Mesoscopic Fluctuations for the Thinned Circular Unitary Ensemble

In this paper we study the asymptotic behavior of mesoscopic fluctuations for the thinned Circular Unitary Ensemble. The effect of thinning is that the eigenvalues start to decorrelate. The decorrelation is stronger on the larger scales than on the smaller scales. We investigate this behavior by studying mesoscopic linear statistics. There are two regimes depending on the scale parameter and the thinning parameter. In one regime we obtain a CLT of a classical type and in the other regime we retrieve the CLT for CUE. The two regimes are separated by a critical line. On the critical line the limiting fluctuations are no longer Gaussian, but described by infinitely divisible laws. We argue that this transition phenomenon is universal by showing that the same transition and their laws appear for fluctuations of the thinned sine process in a growing box. The proofs are based on a Riemann-Hilbert problem for integrable operators.     

Dynamical behavior of a mesoscopic circuit in phonons bath derived by virtue of the IWOP technique

Taking into account the interactions between electrons and phonons, we study the dynamic behavior of a dissipative mesoscopic circuit for pure initial coherent state of phonon bath modes by virtue of the IWOP technique. It shows that if the bath modes are initially in coherent states, some phenomena like Brownian behavior will appear in mean charge and current of the mesoscopic circuit. The quantum fluctuations of charge and current are constant and irrelevant to the coupled coefficients between electrons and phonons.     

Periodic Structure of Equatorial Envelope Rossby Wave Under Influence of Diabatic Heating

A simple shallow-water model with influence of diabatic heating on a β-plane is applied to investigate the nonlinear equatorial Rossby waves in a shear flow. By the asymptotic method of multiple scales, the cubic nonlinear Schro^edinger (NLS for short) equation with an external heating source is derived for large amplitude equatorial envelope Rossby wave in a shear flow. And then various periodic structures for these equatorial envelope Rossby waves are obtained with the help of Jacob/elliptic functions and elliptic equation. It is shown that phase-locked diabatic heating plays an important role in periodic structures of rational form.     

Probing structural relaxation in complex fluids by critical fluctuations

Complex fluids, such as polymer solutions and blends, colloids, and gels, are of growing interest in fundamental and applied soft-condensed-matter science. A common feature of all such systems is the presence of a mesoscopic structural length scale intermediate between the atomic and macroscopic scales. This mesoscopic structure of complex fluids is often fragile and sensitive to external perturbations. Complex fluids are frequently viscoelastic (showing a combination of viscous and elastic behavior), with their dynamic response depending on the time and length scales. Recently, noninvasive methods to infer the rheological response of complex fluids have gained popularity through the technique of microrheology, where the diffusion of probe spheres in a viscoelastic fluid is monitored with the aid of light scattering or microscopy. Here, we propose an alternative to traditional microrheology that does not require doping of probe particles in the fluid (which can sometimes drastically alter the molecular environment). Instead, our proposed method makes use of the phenomenon of “avoided crossing” between modes associated with the structural relaxation and critical fluctuations that are spontaneously generated in the system.     

Crackling noise in plasticity

Plastic deformation is a paradigmatic problem of multiscale materials modelling with relevant processes ranging from the atomistic scale up to macroscopic scales where deformation is treated by continuum mechanics. Recent experiments, investigating deformation fluctuations under conditions where plastic deformation was expected to occur in a smooth and stable manner, demonstrate that deformation is spatially heterogeneous and temporally intermittent, not only on atomic scales, where spatial heterogeneity is expected, but also on mesoscopic scales where plastic fluctuations involve collective events of widely different amplitudes. Evidence for crackling noise in plastic deformation comes from acoustic emission measurements and from deformation of micron-scale samples both in crystalline and amorphous materials. Here we provide a detailed account of our current understanding of crackling noise in crystal and amorphous plasticity stemming from experiments, computational models and scaling theories. We focus our attention on the scaling properties of plastic strain bursts and their interpretation in terms of non-equilibrium critical phenomena.     

Mesoscopic phase statistics of diffuse ultrasound in dynamic matter

Temporal fluctuations in the phase of waves transmitted through a dynamic, strongly scattering, mesoscopic sample are investigated using ultrasonic waves, and compared with theoretical predictions based on circular Gaussian statistics. The fundamental role of phase in diffusing acoustic wave spectroscopy is revealed, and phase statistics are also shown to provide a sensitive and accurate way to probe scatterer motions at both short and long time scales.     

