Space-Time Curvature Induced by Quantum Vacuum Fluctuations as an Alternative to Dark Energy

It is shown that quantum vacuum fluctuations give rise to a curvature of space-time of the order appropriate to explain the observed accelerated expansion of the universe. The fact that the fluctuations produce curvature, even if the expectation of the vacuum energy vanishes, is a consequence of the non-linear character of the Einstein equation. A calculation is made, involving plausible hypotheses within quantized gravity, which establishes a relation between the two-point correlation of the vacuum fluctuations and the space-time curvature.     

Manifestation of changes in the morphology of thin island films in fluctuations of the absorption of focused beams

The relation between the morphology of a thin island film with fluctuations of the absorption of a laser beam scanned over the film is described. An expression for the spectrum of absorption fluctuations, which are determined by the statistics of mutual arrangement of islands in the field and of their sizes, is obtained. It is shown that, as films thicken, absorption fluctuations can decrease and their spectrum narrow. Both phenomena are explained by the correlation between the arrangement and island sizes in films.     

Stress-strain fluctuations in non-linear hydrodynamics

Two different formulations of hydrodynamic fluctuations in the non-linear regime have been proposed. One of these involves a stress-strain fluctuation term of multiplicative type, and consequently this formulation was criticized by Fox three years ago. Recently, Saarloos, Bedeaux and Mazur have proposed such a formulation again, and have criticized Fox's original criticism. In the present paper, it is again shown that multiplicative stress-strain fluctuations lead to unphysical divergences, and that Saarloos, Bedeaux and Mazur have failed to observe that a stochastic quantity, x?, may have zero mean, <x?>=0, but a divergent second moment 〈(x?)²〉=∞. In addition, they have failed to note the limitations of time reversal invariance arguments in macroscopic physics, and they have overlooked important distinctions regarding transverse and longitudinal modes in hydrodynamics. These issues are elucidated in this paper.     

Effect of a fluctuating parameter mismatch and the associated time-scales on coupled Rossler oscillators

We study the effect of parameter fluctuations and the resultant multiplicative noise on the synchronization of coupled chaotic systems. We introduce a new quantity, the fluctuation rate ϕ as the number of perturbations occurring to the parameter in unit time. It is shown that ϕ is the most significant quantity that determines the quality of synchronization. It is found that parameter fluctuations with high fluctuation rates do not destroy synchronization, irrespective of the statistical features of the fluctuations. We also present a quasi-analytic explanation to the relation between ϕ and the error in synchrony.      

QUANTUM CORRELATION IN PHOTOREFRACTIVE THREE WAVE MIXING: SEMICLASSICAL APPROACH

Quantum fluctuations of the fields for three-wave mixing in photorefractive media with drift nonlinearity and nonlocal response are investigated, using a semiclassical input-output theory. It is shown that quantum cor relation and anticorrelation among the three modes will change according to the relative intensity ratio and the direction of energy transfer between the signal and reference modes. The fluctuations in the intensity difference of the two signal modes can be reduced below the corresponding shot-noise level.     

On the low-frequency limit of the Schönfeld pulse 1/f law

On the basis of propositions of the common fluctuation theory, peculiarities of small fluctuations in real physical systems with limited sizes are analyzed. It is established that small fluctuations should necessarily be divided into two types of fluctuations: “small” and “very small”. It is shown that the damping process of “small” fluctuations has relaxation character, while the damping process of “very small” fluctuations is of random character, i.e., it represents a random rectangular signal. The probability density of “very small” fluctuations is shown to be Gaussian. The agreement of the obtained results with experimental data acquired from semiconductor-based devices is analyzed. A relation between the generation–recombination noise and phonon number fluctuations in semiconductors is studied. On the basis of this consideration it is shown that the Schönfeld pulse spectrum preserves its well-known 1/f form only in the range of intermediate frequencies; at lower frequencies the spectrum gets saturated. An expression for the low-frequency limit of Schönfeld pulse 1/f law is obtained.     

