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).     

The effect of disorder on the wave propagation in one-dimensional periodic optical systems

The influence of disorder on the transmission through periodic waveguides is studied. Using a canonical form of the transfer matrix, we investigate the dependence of the Lyapunov exponent γ on the frequency ν and magnitude of the disorder σ. It is shown that in the bulk of the bands γ?～?σ², while near the band edges it has order γ?～?σ^2/3. This dependence is illustrated by numerical simulations.     

Stochastic theory of nonlinear rate processes with multiple stationary states

A comparison has been made between the deterministic and stochastic (master equation) formulation of nonlinear chemical rate processes with multiple stationary states. We have shown, via two specific examples of chemical reaction schemes, that the master equations have quasi-stationary state solutions which agree with the various initial condition dependent equilibrium solutions of the deterministic equations. The presence of fluctuations in the stochastic formulation leads to true equilibrium solutions, i.e. solutions which are independent of initial conditions as t → ∞. We show that the stochastic formulation leads to two distinct time scales for relaxation. The mean time for the reaction system to reach the quasi-stationary states from any initial state is of $\text{O}$(N⁰) where N is a measure of the size of the reaction system. The mean time for relaxation from a quasi-stationary state to the true equilibrium state is $\text{O}$(e^N). The results obtained from the stochastic formulation as regards the number and location of the quasi-stationary states are in complete agreement with the deterministic results.     

Upper Bounds on the Critical Temperature for Kac Potentials

We consider an Ising system in two dimensions with a two body ferromagnetic interaction J _γ(x, y) that depends on the Kac scaling parameter γ. We prove that the inverse critical temperature β_cr(γ) is strictly above the mean-field value (equal to 1), namely that there exists C>0 so that for any b<C, β_cr(γ)> 1 + bγ²log γ^?1 for all γ sufficiently small. The temperature shift Cγ²log γ^?1 is to leading orders equal to the covariance of the magnetization fluctuations.     

The coupled coherent and incoherent motion of excitons and its influence on the line shape of optical absorption

We treat the coupled coherent and incoherent motion of Frenkel excitons by a model calculation. The model contains the four parametersa (distance of neighbouring atoms),J (exchange interaction integral), γ_o (describing the strength of the local energy fluctuations) and γ₁ (a measure of the fluctuations of the exchange interaction integral, i.e. nonlocal fluctuations). Calculation of the optical absorption of systems with two differently oriented molecules/unit cells results in the Davydov-splitting given by Δ=8J and the linewidth given by Γ=γ_o+γ₁. From the equation of motion of the density matrix we derive a diffusion equation. The diffusion constant is given by \(D = \frac{{a^2 }}{\hbar }\left( {2\gamma _1 + \frac{{J^2 }}{{\gamma _1 + \Gamma }}} \right)\) . Comparison with experiment yields γ_o=70cm^?1, γ₁=0.1 cm^?1 at room temperature and Γ<1 cm^?1 at 4.2 °K. Using these numerical values and the criterium of Haken and Strobl we derive that at room temperature the exciton motion is incoherent and may be described by a hopping process whereas at low temperature it is coherent.     

Stokes parameters of γ-quanta in the e+ + e− → Z + γ reaction

A general analysis is made of the polarization properties of γ-quanta in the e⁺ + e^? → Z + γ reaction. Besides the standard mechanism of this reaction; which is determined by the eeZ interaction (neutral weak currents), the possible anomalous magnetic moment χ of the Z boson is also taken into account. A linear contribution in χ. to the differential cross section of the e⁺ + e^? → Z + γ process (with unpolarized particles in the initial and final states) leads to CP-odd asymmetry of the angular distribution of γ-quanta relative to the substitution cos Θ→?cos Θ, where Θ is the angle of emission of the γ-quantum relative to the electron. Measurement of this asymmetry with an accuracy of the order of 1% makes it possible to get a “sense” of the contribution of the magnetic moment of a Z boson of the order of 10^?3 GeV^?1.     

First observation of the excited states in the doubly odd nucleus118Cs identified throughγ-recoil coincidences

The previously unknown nucleus¹¹⁸Cs has been identified through γ-γ and γ-recoil coincidences using the GASP γ-spectrometer and Recoil Mass Spectrometer. The level scheme constructed on the base of triple γ coincidences shows a collective structure based on the π^?1g_9/2?νh_11/2 configuration.     