Moderate point: Balanced entropy and enthalpy contributions in soft matter

Various soft materials share some common features, such as significant entropic effect, large fluctuations, sensitivity to thermodynamic conditions, and mesoscopic characteristic spatial and temporal scales. However, no quantitative definitions have yet been provided for soft matter, and the intrinsic mechanisms leading to their common features are unclear. In this work, from the viewpoint of statistical mechanics, we show that soft matter works in the vicinity of a specific thermodynamic state named moderate point, at which entropy and enthalpy contributions among substates along a certain order parameter are well balanced or have a minimal difference. Around the moderate point, the order parameter fluctuation,the associated response function, and the spatial correlation length maximize, which explains the large fluctuation, the sensitivity to thermodynamic conditions, and mesoscopic spatial and temporal scales of soft matter, respectively. Possible applications to switching chemical bonds or allosteric biomachines determining their best working temperatures are also briefly discussed.     

Large Deviation Principle for Benedicks-Carleson Quadratic Maps

Since the pioneering works of Jakobson and Benedicks &; Carleson and others, it has been known that a positive measure set of quadratic maps admit invariant probability measures absolutely continuous with respect to Lebesgue. These measures allow one to statistically predict the asymptotic fate of Lebesgue almost every initial condition. Estimating fluctuations of empirical distributions before they settle to equilibrium requires a fairly good control over large parts of the phase space. We use the sub-exponential slow recurrence condition of Benedicks &; Carleson to build induced Markov maps of arbitrarily small scale and associated towers, to which the absolutely continuous measures can be lifted. These various lifts together enable us to obtain a control of recurrence that is sufficient to establish a level 2 large deviation principle, for the absolutely continuous measures. This result encompasses dynamics far from equilibrium, and thus significantly extends presently known local large deviations results for quadratic maps.     

Asymptotics of Selberg-like integrals by lattice path counting

We obtain explicit expressions for positive integer moments of the probability density of eigenvalues of the Jacobi and Laguerre random matrix ensembles, in the asymptotic regime of large dimension. These densities are closely related to the Selberg and Selberg-like multidimensional integrals. Our method of solution is combinatorial: it consists in the enumeration of certain classes of lattice paths associated to the solution of recurrence relations.     

Chaotic scattering and transmission fluctuations

We discuss the phenomenon of chaotic scattering and its application in the study of transmission of electrons in mesoscopic devices as well as the transmission of microwaves through junctions. We show that the fact that the ray optics (classical dynamics) is chaotic, implies fluctuations in the observed transmission coefficients, whose statistics is determined by the theory of random matrices. We also show how the classical distribution functions which reflect the chaotic nature of the classical dynamics, determine the dependence of the correlations observed in the fluctuating transmission coefficients on external parameters. The time domain properties of chaotic scattering systems are also examined, and are shown to depend on the chaotic nature of the classical dynamics, together with a wave mechanical enhancement in time reversal invariant systems. Finally, we study the role of absorption and discuss its effects on the transmission fluctuations and their statistics.     

Energy and number of collision fluctuations in inelastic gases

The two-dimensional Inelastic Maxwell Model (IMM) is studied by numerical simulations. It is shown how the inelasticity of collisions together with the fluctuations of the number of collisions undergone by a particle lead to energy fluctuations. These fluctuations are associated to a shrinking of the available phase space. We find the asymptotic scaling of these energy fluctuations and show how they affect the tail of the velocity distribution during long time intervals. We stress that these fluctuations relax like power laws on much slower time scales than the usual exponential relaxations taking place in kinetic theory.     

The structural function of entropy and turbulence scales

Structure functions of sound speed and local entropy in the turbulent atmosphere are analyzed. By long-term measurements in the atmospheric boundary layer the power dependence of these characteristics in the inertial sub-range is significantly diverged from the ??2/3 law??. Behavior of structure functions indicates deviation from the asymptotic Kolmogorov-Obukhov law on scales, which significantly exceed Taylor microscale. The exponent of 2/3 is regarded as the limit value, which can be reached under different synoptic conditions. Analytical expressions for the internal and ??energy?? scales of entropy fluctuations, as well as for relation of these scales with entropy dissipation rate and energy of adiabatic fluctuations are proposed.     

