Hopping Probabilities Research Articles

The KPZ fixed point for discrete time TASEPs

We consider two versions of discrete time totally asymmetric simple exclusion processes (TASEPs) with geometric and Bernoulli hopping probabilities. For the process mixed with these and continuous time dynamics, we obtain a single Fredholm determinant representation for the joint distribution function of particle positions with arbitrary initial data. This formula is a generalization of the recent result by Mateski, Quastel and Remenik and allows us to take the KPZ scaling limit. For both the discrete time geometric and Bernoulli TASEPs, we show that the distribution functions converge to the one describing the KPZ fixed point.

IMPACT OF CHROMIUM DOPING ON STRUCTURAL, OPTICAL, MAGNETIC AND ELECTRICAL PROPERTIES OF NANO-COPPER FERRITE

Nanoparticles copper ferrites doped with chromium CuCrxFe2- xO4 (0≤x≤ 0.25) were prepared using sol-gel auto combustion. Analysis of XRD revealed that the samples crystallized in single phase tetragonal CuFe2O4 structure. Results of Rietveld refinement using Full proff program showed that the lattice parameter a increased, lattice parameter c, the unit cell volume and tetragonal distortion decreased with increasing Cr3+ concentration. A cation distribution ensured that a system (CuCrFeO4) is completely inverse and distorted. In addition, crystallite size increased with the increase of Cr3+content.Furthermore, optical energy band gap of the obtained spinel ferrite decreased from 2.441eV to 2.228 eV with the increase of Cr. Results of magnetic properties indicated that the saturation magnetization decreased from 24.1 to18.3 emu/g with Cr increment, due to a lower magnetic moment of Cr3+ ion (3mB) than that of Fe3+ ion (5mB).Coercivity decreases with increasing Cr-concentration can be attributed to the reduction in magnetocrystalline anisotropy (K) where, chromium ferrite has negative magnetocrystalline anisotropy. Squareness ratio decreased continuously with Cr content, which it displayed that the materials exhibited to soft magnetic properties. Dielectric properties were analyzed in frequency range (0.1-7MHz) at different temperatures (50- 150ºC).From electrical measurements, it was found that έ decreased at lower frequency, become nearly constant at higher frequencies for all samples and increased with increasing temperature. έ was found to increase with increasing Cr because the Cr is reducing the hopping probabilities across the grain boundaries. . Also, it was found that activation energy ΔE decreased with increasing Cr concentration.

Rhombic alternative tableaux, assemblees of permutations, and the ASEP

In this paper, we introduce therhombic alternative tableaux, whose weight generating functions providecombinatorial formulae to compute the steady state probabilities of the two-species ASEP. In the ASEP, there aretwo species of particles, oneheavyand onelight, on a one-dimensional finite lattice with open boundaries, and theparametersα,β, andqdescribe the hopping probabilities. The rhombic alternative tableaux are enumerated by theLah numbers, which also enumerate certainassembl ́ees of permutations. We describe a bijection between the rhombicalternative tableaux and these assembl ́ees. We also provide an insertion algorithm that gives a weight generatingfunction for the assemb ́ees. Combined, these results give a bijective proof for the weight generating function for therhombic alternative tableaux.

Charge Carrier Transport Behavior and Dielectric Properties of BaF2:Tb3+ Nanocrystals.

The charge carrier behavior and dielectric properties of BaF2:Tb3+ nanocrystals have been studied by alternating current (AC) impedance spectroscopy. The electron and ion coexist in the transport process. The F− ion’s contribution to the total conduction increases with the doping concentration up to 4% and then decreases. Tb doping leads to the increase of defect quantities and a variation of charge carrier transport paths, which causes the increase of the ion diffusion coefficient and the decreases of bulk and grain boundary resistance. When the Tb-doped concentration is higher than 4%, the effect of deformation potential scattering variation on the transport property is dominant, which results in the decrease of the ion diffusion coefficient and increases of bulk and grain boundary resistance. The conduction properties of our BaF2:Tb3+ nanocrystals are compared with previous results that were found for the single crystals of rare earth-doped BaF2. Tb doping causes increases of both the quantity and the probability of carrier hopping, and it finally leads to increases of BaF2 nanocrystals’ permittivity in the low frequency region.

Dependence of the transportation time on the sequence in which particles with different hopping probabilities enter a lattice.

