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.     

Atomistic origin of urbach tails in amorphous silicon

Exponential band edges have been observed in a variety of materials, both crystalline and amorphous. In this Letter, we infer the structural origins of these tails in amorphous and defective crystalline Si by direct calculation with current ab initio methods. We find that exponential tails appear in relaxed models of diamond silicon with suitable extended defects that emerge from relaxing point defects. In amorphous silicon (a-Si), we find that structural filaments of short bonds and long bonds exist in the network, and that the tail states near the extreme edges of both band tails are also filamentary, with much localization on the structural filaments. We connect the existence of both filament systems to structural relaxation in the presence of defects and of topological disorder.     

A Langevin approach to the Log–Gauss–Pareto composite statistical structure

The distribution of wealth in human populations displays a Log–Gauss–Pareto composite statistical structure: its density is Log–Gauss in its central body, and follows power-law decay in its tails. This composite statistical structure is further observed in other complex systems, and on a logarithmic scale it displays a Gauss-Exponential structure: its density is Gauss in its central body, and follows exponential decay in its tails. In this paper we establish an equilibrium Langevin explanation for this statistical phenomenon, and show that: (i) the stationary distributions of Langevin dynamics with sigmoidal force functions display a Gauss-Exponential composite statistical structure; (ii) the stationary distributions of geometric Langevin dynamics with sigmoidal force functions display a Log–Gauss–Pareto composite statistical structure. This equilibrium Langevin explanation is universal — as it is invariant with respect to the specific details of the sigmoidal force functions applied, and as it is invariant with respect to the specific statistics of the underlying noise.     

Scaling Properties of Field-Induced Superdiffusion in Continuous Time Random Walks

We consider a broad class of Continuous Time Random Walks (CTRW) with large fluctuations effects in space and time distributions: a random walk with trapping, describing subdiffusion in disordered and glassy materials, and a Lévy walk process, often used to model superdiffusive effects in inhomogeneous materials. We derive the scaling form of the probability distributions and the asymptotic properties of all its moments in the presence of a field by two powerful techniques, based on matching conditions and on the estimate of the contribution of rare events to power-law tails in a field.     

Hydrodynamic interactions in the structural fluctuation of a ternary amphiphilic system C12E5/water/ n-octane

Dynamical fluctuations of microemulsion and lamellar structures in a ternary amphiphilic system C₁₂E ₅/water/n-octane are studied by means of neutron spin echo spectrometry. The decay rate of the time correlation of the concentration was analyzed in terms of a theory (M. Nonomura, T. Ohta, J. Chem. Phys. 110, 7516 (1999)), in which both van Hove and hydrodynamic interactions are considered. The result shows that the time correlation function is expressed mostly by a single exponential determined exclusively by hydrodynamic interactions. Received 1 December 1999 and Received in final form 12 March 2001     

Stress relaxation in crumpled surfaces

The stress relaxation in crumpled surfaces maintained at a fixed compressive strain is investigated. The experiments indicate a slow relaxation of the mechanical stress in these non-equilibrium disordered systems. The experimental data indicate an anomalous stretched exponential decay with exponent β=0.28±0.03 along six decades in the rescaled variable t/τ, for a wide interval of strain. The results are compared with the similar behaviour of glassy materials, among others.     

Visible and near-infrared excited-state dynamics of single-walled carbon nanotubes

Excited-state lifetimes of isolated single-walled semiconducting carbon nanotubes (SWNTs) have been measured for the first time; these excited states, observed over the 400- to 1800-nm spectral domain, possess lifetimes that range from several ps to more than 100 ps. Sub-ps to ps decay components are assigned to relaxation in SWNT bundles. Interrogation of the samples with different SWNT mean diameters further confirms the dependence of the excited-state lifetime on roll-up vector. The ratio of fast and slow decaying component contributions in the first van Hove band can be viewed as a measure of the bundle content. PACS 78.67.Ch; 78.47.+p; 61.46.+w; 73.22.-f     