Relation between quantum and thermal fluctuations

A relation between quantum and thermal fluctuations, called the generalized uncertainty relation, is derived and discussed. It is given in the terminology of thermo field dynamics. The relation enables us to separate the purely thermal fluctuation from the total fluctuation.     

微粗糙圆柱的各向异性散斑特性研究

分析了高斯光束照射微粗糙圆柱在菲涅尔衍射区形成的散斑图像统计特性,给出了强度起伏自相关函数与表面曲率及粗糙程度等参数之间的关系.根据强度起伏自相关函数的离散化定义,实验并计算了圆柱轴向与径向结构有差异情况下的散斑强度起伏相关函数.结果表明,对于C1和C2圆柱沿垂直于圆柱轴向的散斑尺寸变长,强度起伏自相关函数沿平行和垂直于圆柱轴两个方向的波动相差较大;对于C3和C4圆柱两个方向上的散射特性基本相同;测量C1和C3的结果表明,散斑尺寸和形状依赖于圆柱表面的皱褶和圆柱表面曲率两个因素.研究结果对于如柱型管道、轴承等方面的机械制造的质量控制有重要的应用价值.     

Drift dissipative instabilities in hybrid frequency range

Summary The instabilities of electron convection mode in a collisional plasma including electromagnetic effects are investigated. It is found that all the three solutions of the linear-dispersion relation are unstable. It is shown that the ion temperature fluctuations can play a stabilizing role. An application to a typical low-temperature plasma is discussed. The authors of this paper have agreed to not receive the proofs for correction.     

Fluctuations with a 1/f α spectrum in nonequilibrium phase transitions in a spatially distributed system

Statistics of fluctuations in a spatially distributed system describing the interaction of nonequilibrium phase transitions is studied. It is shown that for a certain value of the intensity of external white noise acting on phase transitions, the time and spatial spectra of fluctuations exhibit power dependences S(f) ～ f ^?α and S(k) ～ k ^?γ. The dependence of exponents α and γ on the diffusion coefficient determining the spatial interaction of fluctuations is determined. Extremal low-frequency fluctuations are singled out and the distribution functions of their duration (P(τ) ～ τ^?β) and size (P(s) ～ s^?ν)) are constructed. It is found that exponent α in the time spectral dependence and exponent β in the duration of fluctuations are connected via the relation α + β = 2. Exponents γ and ν in the spatial spectral dependence and in the size distribution function are connected via an analogous relation (γ + ν = 2).     

Time Ordering and Counting Statistics

The basic quantum mechanical relation between fluctuations of transported charge and current correlators is discussed. It is found that, as a rule, the correlators are to be time-ordered in an unusual way. Instances where the difference with the conventional ordering matters are illustrated by means of a simple scattering model. We apply the results to resolve a discrepancy concerning the third cumulant of charge transport across a tunnel junction.     

Dense nuclear matter: Landau Fermi-liquid theory and chiral Lagrangian with scaling

The relation between the effective chiral Lagrangian whose parameters scale according to Brown and Rho scaling (“BR scaling”) and Landau Fermi-liquid theory for hadronic matter is discussed in order to make a basis to describe the fluctuations under the extreme condition relevant to neutron stars. It is suggested that BR scaling gives the background around which the fluctuations are weak. A simple model with BR-scaled parameters is constructed and reproduces the properties of the nuclear ground state at normal nuclear matter density successfully. It shows that the tree level in the model Lagrangian is enough to describe the fluctuations around BR-scaled background. The model Lagrangian is consistent thermodynamically and reproduces relativistic Landau Fermi-liquid properties. Such points are important for dealing with hadronic matter under extreme condition. On the other hand, it is shown that the vector current obtained from the chiral Lagrangian is the same as that obtained from Landau–Migdal approach. We can determine the Landau parameter in terms of BR-scaled parameter. However, these two approaches provide different results, when applied to the axial charge. The numerical difference is small. It shows that the axial response is not included properly in the Landau–Migdal approach.     