Smooth transportation has drawn the attention of many researchers and practitioners in several fields. In the present study, we propose a modified model of a totally asymmetric simple exclusion process (TASEP), which includes multispecies of particles and takes into account the sequence in which the particles enter a lattice. We investigate the dependence of the transportation time on this "entering sequence" and show that, for a given collection of particles, group sequence in some cases minimizes the transportation time better than a random sequence. We also introduce the "sorting cost" necessary to transform a random sequence into a group sequence and show that when this is included a random sequence can become advantageous in some conditions. We obtain these results not only from numerical simulations but also by theoretical analyses that generalize the simulation results for some special cases.

Micromagnetic Study of Edge-Damage Effects in Perpendicular CoFeB/MgO Magnetic Tunnel Junction

Micromagnetic simulation was used to investigate the effects of edge damage in a perpendicular magnetic tunnel junction (MTJ) on thermal stability factor ( $\Delta$ ) and spin transfer torque switching behavior at 300 K. A significant decrease in $\Delta $ was observed in smaller MTJs with severe anisotropy field ( $H_{k}$ )-degradation of the damaged region. It was found that $H_{k}$ degradation has a crucial influence on reference layer magnetization, causing “back hopping.” The probability of back hopping is higher for AP to P switching and increases with increasing $H_{k}$ degradation. This back hopping can be suppressed by using a more stable reference layer or reducing the edge damage. In addition, it was shown that if saturation magnetization ( $M_{s}$ ) at edge-damaged region decreased, no back hopping was observed.

Transport in Quantum Multi-barrier Systems as Random Walks on a Lattice

A quantum finite multi-barrier system, with a periodic potential, is considered and exact expressions for its plane wave amplitudes are obtained using the Transfer Matrix method (Colangeli et al. in J Stat Mech Theor Exp 6:P06006, 2015). This quantum model is then associated with a stochastic process of independent random walks on a lattice, by properly relating the wave amplitudes with the hopping probabilities of the particles moving on the lattice and with the injection rates from external particle reservoirs. Analytical and numerical results prove that the stationary density profile of the particle system overlaps with the quantum mass density profile of the stationary Schrödinger equation, when the parameters of the two models are suitably matched. The equivalence between the quantum model and a stochastic particle system would mainly be fruitful in a disordered setup. Indeed, we also show, here, that this connection, analytically proven to hold for periodic barriers, holds even when the width of the barriers and the distance between barriers are randomly chosen.

Application of elements of quantum mechanics in analysing AC conductivity and determining the dimensions of water nanodrops in the composite of cellulose and mineral oil

The paper presents a model of hopping conductivity at direct and alternating current, developed on the basis of the quantum phenomenon of electron tunnelling between neighbouring potential wells. The tunnelling takes place between neutral potential wells, resulting in an electrical dipole and additional thermally activated polarisation. An important parameter of the model is the time of existence of the dipole (relaxation time). After this time, the electron with the probability p can hop to the third well, which causes a direct current flow, or return with the probability (1 − p) to the first well, thus causing the flow of high frequency current. The model shows that for direct or low frequency current, the current density and conductivity do not depend on the frequency. In the high frequency region, the current density does not depend on the frequency either. Low-frequency conductivity is 2p times smaller than high-frequency conductivity. In the transitional region there is a frequency dependence of the current density. A formula was derived for the dependence of the relaxation time on the distance between neighbouring potential wells and temperature. The dependence of the hopping probability on activation energy, potential dipole energy and temperature was determined. A model of hopping conductivity at direct and alternating current was used to analyse the experimental frequency dependence of conductivity and permittivity of the composite of electrotechnical pressboard, mineral oil and water nanoparticles. It was found that there is a high compatibility of the experimental course with the model. It was also found that in the composite of electrotechnical pressboard, mineral oil and water nanodrops there are at least two mechanisms of changes in low frequency and high frequency conductivity. For the low-frequency stage, the value of the probability of p1 ≈ 0.2 and the relaxation time τ1 ≈ 0.02 s. The probability of hops for the high-frequency growth stage is p2 ≈ 0.0005 and the value of relaxation time τ2 ≈ 2 × 10−7 s. The occurrence of two episodes of increase in conductivity is related to the presence in the composite of electrotechnical pressboard, mineral oil and water nanoparticles of differences in distances between neighbouring nanoparticles. For a large number of nanoparticles randomly distributed in the percolation channel, the distribution of the probability of the occurrence of the distance is in a good approximation normal. This means that in the percolation channel there are pairs of neighbouring wells, the distances between which are both much smaller than the average and much larger. A pair of wells, the distance between which is smaller than medium, participates in the conductivity on the high-frequency stage with a short relaxation time. On the other hand, a pair of neighbouring wells for which the distance is greater than average causes a high resistance to DC or low-frequency current flow as well as a higher relaxation time. On the basis of the dependences designated in laboratory tests of low-frequency conductivity (10−4 Hz) from the moisture content, using the elements of quantum mechanics, the dimensions of water nanoparticles in electrotechnical pressboard impregnated with mineral insulating oil were determined. It was found that nanoparticles contain on average about 200 molecules of water, and their diameters are about 2.24 nm. This approach allowed to calculate the dielectric permittivity of cellulose and to determine that water nanoparticles are located inside the cellulose fibres.Graphical abstract