非晶态物质原子局域连接度与弛豫动力学

非晶态物质的本质及形成过程是凝聚态物理领域最困难也是最有趣的问题之一.非晶形成过程在原子结构上不会衍生出人们在传统晶体结构里所熟悉的长程有序性,因此对于此类在自然界中广泛存在的物质形态,至今还没有有效的实验表征手段和理论研究方法.非晶态物质的原子结构及其构效关系的研究是凝聚态物理和材料科学等众多研究领域所关注的热点问题之一.随着对非晶态物质物性研究的深入,人们逐渐意识到非晶态物质中原子中程序对系统性质的重要影响,建立以中程序为基础的结构-动力学关系对于理解玻璃及玻璃转变的本质起着重要的作用.本文简要综述了基于图论提出的原子局域连接度这一新的结构序参量在液体和玻璃的结构及构效关系研究中的应用.新的结构序参量从过去侧重于关注局域原子团簇的种类和分布,转移到更加关注某一类具有特殊对称性的原子的空间连接情况,即更多地尝试从原子中程序的角度来建立非晶态物质中的构效关系.新的研究结果表明,局域连接度可与非晶态物质中原子的短时或长时动力学行为、输运方式、以及振动模态等一系列物理性质建立联系.     

Analytical and Numerical Studies of the One-Dimensional Spin Facilitated Kinetic Ising Model

The one-dimensional spin facilitated kinetic Ising model is studied analytically using the master equation and by simulations. The local state of the spins (corresponding to mobile and immobile cells) can change depending on the state of the neighbored spins, which reflects the high cooperativity inherent in glassy materials. The short-time behavior is analyzed using a Fock space representation for the master equation. The hierarchy of evolution equations for the averaged spin state and the time dependence of the spin autocorrelation function are calculated with different methods (mean-field theory, expansion in powers of the time, partial summation) and compared with numerical simulations. The long-time behavior can be obtained by mapping the one-dimensional spin facilitated kinetic Ising model onto a one-dimensional diffusion model containing birth and death processes. The resulting master equation is solved by van Kampen's size expansion, which leads to a Langevin equation with Gaussian noise. The predicted autocorrelation function and the global memory offer in the long-time limit a screened algebraic decay and a stretched exponential decay, respectively, consistent with numerical simulations.     

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.     

Measurement of the nuclear spin diffusion coefficient in organic glasses doped with paramagnetic centers: Orthoterphenyl and polymeric glasses

We have recently developed a method of studying spin diffusion coefficients by doping the materials with paramagnetic centers and measuring the nuclear relaxation in a tilted rotating frame. Using this method, we measure here the spin diffusion coefficient of orthoterphenyl, a molecular organic glass, and of three polymer glasses: poly(4-vinylpyridine), poly(vinylacetate) and poly(methyl methacrylate). We explore a possible dependence of the measured orthoterphenyl spin diffusion coefficient on the electronic relaxation time and concentration of the paramagnetic centers. We conclude that the experiments can be performed at higher concentrations than previously thought. We also show that our method applies to polymers in the glassy state if one works at sufficiently small tilt angle, in spite of a short value ofT _1ρ. We had anticipated that the distribution of proton pairs in these materials precludes the standard dependence of the spin diffusion coefficient on the proton density and free induction decay characteristic decay time. Our results fully confirm such expectation.     

Anomalous NMR relaxation in cartilage matrix components and native cartilage: fractional-order models

We present a fractional-order extension of the Bloch equations to describe anomalous NMR relaxation phenomena (T(1) and T(2)). The model has solutions in the form of Mittag-Leffler and stretched exponential functions that generalize conventional exponential relaxation. Such functions have been shown by others to be useful for describing dielectric and viscoelastic relaxation in complex, heterogeneous materials. Here, we apply these fractional-order T(1) and T(2) relaxation models to experiments performed at 9.4 and 11.7 Tesla on type I collagen gels, chondroitin sulfate mixtures, and to bovine nasal cartilage (BNC), a largely isotropic and homogeneous form of cartilage. The results show that the fractional-order analysis captures important features of NMR relaxation that are typically described by multi-exponential decay models. We find that the T(2) relaxation of BNC can be described in a unique way by a single fractional-order parameter (α), in contrast to the lack of uniqueness of multi-exponential fits in the realistic setting of a finite signal-to-noise ratio. No anomalous behavior of T(1) was observed in BNC. In the single-component gels, for T(2) measurements, increasing the concentration of the largest components of cartilage matrix, collagen and chondroitin sulfate, results in a decrease in α, reflecting a more restricted aqueous environment. The quality of the curve fits obtained using Mittag-Leffler and stretched exponential functions are in some cases superior to those obtained using mono- and bi-exponential models. In both gels and BNC, α appears to account for micro-structural complexity in the setting of an altered distribution of relaxation times. This work suggests the utility of fractional-order models to describe T(2) NMR relaxation processes in biological tissues.     

