1+1维Wolf-Villain模型生长表面高度极值统计分布的数值模拟

为全面研究Wolf-Villain(WV)模型生长表面的统计性质,基于极值统计理论,模拟计算1+1维WV模型在饱和生长阶段表面的极大高度分布(maximal-height distribution,MAHD)和极小高度分布(minimal-height distribution,MIHD).结果表明,MAHD和MIHD在不同的系统尺寸下分别有较好的标度规律,这两个分布之间存在不对称性.其中,MAHD遵循-种常见的极值分布,即广义的Fisher-Tippett-Gumbel(FTG)型分布;而MIHD可以用-个修正的Fisher-Tippett-Gumbel(MFTG)型分布来描述.     

Statistics of deep energy states in Coulomb glasses

We study the statistics of local energy minima in the configuration space and the energy relaxation due to activated hopping in a system of interacting electrons in a random environment. The distribution of the local minima is exponential, which is in agreement with extreme value statistics considerations. The relaxation of the system energy shows logarithmic time dependence reflecting the ultrametric structure of the system.     

New class of level statistics in correlated disordered chains

We study the properties of the level statistics of 1D disordered systems with long-range spatial correlations. We find a threshold value in the degree of correlations below which in the limit of large system size the level statistics follows a Poisson distribution (as expected for 1D uncorrelated-disordered systems), and above which the level statistics is described by a new class of distribution functions. At the threshold, we find that with increasing system size, the standard deviation of the function describing the level statistics converges to the standard deviation of the Poissonian distribution as a power law. Above the threshold we find that the level statistics is characterized by different functional forms for different degrees of correlations.     

Global fluctuations and Gumbel statistics

We explain how the statistics of global observables in correlated systems can be related to extreme value problems and to Gumbel statistics. This relationship then naturally leads to the emergence of the generalized Gumbel distribution Ga(x), with a real index a, in the study of global fluctuations. To illustrate these findings, we introduce an exactly solvable nonequilibrium model describing an energy flux on a lattice, with local dissipation, in which the fluctuations of the global energy are precisely described by the generalized Gumbel distribution.     

Extremal Properties for Weakly Correlated Random Variables Arising in Speckle Patterns

Extremal properties of the statistics of speckle pattern are studied in the context of so-called “optically smoothed” light beams of laser-matter interaction. It is shown that the asymptotic statistics of the highest intensity in a speckle pattern, which can be associated with the most intense speckles, follows a Gumbel law, which is in agreement with numerical simulations. It is found that the probability density function of the most intense speckle peaks around the value corresponding to the logarithm of the number of speckles in the considered volume times the average intensity value of the speckle pattern. This result is of great interest for nonlinear processes, like instabilities, where extreme speckles play an important role.     

Universal statistics of the critical depinning force of elastic systems in random media

We study the rescaled probability distribution of the critical depinning force of an elastic system in a random medium. We put in evidence the underlying connection between the critical properties of the depinning transition and the extreme value statistics of correlated variables. The distribution is Gaussian for all periodic systems, while in the case of random manifolds there exists a family of universal functions ranging from the Gaussian to the Gumbel distribution. Both of these scenarios are a priori experimentally accessible in finite, macroscopic, disordered elastic systems.     

Fractional exclusion statistics applied to relativistic nuclear matter

The effect of statistics of the quasiparticles in the nuclear matter at extreme conditions of density and temperature is evaluated in the relativistic mean-field model generalized to the framework of the fractional exclusion statistics (FES). In the model, the nucleons are described as quasiparticles obeying FES and the model parameters were chosen to reproduce the ground state properties of the isospin-symmetric nuclear matter. In this case, the statistics of the quasiparticles is related to the strengths of the nucleon-nucleon interaction mediated by the neutral scalar and vector meson fields. The relevant thermodynamic quantities were calculated as functions of the nucleons density, temperature and fractional exclusion statistics parameter α. It has been shown that at high temperatures and densities the thermodynamics of the system has a strong dependence on the statistics of the particles. The scenario in which the nucleon-nucleon interaction strength is independent of the statistics of particles was also calculated, but it leads in general to unstable thermodynamics.     

Quantum Integrability of 1D Ionic Hubbard Model

The quantum integrability of the 1D ionic Hubbard model (IHM) is established using two independent numerical methods, namely i) energy level spacing statistics and ii) occupation profile of one-particle density matrix (OPDM) eigen-values. Both methods suggest that the 1D IHM is integrable. The calculations of energy level statistics reproduce the known results for the standard Hubbard model. Upon turning on the the ionic term, the energy level spacing distribution of this model continues to obey the Poissonian distribution. Occupation patterns as extracted from OPDM indicate that quasi-particles are sharpened upon increasing the ionic potential. This is evidenced by a larger jump in the occupation number distribution.     

High density matter at RHIC

QCD predicts a phase transition between hadronic matter and a quark-gluon plasma at high energy density. The relativistic heavy ion collider (RHIC) at Brookhaven National Laboratory is a new facility dedicated to the experimental study of matter under extreme conditions. Already the first round of experimental results at RHIC indicated that the conditions to create a new state of matter are indeed reached in the collisions of heavy nuclei. Studies of particle spectra and their correlations at low transverse momenta provide evidence of strong pressure gradients in the highly interacting dense medium and hint that we observe a system in thermal equilibrium. Recent runs with high statistics allow us to explore the regime of hard-scattering processes where the suppression of hadrons at large transverse momentum, and quenching of di-jets are observed thus providing further evidence for extreme high density matter created in collisions at RHIC.     

