A simple particle hopping model is proposed to investigate the interaction of two groups of pedestrians, namely straight walking pedestrians and cross-pedestrians. In the model, the straight walking pedestrians have greater priority walking on a main road, while other pedestrians arrive at the roadside and check to cross. Herding behavior, by which cross-pedestrians communicate with each other and self-organize to compete for common space with their straight walking counterparts, are newly introduced to reflect realistic crossing behavior in a crowed street. The results demonstrate that herding behavior brings adverse consequences to both types of pedestrians as a whole, although the pedestrians adopting prompt herding behavior can benefit. Furthermore, an increased number of crossing points to avoid the inefficiency of the coupled system is also investigated.

Quantitative Analysis of Water Dynamics in and near Proteins

Proteins exist in aqueous solution. Hydration can be viewed as a description of how the protein disturbs the structure and dynamics of water. Water molecules in the vicinity of proteins are generally seen as either external or internal water molecules. Internal water molecules occupy cavities, exchange on a time-scale of 0.1--10 microseconds with bulk water, are almost as conserved as amino acids, and are therefore likely to be important for function. External water molecules tend to be found in protein crevices and are typically not conserved, even between crystal structures of the same protein. We introduce a method to analyze the behavior of water molecules in molecular dynamics (MD) simulations in terms of graphs. The graph encodes a simple hopping model: Nodes in the graph correspond to hydration sites, typically defined from the density in computer simulations or observed water sites in crystal structures. Directed edges correspond to transitions (“hops”) between sites, with transition rates computed from MD simulations. We apply this analysis to the water-filled cavity of intestinal fatty acid binding protein (I-FABP) in its apo and holo (palmitate-bound) state. This demonstrates how ligand binding influences the well-defined set of hydration sites in and around the protein's cavity. The ligand displaces a number of hydration sites but does not affect others close by. The parameters extracted from the network model allow us to model the movement of water molecules with a Markov Chain Monte Carlo model. The graphical construct reproduces the average site occupancy found in the MD simulations and the fluctuations of the occupancy. This approach suggests new types of sampling and analysis that can be applied to extend the range of molecular dynamics models and the role of water in ligand binding.

A multi-scale method for the calculation of charge transfer rates through the Π-stack of DNA: application to DNA dynamics

We describe an ultra-fast, multi-scale method for calculating charge transfer rates through the pi-stack of DNA using a simple charge hopping model in conjunction with the Marcus equation. The calculation of the parameters required as input to the Marcus equation, such as the electronic coupling and the driving force, are calculated with a combination of quantum mechanical methods and conformations sampled from classical molecular dynamics (MD) simulations. The resulting set of time dependent rate equations are then solved stochastically using Monte Carlo (MC) methods. We have applied this model to investigate the importance of thermal fluctuations in DNA conformation over picosecond and nanosecond timescales, and have identified the timescales of most relevance to hole transfer through DNA.

Ion diffusion and mechanical losses in mixed alkali glasses

Based on general theoretical considerations we show that the fraction cV of vacant sites for the mobile ions in glasses should be small in order to understand the peculiar behavior of the internal friction in the mixed alkali effect. Moreover, for small cV, the steep fall of the conductivity in the dilute foreign alkali region can be explained by a trapping of vacancies induced by the minority ions. To demonstrate our general analysis we study a simple hopping model and show that it allows one to recover both the typical behavior of the internal friction (shifts of single and mixed alkali peak positions with the mixing ratio and associated changes in activation energies, changes of peak heights) and the typical behavior of tracer diffusion coefficients (drastic fall of mobility of one type of ion by replacement with a second type of mobile ion and associated changes in activation energies). Reasonable values of model parameters can be estimated from measured data and predictions are made for experiments.

Molecular Motion of Tethered Molecules in Bulk and Surface-Functionalized Materials: A Comparative Study of Confinement