Multifractal clustering in compressible flows

A quantitative relationship is found between the multifractal properties of the asymptotic mass distribution in a random dissipative system and the long-time fluctuations of the local stretching rates of the dynamics. It captures analytically the fine aspects of the strongly intermittent clustering of dynamical trajectories. Applied to a simple compressible hydrodynamical model with known stretching-rate statistics, the relation produces a nontrivial spectrum of multifractal dimensions that is confirmed numerically.     

Leptogenesis

I present the theoretical basis for leptogenesis and its implications for the structure of the universe. It is suggested that density fluctuations grow during the transition period and remnants of this effect should be sought in the universe. The relation between theories with Majorana neutrinos and low energy phenomena, including oscillations, advanced considerably during the past two years with a consistent picture developed in several models.     

Time-Dependent Variational Approach to the Phonon Dispersion Relation of the Commensurate Quantum Frenkel-Kontorova Model

The phonon dispersion relation of the commensurate quantum Frenkel-Kontorova model is studied by means of the time-dependent variational approach combined with a Hartree-type many-body trial wavefunction for the particles. The single-particle state is taken to be a frozen Jackiw-Kerman wavefunction. Under the condition of minimum uncertainty, equations of motion for the particle expectation values are derived to obtain the phonon dispersion relation. It is shown that the strength of the substrate potential and the phonon excitation gap are reduced due to the quantum fluctuations in comparison with those of the classical model. We also compare our results with those previously obtained by using the path-integral molecular dynamics.     

On the Spectral Distribution of Equilibrium Radiation and Zero-Point Fluctuations in the Coulomb System

The consideration of equilibrium radiation in plasma-like media shows that the spectral energy distribution of such radiation differs from that of Planck equilibrium radiation. Based on the previously derived relation for the spectral energy density of equilibrium radiation in the system of charged particles, accounting for finite damping in a medium with spatial dispersion, the limiting case of infinitesimal damping dispersion is considered. It was shown that zero-point vacuum fluctuations being a component of the total spectral energy distribution in the medium should be renormalized when using certain models for the transverse plasma permittivity. In this case, renormalized zero-point vacuum fluctuations become dependent on plasma parameters. The possibility of the manifestation of this effect is discussed.     

The Einstein-Smoluchowski promeasure for (quasiparticle) gases

Considering an ideal Bose-Einstein gas composed of quasiparticles (phonons, magnons, rotons, etc.), the object of this paper is the development of a tractable generalization of Einstein's theory of equilibrium fluctuations. It is assumed that the state of the gaseous system may be characterized by the distribution function f(k) which determines the number of quasiparticles with quasimomentum k. It allows one to embark on a program in which the inversion of Boltzmann's relation connecting entropy and probability can be used as an organizing principle for the development of the theory dealing with the equilibrium fluctuations of f(k). In the present approach, Einstein's distribution law in the Gaussian approximation is identified with the equilibrium promeasure μ_ε defined on the suitably chosen, infinite-dimensional Hilbert space H. This promeasure gives the possibility of calculating the fluctuations in the value of f(k) and its moments. Although μ_ε cannot be extended to a measure on H, what one discovers is that, in this case, one obtains a manifestly infinite-dimensional analog of Einstein's theory of equilibrium fluctuations. The generalization of the method to the case of classical and relativistic gases is straightforward.     

Exact scaling relations in relativistic hydrodynamic turbulence

We consider the steady state statistics of turbulence in general classes of dissipative hydrodynamic equations, where the fluctuations are sustained by a random source concentrated at large scales. It is well known that in some particular cases, such as non-relativistic incompressible turbulence, a Kolmogorov-type exact scaling relation for a correlation function holds. We show that all such scaling relations follow from a general relation on the current-density correlation function. The derivation does not require an energy cascade picture and suggests that this traditional interpretation of the Kolmogorov relation for incompressible turbulence may be misleading. Using this we derive exact scaling results for compressible turbulence in relativistic hydrodynamics, which reduce in the slow motion limit to the Kolmogorov relation. We discuss the experimental implications of the results.