Multi-scale model for the structure of hybrid perovskites: analysis of charge migration in disordered MAPbI3 structures

We have developed a multi-scale model for organic–inorganic hybrid perovskites (HPs) that applies quantum mechanical (QM) calculations of small HP supercell models to large coarse-grained structures. With a mixed quantum–classical hopping model, we have studied the effects of cation disorder on charge mobilities in HPs, which is a key feature to optimize their photovoltaic performance. Our multi-scale model parametrizes the interaction between neighboring methylammonium cations (MA+) in the prototypical HP material, methylammonium lead triiodide (CH3NH3PbI3, or MAPbI3). For the charge mobility analysis with our hopping model, we solved the QM site-to-site hopping probabilities analytically and computed the nearest-neighbor electronic coupling energies from the band structure of MAPbI3 with density-functional theory. We investigated the charge mobility in various MAPbI3 supercell models of ordered and disordered MA+ cations. Our results indicate a structure-dependent mobility, in the range of 50–66 cm2 V−1 s−1, with the highest observed in the ordered tetragonal phase.

Current Enhancement and Bipolar Current Modulation of Top-Gate Transistors Based on Monolayer MoS2 on Three-Layer W xMo1- xS2.

We demonstrated the top-gate transistors composed of monolayer MoS2 grown on three-layer alloys Mo xW1- xS2 prepared by sequential sulfurization of predeposited transition metal films. The elemental mapping of the alloy indicates a uniform distribution of both cations Mo and W in the grown samples. Surprisingly, we find that the drain current of transistors could be enhanced by 2 orders of magnitude as the composition of Mo increases, whereas the gate-controlled current modulation turns bipolar and ultimately vanishes. These features might originate from the formation of in-gap defect states, with modest activation energy for transport and moderate hopping probability for current conduction, or a reduced electronic band gap of the conducting channel because of strain.

Rhombic alternative tableaux and assemblées of permutations

In this paper, we study rhombic alternative tableaux, whose weight generating functions provide combinatorial formulae to compute the steady state probabilities of the two-species ASEP. In the ASEP, there are two species of particles, one heavy and one light, hopping right and left on a one-dimensional finite lattice with open boundaries. Parameters α, β, and q describe the hopping probabilities. The rhombic alternative tableaux are enumerated by the Lah numbers, which also enumerate certain assemblées of permutations. We describe a bijection between the rhombic alternative tableaux and these assemblées. We also provide an insertion algorithm that gives a weight generating function for the assemblées. Combined, these results give a bijective proof for the weight generating function for the rhombic alternative tableaux, which is also the partition function of the two-species ASEP at q=1.

Magnetoreresistance of carbon nanotube-polypyrrole composite yarns

Three types of samples, carbon nanotube yarn and carbon nanotube-polypyrrole composite yarns had been investigated by measurement of the electrical conductivity as a function of temperature and magnetic field. The conductivity was well explained by 3D Mott variable range hopping (VRH) law at T < 100 K. Both positive and negative magnetoresistance (MR) were observed by increasing magnetic field. The MR data were analyzed based a theoretical model. A quadratic positive and negative MR was observed for three samples. It was found that the localization length decreases with applied magnetic field while the density of states increases. The increasing of the density of states induces increasing the number of available energy states for hopping. Thus the electron hopping probability increases in between sites with the shorter distance that results to small the average hopping length.

Role of Proton Diffusion in the Nonexponential Kinetics of Proton-Coupled Electron Transfer from Photoreduced ZnO Nanocrystals.