Achieving high degrees of molecular confinement in materials is a difficult synthetic challenge that is critical for understanding supramolecular chemistry on solid surfaces and control of host-guest complexation for selective adsorption and heterogeneous catalysis. In this Article, using 2H MAS NMR spectroscopy of tethered carbamates as a molecular probe, we systematically investigate the degree of steric confinement within three types of materials: two-dimensional silica surface, bulk amorphous microporous silica, and bulk amorphous mesoporous silica. The resulting NMR spectra are described with a simple two-site hopping model for motion and prove that the bulk silica network severely limits the molecular mobility of the immobilized carbamate at room temperature to the same degree as surface-functionalized materials at low-temperatures (approximately 210 K). Raising the temperature of the bulk materials to 413 K still demonstrates the effect of confinement, as manifested in significantly longer characteristic times for the immobilized carbamate relative to surface-functionalized materials at room temperature. The environment surrounding the carbonyl functionality of the immobilized carbamate is investigated using FT-IR spectroscopy, which shows the carbonyl stretching band to be equally shifted for all materials to lower wavenumbers relative to its noninteracting value in carbon tetrachloride solvent. These results suggest that electrostatic interactions between the carbonyl of the immobilized carbamate and silica surface may play an important role in confining the immobilized carbamate and nucleating the formation of a pore wall close to the immobilized carbamate during bulk materials synthesis.

On a Stochastic Theory of Ion Transfer at Intermediate Damping

The stochastic method, which was formulated earlier by Gurevich and Kharkats on the basis of a classic solution of the Fokker-Planck equation in a phase space of coordinates and momenta, is developed to extend it to the case of intermediate damping. In contradistinction to the Gurevich-Kharkats model, the new theory is based on the Fokker-Planck equation in the energy-action coordinates. Analytical expressions for the exchange current and conductance are derived. The expressions are valid in a broad damping regime. As compared with the Gurevich-Kharkats model, the expression for the exchange current contains an additional factor, which depends on the energy losses sustained by the ion upon its collision with the cage of a crystal lattice. An explanation for the isotope effect in the high-temperature protonic conductors is suggested. It is demonstrated that the friction coefficient for these solid electrolytes may correspond to the underdamped-to-intermediate-damping regime. This fact makes it possible to put forth an explanation for the existing contradictions between their properties and simple hopping models, which ignore the interaction of ions with the crystal lattice.

Driven steady states: rules for transition rates

It is well known that transition rates in a canonical ensemble should respect the principle of detailed balance. What are the equivalent constraints that apply in non-equilibrium steady states, implied by maximization of information-entropy? The exact theorem for the non-equilibrium rates yields a substantial amount of non-trivial physics, illustrated in some examples including new results for a simple stochastic hopping model. Some of the implications for shear-controlled phase transitions are discussed.

High temperature proton NMR study of yttrium doped barium cerates

The mobility of protons in BaCe1−xYxO3−δ perovskite (x=0.01 to 0.10) was investigated by high temperature 1H NMR spin-lattice relaxation time (T1) and ac conductivity measurements. The temperature variation of T1 was obtained from room temperature to 1073 K. The absolute magnitude of T1 shows a complex dependence on doping concentration. However, the shape of the temperature dependence of T1 was independent of the doping concentration, suggesting the absence of major differences of the proton hopping mechanism on doping level of this material. The measured conductivity was well reproduced by a simple hopping model using correlation times of proton migration and proton concentrations estimated from the NMR measurement.

CONGESTION AND CENTRALITY IN TRAFFIC FLOW ON COMPLEX NETWORKS

The central points of communication network flow have often been identified using graph theoretical centrality measures. In real networks, the state of traffic density arises from an interplay between the dynamics of the flow and the underlying network structure. In this work we investigate the relationship between centrality measures and the density of traffic for some simple particle hopping models on networks with emerging scale-free degree distributions. We also study how the speed of the dynamics are affected by the underlying network structure. Among other conclusions, we find that, even at low traffic densities, the dynamical measure of traffic density (the occupation ratio) has a non-trivial dependence on the static centrality (quantified by "betweenness centrality"), where non-central vertices get a comparatively large portion of the traffic.

Charge Hopping in Molecular Wires as a Sequence of Electron-Transfer Reactions

Charge transport in molecular wires is investigated theoretically within the framework of a simple hopping model. The model suggests that each elementary hopping step can be treated as an electron-transfer reaction between ionic and neutral states of π-conjugated structural units coupled through σ-bonded spacers. Within this mechanistic picture, the ability of wire to transport a charge depends crucially on the internal reorganization energy, λ. Using unrestricted Hartree−Fock and density functional theory methods, we evaluate λ for benzene, 3-methylbiphenyl, 2,6-dimethyl-1-phenyl-pyridinium (DMPP), and 4-(p-suflhydrylphenylpyridinium-1‘-yl)-2,6-dimethylpyridinium, selected as representative examples of structures used for chemical attachment to σ-bonded structural spacers in real molecular wires. The results are exploited to estimate the upper and lower limits of hole and electron mobility in wires that consist of aromatic ring units linked to the antipodal bridgeheads of σ-bonded molecular “cages”, bicy...