Heterogeneous relaxation patterns in supercooled liquids studied by solvation dynamics

We have measured the solvation dynamics of a dipolar supercooled liquid near its glass transition in a temperature range in which the average structural relaxation time varies more than four orders of magnitude. The analysis of the time dependent average emission energy and the inhomogeneous linewidth of the S0<--T1(0-0) transition reveals that the orientation correlation decay pattern intrinsic in each relaxing unit is associated with a stretching exponent beta(intr)=1.00+/-0.08 in the entire range T(g)(KWW) the individual time constants remain correlated to their initial values at t=0.     

Urban road networks — spatial networks with universal geometric features?

Urban road networks have distinct geometric properties that are partially determined by their (quasi-) two-dimensional structure. In this work, we study these properties for 20 of the largest German cities. We find that the small-scale geometry of all examined road networks is extremely similar. The object-size distributions of road segments and the resulting cellular structures are characterised by heavy tails. As a specific feature, a large degree of rectangularity is observed in all networks, with link angle distributions approximately described by stretched exponential functions. We present a rigorous statistical analysis of the main geometric characteristics and discuss their mutual interrelationships. Our results demonstrate the fundamental importance of cost-efficiency constraints for the time evolution of urban road networks.     

Marginal scaling scenario and analytic results for a glassy compaction model

A diffusion-deposition model for glassy dynamics in compacting granular systems is treated by time scaling and by a method that provides the exact asymptotic (long-time) behavior. The results include Vogel-Fulcher dependence of rates on density, inverse logarithmic time decay of densities, exponential distribution of decay times, and broadening of noise spectrum. These are all in broad agreement with experiments. The main characteristics result from a marginal rescaling in time of the control parameter (density); this is argued to be generic for glassy systems.     

Asset returns and volatility clustering in financial time series

An analysis of the stylized facts in financial time series is carried out. We find that, instead of the heavy tails in asset return distributions, the slow decay behaviour in autocorrelation functions of absolute returns is actually directly related to the degree of clustering of large fluctuations within the financial time series. We also introduce an index to quantitatively measure the clustering behaviour of fluctuations in these time series and show that big losses in financial markets usually lump more severely than big gains. We further give examples to demonstrate that comparing to conventional methods, our index enables one to extract more information from the financial time series.     

Multiple scaling regimes in simple aging models

We investigate aging in glassy systems based on a simple model, where a point in configuration space performs thermally activated jumps between the minima of a random energy landscape. The model allows us to show explicitly a subaging behavior and multiple scaling regimes for the correlation function. Both the exponents characterizing the scaling of the different relaxation times with the waiting time and those characterizing the asymptotic decay of the scaling functions are obtained analytically by invoking a "partial equilibrium" concept.     

Optical conductivity of twisted bilayer graphene near the magic angle

We theoretically study the band structure and optical conductivity of twisted bilayer graphene(TBG) near the magic angle considering the effects of lattice relaxation. We show that the optical conductivity spectrum is characterized by a series of peaks associated with the van Hove singularities in the band structure, and the peak energies evolve systematically with the twist angle. Lattice relaxation effects in TBG modify its band structure, especially the flat bands, which leads to significant shifts of the peaks in the optical conductivity. These results demonstrate that spectroscopic features in the optical conductivity can serve as fingerprints for exploring the band structure, band gap, and lattice relaxation in magic-angle TBG as well as identifying its rotation angle.