Experiments have suggested that photoreduced ZnO nanocrystals transfer an electron and a proton to organic radicals through a concerted proton-coupled electron transfer (PCET) mechanism. The kinetics of this process was studied by monitoring the decay of the absorbance that reflects the concentration of electrons in the conduction bands of the nanocrystals. Interestingly, this absorbance exhibited nonexponential decay kinetics that could not be explained by heterogeneities of the nanoparticles or electron content. To determine if proton diffusion from inside the nanocrystal to reactive sites on the surface could lead to such nonexponential kinetics, herein this process is modeled using kinetic Monte Carlo simulations. These simulations provide the survival probability of a proton hopping among bulk, subsurface, and surface sites within the nanocrystal until it reaches a reactive surface site where it transfers to an organic radical. Using activation barriers predominantly obtained from periodic density functional theory, the simulations reproduce the nonexponential decay kinetics. This nonexponential behavior is found to arise from the broad distribution of lifetimes caused by different types of subsurface and surface sites. The longer lifetimes are associated with the proton becoming temporarily trapped in a subsurface site that does not have direct access to a reactive surface site due to capping ligands. These calculations suggest that movement of the protons rather than the electrons dominate the nonexponential kinetics of the PCET reaction. Thus, the impact of both bulk and surface properties of metal-oxide nanoparticles on proton conductivity should be considered when designing heterogeneous catalysts.

Understanding Photoinduced Charge Transfer Dynamics of Single Perylenediimide Dyes in a Polymer Matrix by Bin-Time Dependence of their Fluorescence Blinking Statistics

Fluorescence on–off blinking of single perylenediimide (DMP–PDI) dyes embedded in a disordered matrix of poly(methyl methacrylate) (PMMA) was investigated by single-molecule fluorescence spectroscopy. In particular, we examined the bin-time dependencies of the complementary cumulative distribution functions (cCDF) of the on-time and off-time durations. It appears that intersystem crossing (ISC) within DMP–PDI competes with charge transfer between DMP–PDI and PMMA. The single-molecule and ensemble cCDFs of the on-time and off-time durations (induced by charge transfer) were best described by Weibull functions and log-normal functions, respectively. The dispersive kinetics of the on-time duration were attributed to radical ion pair ISC from triplet charge separation (3CS) state to the corresponding singlet (1CS) state via charge hopping between charge trap sites in PMMA. This process should compete with triplet charge recombination (3CR), which restores the triplet state. On-to-off switching occurs only when 3CS → 1CS ISC overcomes the 3CR process. The resultant Weibull distribution (with A < 1) reflects that the probability of charge hopping rapidly decreases with time. On the other hand, the off-time log-normal kinetics of single-molecules are explained by a Gaussian distribution of activation energies for charge recombination (the so-called Albery model). A simulation study revealed that the ensemble off-time cCDF included power-law kinetics of charge hopping in the polymer matrix.

Non-adiabatic dynamics around a conical intersection with surface-hopping coupled coherent states.

A surface-hopping extension of the coupled coherent states-method [D. Shalashilin and M. Child, Chem. Phys. 304, 103-120 (2004)] for simulating non-adiabatic dynamics with quantum effects of the nuclei is put forward. The time-dependent Schrödinger equation for the motion of the nuclei is solved in a moving basis set. The basis set is guided by classical trajectories, which can hop stochastically between different electronic potential energy surfaces. The non-adiabatic transitions are modelled by a modified version of Tully's fewest switches algorithm. The trajectories consist of Gaussians in the phase space of the nuclei (coherent states) combined with amplitudes for an electronic wave function. The time-dependent matrix elements between different coherent states determine the amplitude of each trajectory in the total multistate wave function; the diagonal matrix elements determine the hopping probabilities and gradients. In this way, both interference effects and non-adiabatic transitions can be described in a very compact fashion, leading to the exact solution if convergence with respect to the number of trajectories is achieved and the potential energy surfaces are known globally. The method is tested on a 2D model for a conical intersection [A. Ferretti, J. Chem. Phys. 104, 5517 (1996)], where a nuclear wavepacket encircles the point of degeneracy between two potential energy surfaces and interferes with itself. These interference effects are absent in classical trajectory-based molecular dynamics but can be fully incorpo rated if trajectories are replaced by surface hopping coupled coherent states.