Infrared studies of single crystals of polycaprolactam

Infrared studies of the α-crystalline form of polycaprolactam (nylon 6) have confirmed the assignment of the 1288 and 1210-cm^?1 bands to a unique fold conformation. The γ-crystalline phase has a band at 1212 cm^?1 which overlaps the 1210-cm^?1 fold band in samples containing both α and γ phases. The 1288-cm^?1 band was, therefore, used to monitor regular fold content. No unique fold bands were detected in the γ form. Irregular folds present in solution-grown crystals regularize to the unique fold conformation upon annealing. Crystals which originally exhibit slight differences in regular folding as a result of different crystallization history have similar amounts of regular folds upon annealing at 220°C. Crystals grown from solutions of very dilute concentrations of polymer have different amounts of regular folding. The annealing behavior of crystals prepared from two different solution concentrations reflect the processes of regularization and long period increase.     

Evidence for intruder states in111Rh

Levels in¹¹¹Rh have been investigated via the γ -rays following the β^?-decay of 2.1 s¹¹¹Ru. The Ru activity was produced in the fission of²⁴⁹Cf and separated chemically from the fission product mixture. The emitted γ-rays were studied by γ singles and γ(t) coincidence measurements. Evidence for intruder states in¹¹¹Rh has been obtained. Their properties are discussed and compared with those in the lighter Rh isotopes.     

Changes in the Effective Parameters of Averaged Motion in Nonlinear Systems Subject to Noise

We discuss how the effective parameters characterising averaged motion in nonlinear systems are affected by noise (random fluctuations). In this approach to stochastic dynamics, the stochastic system is replaced by its deterministic equivalent but with noise-dependent parameters. We show that it can help to resolve certain paradoxes and that it has a utility extending far beyond its usual application in passing from the microscopic equations of motion to the macroscopic ones. As illustrative examples, we consider the diode-capacitor circuit, a Brownian ratchet, and a generic stochastic resonance system. In the latter two cases we calculate for the first time their effective parameters of averaged motion as functions of noise intensity. We speculate that many other stochastic problems can be treated in a similar way. PACS: 05.10.Gg, 05.40.-a, 05.40.Jc     

Time distribution of γ-rays from spontaneous fission of 252Cf at short times

The gross time distribution of γ-rays from spontaneous fission of ²⁵²Cf has been measured in the time range 10^?14?10^?10 s after fission for γ-ray energies greater than 0.15 MeV. The measurements have been made by a new method based upon the solid angle aberration. From the measured correlation between half-lives and γ-ray transition energies it is concluded that the transitions are predominantly E2, single-particle transitions at high energies, and mostly vibrational and rotational transitions at lower energies. Some contribution of E1 transitions and M1-E2 mixtures cannot be excluded, however. It was found that about 30% ofthe γ-rays emitted within 12 ns with energies greater than 0.10 MeV, have half-lives shorter than 1 ps and about 52 % half-lives between 1 and 100 ps. The relative yield of γ -rays and γ-ray energy in the time range 10^?14 to 1.2 × 10^?7 s ater fission is given.     

The Random Average Process and Random Walk in a Space-Time Random Environment in One Dimension

We study space-time fluctuations around a characteristic line for a one-dimensional interacting system known as the random average process. The state of this system is a real-valued function on the integers. New values of the function are created by averaging previous values with random weights. The fluctuations analyzed occur on the scale n ^1/4, where n is the ratio of macroscopic and microscopic scales in the system. The limits of the fluctuations are described by a family of Gaussian processes. In cases of known product-form invariant distributions, this limit is a two-parameter process whose time marginals are fractional Brownian motions with Hurst parameter 1/4. Along the way we study the limits of quenched mean processes for a random walk in a space-time random environment. These limits also happen at scale n ^1/4 and are described by certain Gaussian processes that we identify. In particular, when we look at a backward quenched mean process, the limit process is the solution of a stochastic heat equation.     

Schwinger mechanism of electron-positron pair production by the field of optical and X-ray lasers in vacuum

The probability W of e ⁺ e ^?-pair production in vacuum by an intense time-varying electric field created by optical or X-ray laser is calculated. Two characteristic regions γ?1 and γ?1 of adiabaticity parameter γ are considered. With an increase in γ and on passing from monochromatic radiation to a finite laser pulse, the probability W increases sharply (for the same field intensity). The dependence of the probability W and the electron and positron momentum spectrum on the pulse shape is discussed (the dynamic Schwinger effect).     