Extremum statistics in scale-free network models

We investigate the statistics of the most connected node in scale-free networks. For a scale-free network model with homogeneous nodes, we show by means of extensive simulations that the exponential truncation, due to the finite size of the network, of the degree distribution governs the scaling of the extreme values and that the distribution of maxima follows the Gumbel statistics. For a scale-free network model with heterogeneous nodes, we show that scaling no longer holds and that the truncation of the degree distribution no longer controls the maxima distribution.     

The near-extreme density of intraday log-returns

The extreme event statistics plays a very important role in the theory and practice of time series analysis. The reassembly of classical theoretical results is often undermined by non-stationarity and dependence between increments. Furthermore, the convergence to the limit distributions can be slow, requiring a huge amount of records to obtain significant statistics, and thus limiting its practical applications. Focussing, instead, on the closely related density of “near-extremes”–the distance between a record and the maximal value–can render the statistical methods to be more suitable in the practical applications and/or validations of models. We apply this recently proposed method in the empirical validation of an adapted financial market model of the intraday market fluctuations.     

Distribution of extremes in the fluctuations of two-dimensional equilibrium interfaces

We investigate the statistics of the maximal fluctuation of two-dimensional Gaussian interfaces. Its relation to the entropic repulsion between rigid walls and a confined interface is used to derive the average maximal [EQUATION: SEE TEXT]and the asymptotic behavior of the whole distribution for [EQUATION: SEE TEXT] for m finite with N2 and K the interface size and tension, respectively. The standardized form of P(m) does not depend on N or K, but shows a good agreement with Gumbel's first asymptote distribution with a particular noninteger parameter. The effects of the correlations among individual fluctuations on the extreme value statistics are discussed in our findings.     

Distribution of return intervals of extreme events

The distribution of return intervals of extreme events is studied in time series characterized by finite-term correlations with non-exponential decay. Precisely, it has been analyzed the statistics of the return intervals of extreme values of the resistance fluctuations displayed by resistors with granular structure in nonequilibrium stationary states. The resistance fluctuations are calculated by Monte Carlo simulations using a resistor network approach. It has been found that for highly disordered networks, when the auto-correlation function displays a non-exponential and non-power-law decay, the distribution of return intervals of the extreme values is a stretched exponential, with exponent independent of the threshold.     

Directed polymers with tilted columnar disorder and Burgers-like turbulence

The minimal energy variations of a directed polymer with tilted columnar disorder in two dimensions are shown numerically to obey multiscaling at short distances which crosses over to global simple scaling at large distances. The scenario is analogous to that of structure functions in bifractal Burgers turbulence. Some scaling properties are predicted from extreme value statistics. The multiscaling disappears for zero tilt.     

Low-frequency noise controls on-off intermittency of bifurcating systems

A bifurcating system subject to multiplicative noise can display on-off intermittency. Using a canonical example, we investigate the extreme sensitivity of the intermittent behavior to the nature of the noise. Through a perturbative expansion and numerical studies of the probability density function of the unstable mode, we show that intermittency is controlled by the ratio between the departure from onset and the value of the noise spectrum at zero frequency. Reducing the noise spectrum at zero frequency shrinks the intermittency regime drastically. This effect also modifies the distribution of the duration that the system spends in the off phase. Mechanisms and applications to more complex bifurcating systems are discussed.     

1+1维抛射沉积模型内部结构动力学行为的数值研究

采用Kinetic Monte Carlo方法对1+1维抛射沉积(BD)模型内部结构的动力学行为进行了大量的数值模拟研究.分别分析了空洞密度和内部界面的动力学行为.研究表明,空洞密度呈高斯型分布,其平均值首先随生长时间快速增长,然后达到一个与基底尺寸无关的饱和值.除表面宽度,还引入了新的极值统计方法来分析该模型内部界面的动力学行为,分析结果显示,1+1维BD模型内部界面的演化满足标准的Family-Vicsek标度规律,并且属Kardar-Parisi-Zhang方程所描述的普适类.最后对表面宽度和极值统计两种理论方法的有限尺寸效应进行了比较.     

关于p-n合金结中少数载流者的注射理论

本文用一维模型计算了p-n合金结中少数载流者的一般注射理论。这里假设复合率是与注入载流者的密度成正比。首先,我们讨论了大注射和小注射的两种极端情况,这样得到的结果被用作零级近似解来计算p-n结中注入少数载流者的分布情况。用逐步近似的方法我们得到了注射效率和注射强度(即注入少数载流者的密度与原有多数载流者的密度之比)间的解析关系。在同样的基础上也得到了通过结的总电流密度和注射强度间的类似关系。这理论的结果表明;对一个平常的合金结晶体三极管来说,当发射极电流增加时,发射极的注射效率逐渐下降。在很大的注射强度下,注射效率趋近于极限值1/(1+b),其中b是电子迁移率与空穴迁移率之比。对一个具有很低注射效率的p-n合金结来说,在注射电流小的时候,注射效率是正比于通过结的总电流;当往射电流很大时,注射效率趋近于极限值1/(1+b)。理论结果还表明,在小注射情下,通过p-n合金结的总电流是正比于注射强度;而在大注射情况下,它是正比于注射强度的平方。     

Magnetic field dependence of charge density waves in PbTe

Previous work by the authors indicated the possible existence of charge density waves in PbTe in the presence of strong magnetic fields so that the extreme quantum limit conditions prevail. The present work follows the transition as the field is lowered so that successively higher Landau levels become occupied. The transition persists at increasingly lower temperatures, having a maximum value, T_cmax, identifiable with each value, N, of the last (partially) occupied Landau level.