Analysis of the Trajectory Surface Hopping Method from the Markov State Model Perspective

We analyze the applicability of the seminal fewest switches surface hopping (FSSH) method of Tully to modeling quantum transitions between electronic states that are not coupled directly, in the processes such as Auger recombination. We address the known deficiency of the method to describe such transitions by introducing an alternative definition for the surface hopping probabilities, as derived from the Markov state model perspective. We show that the resulting transition probabilities simplify to the quantum state populations derived from the time-dependent Schrodinger equation, reducing to the rapidly switching surface hopping approach of Tully and Preston. The resulting surface hopping scheme is simple and appeals to the fundamentals of quantum mechanics. The computational approach is similar to the FSSH method of Tully, yet it leads to a notably different performance. We demonstrate that the method is particularly accurate when applied to superexchange modeling. We further show improved accuracy of ...

Effective ergodicity breaking in an exclusion process with varying system length

Stochastic processes of interacting particles in systems with varying length are relevant e.g. for several biological applications. We try to explore what kind of new physical effects one can expect in such systems. As an example, we extend the exclusive queueing process that can be viewed as a one-dimensional exclusion process with varying length, by introducing Langmuir kinetics. This process can be interpreted as an effective model for a queue that interacts with other queues by allowing incoming and leaving of customers in the bulk. We find surprising indications for breaking of ergodicity in a certain parameter regime, where the asymptotic growth behavior depends on the initial length. We show that a random walk with site-dependent hopping probabilities exhibits qualitatively the same behavior.

Features of the hopping conductivity in gallium and cobalt doped ZnO thin films

The effect of Ga and Co doping on the hopping transport of electrons in ZnO films was studied. All investigated films were deposited on monocrystalline substrates by water assisted metal organic chemical vapour deposition method. Temperature dependencies of the resistivity of all films obeyed the Mott's law at low temperatures. Both positive and negative magnetoresistance were observed in the temperature range of the Mott's law. The values of the localization length obtained from magneto transport data for ZnO and ZnO:Ga films are larger than the effective Bohr radii of a shallow donor state and are independent on the Ga content. These observations point to the localization of electrons in the random potential originating from the structural disorder. In Co doped ZnO films large positive magnetoresistance was observed in low magnetic fields at low temperatures. The value of positive magnetoresistance increases with an increase of Co content and decrease of temperature. Observed magneto transport properties of Co-doped films were interpreted by the decrease of electron hopping probability due to decrease of the density of localized states in magnetic field.

Resource Optimization in Device-to-Device Cellular Systems Using Time-Frequency Hopping

We develop a flexible and accurate framework for device-to-device (D2D) communication in the context of a conventional cellular network, which allows for time-frequency resources to be either shared or orthogonally partitioned between the two networks. Using stochastic geometry, we provide accurate expressions for SINR distributions and average rates, under an assumption of interference randomization via time and/or frequency hopping, for both dedicated and shared spectrum approaches. We obtain analytical results in closed or semi-closed form in high SNR regime, that allow us to easily explore the impact of key parameters (e.g., the load and hopping probabilities) on the network performance. In particular, unlike other models, the expressions we obtain are tractable, i.e., they can be efficiently optimized without extensive simulation. Using these, we optimize the hopping probabilities for the D2D links, i.e., how often they should request a time or frequency slot. This can be viewed as an optimized lower bound to other more sophisticated scheduling schemes. We also investigate the optimal resource partitions between D2D and cellular networks when the dedicated spectrum approach is used.

Phase transition in 2D partially asymmetric simple exclusion process with two species

The dynamics of two species of particles undergoing asymmetric simple exclusion process (ASEP) on the 2D lattice are investigated in this paper. A sharp transition from moving phase to jamming phase was shown under periodic boundary conditions. We have developed a mean field analysis for the moving phase by extending the method of [] and this produces good agreement with simulation results. Two types of jamming phase were observed. In the first type of jamming phase, some particles at the border of the jamming cluster could move back and forth due to the ASEP rule. The first type of jamming phase reduces to the 1D ASEP with a barrier at the boundary of the lattice. We also have analyzed the average hops for the first type of jamming phase by analyzing the 1D ASEP model. The analytical results agree with the simulation results well. Under open boundary conditions, the system exhibits two phases when forward hopping probability q is larger than 0.5. The particles form a wall at the entrance when q is smaller than 0.5. The dependence of the average velocity, the density and the flow rate on the injection probability in the moving phase have also been obtained through mean field analysis.