Dissipation coefficients and conductances in mesoscopic systems without time reversal invariance

It is shown that in the presence of a magnetic field a multi-probe generalization of the Landauer formula can be derived from linear response theory. The symmetric and antisymmetric parts of the current with respect to magnetic field reversal are discussed separately to show that the symmetrized conductances obtained by Stone and Szafer for zero magnetic field are the coefficients in the quadratic form which relates the asymptotic values of the potential to the power dissipated outside the mesoscopic sample. A derivation of the reciprocity theorem is given without using Büttiker's version of the Landauer formula.     

Mesoscopic fluctuations of the Josephson current of an S-I-S junction with weak structural disorder

It is shown that in the range of tunneling resonance energies of an S-I-S (superconductor-insulator-superconductor) junction with weak (low impurity concentrations) structural disorder in the I-layer, the average critical current and the magnitude of its mesoscopic fluctuations are determined by tunneling along quantum resonance-percolation trajectories. For a “small” junction situated in a parallel magnetic field at temperature T = 0 conditions for smallness of the mesoscopic fluctuations are obtained and an estimate is made of the range of parameters in which the resonance mechanism for supercurrent propagation predominates.     

Stochastic simulation of variations in the autoignition delay time of premixed methane and air

A mesoscopic stochastic particle model for homogeneous combustion is introduced. The model can be used to investigate the physical fluctuations in a system of coupled chemical reactions with energy (heat) release/consumption. In the mesoscopic model, the size of the homogeneous gas volume is an additional variable, which is eliminated in macroscopic continuum models by the thermodynamic limit N→∞. Thus, continuous homogeneous models are macroscopic models wherein fluctuations are excluded by definition. Fluctuations are known to be of particular importance for systems close to the autoignition limits. The new model is used to investigate the stochastic properties of the autoignition delay time in a homogeneous system with stoichiometric premixed methane and air. Temperature and species concentrations during autoignition of sub-macroscopic volumes, including physically meaningful fluctuations, are presented. It is found that different realizations mainly differ in the time when ignition occurs; besides this the development is similar. The mesoscopic range and the macroscopic limit are identified. Which range a specific system is assigned to is not only a question of the length scale or particle number, but also depends on the complete thermodynamic state. The stochastic algorithm yields the correct results for the macroscopic limit compared to the continuous balance equations. The sensitivity of the results to two different detailed reaction mechanisms (for the same system) is studied and found to be low. We show that when approaching the autoignition limit by decreasing the temperature, the fluctuations in the autoignition delay time increase and an increasing number of realizations will have exceedingly long ignition delay times, meaning they are in practice not autoignitable. With this result the mesoscopic simulations offer an explanation of the transition between autoignitable and non-autoignitable conditions. The calculated distributions were compared with ten repetitions of the same experiment. A mesoscopic distribution that matches the experimental results was found.     

压缩真空态下介观耦合电路的量子涨落及电源对量子涨落的影响

通过对无耗耦合含源介观电路的量子化和哈密顿量的对角化,求出了耦合电路的能谱,研究了压缩真空态下介观电路中电荷、电流的量子涨落和电源对量子涨落的影响。     

Asymptotic Fitness Distribution in the Bak–Sneppen Model of Biological Evolution with Four Species

We suggest a new method to compute the asymptotic fitness distribution in the Bak–Sneppen model of biological evolution. As applications we derive the full asymptotic distribution in the four-species model, and give an explicit linear recurrence relation for a set of coefficients determining the asymptotic distribution in the five-species model.     

Coulomb-induced positive current-current correlations in normal conductors

In the white-noise limit current correlations measured at different contacts of a mesoscopic conductor are negative due to the antisymmetry of the wave function (Pauli principle). We show that current fluctuations at capacitive contacts induced via the long range Coulomb interaction due to charge fluctuations in the mesoscopic sample can be positively correlated. The positive correlations are a consequence of the extension of the wave functions into areas near both contacts. As an example we investigate in detail a quantum point contact in a high magnetic field under conditions in which transport is along an edge state.