Effects of Noise on Ecological Invasion Processes: Bacteriophage-Mediated Competition in Bacteria

Pathogen-mediated competition, through which an invasive species carrying and transmitting a pathogen can be a superior competitor to a more vulnerable resident species, is one of the principle driving forces influencing biodiversity in nature. Using an experimental system of bacteriophage-mediated competition in bacterial populations and a deterministic model, we have shown in Joo et al. [Proc. R. Soc. B 273,1843–1848 (2006)] that the competitive advantage conferred by the phage depends only on the relative phage pathology and is independent of the initial phage concentration and other phage and host parameters such as the infection-causing contact rate, the spontaneous and infection-induced lysis rates, and the phage burst size. Here we investigate the effects of stochastic fluctuations on bacterial invasion facilitated by bacteriophage, and examine the validity of the deterministic approach. We use both numerical and analytical methods of stochastic processes to identify the source of noise and assess its magnitude. We show that the conclusions obtained from the deterministic model are robust against stochastic fluctuations, yet deviations become prominently large when the phage are more pathological to the invading bacterial strain.     

Hamiltonian and Brownian systems with long-range interactions: V. Stochastic kinetic equations and theory of fluctuations

We developed a theory of fluctuations for Brownian systems with weak long-range interactions. For these systems, there exists a critical point separating a homogeneous phase from an inhomogeneous phase. Starting from the stochastic Smoluchowski equation governing the evolution of the fluctuating density field of Brownian particles, we determine the expression of the correlation function of the density fluctuations around a spatially homogeneous equilibrium distribution. In the stable regime, we find that the temporal correlation function of the Fourier components of density fluctuations decays exponentially rapidly, with the same rate as the one characterizing the damping of a perturbation governed by the deterministic mean field Smoluchowski equation (without noise). On the other hand, the amplitude of the spatial correlation function in Fourier space diverges at the critical point T=T_c (or at the instability threshold k=k_m) implying that the mean field approximation breaks down close to the critical point, and that the phase transition from the homogeneous phase to the inhomogeneous phase occurs sooner. By contrast, the correlations of the velocity fluctuations remain finite at the critical point (or at the instability threshold). We give explicit examples for the Brownian Mean Field (BMF) model and for Brownian particles interacting via the gravitational potential and via the attractive Yukawa potential. We also introduce a stochastic model of chemotaxis for bacterial populations generalizing the deterministic mean field Keller-Segel model by taking into account fluctuations and memory effects.     

Pion and kaon production in 70 GeV/c K − p interactions

Results are presented on the total and differential cross sections for the production of π⁺, π^?, γ, \(\bar K^0 \) ,K ⁰,K ⁺, andK ^? in theK ^? p interactions at 70 GeV/c. The energy dependence of the various production processes shows in paticular a strong rise of the γ cross section and an increase of the average transverse momentum of the charged pion in the fragmentation regions.     

On Perturbations of Generalized Landau-Lifshitz Dynamics

We consider deterministic and stochastic perturbations of dynamical systems with conservation laws in ℝ³. The Landau-Lifshitz equation for the magnetization dynamics in ferromagnetics is a special case of our system. The averaging principle is a natural tool in such problems. But bifurcations in the set of invariant measures lead to essential modification in classical averaging. The limiting slow motion in this case, in general, is a stochastic process even if pure deterministic perturbations of a deterministic system are considered. The stochasticity is a result of instabilities in the non-perturbed system as well as of existence of ergodic sets of a positive measure. We effectively describe the limiting slow motion.     

Electrical conductivity for Lloyd's disorder model in one dimension

We consider the electrical dc-conductivity for Lloyd's disorder model in one dimension. First we calculate the conductivity within the CPA and the MCPA theory of electronic transport. For all values of the disorder parameter γ, which is the fluctuation width of random site energies, the MCPA leads to a substantial reduction of the conductivity as compared with the CPA-treatment. Secondly we investigate the case of large disorder, γ → ∞, by an asymptotic expansion. It is found that the conductivity vanishes order by order in an expansion in γ^?1 which strongly suggests that it vanishes identically for all γ.     

Winkelkorrelationsmessungen an88Sr

The γγ ande _? ^KL γ directional correlations have been measured for the (898–1836) keV cascade in⁸⁸Sr following the decay of⁸⁸Y. The observed correlation coefficients areA ₂₂(γγ)=?0.0784±0.0042 andA ₂₂(e _? ^KL γ)=0.0102±0.0046. The γγ experiment is consistent with a mixing ratio δ(γ)=0.009±0.005 for the 898 keV transition. Using the result of thee _? ^KL γ experiment the most probable value of the ratio of the penetration matrix element to the normal γ-ray matrix element was determined to be η=0.03±0.30 showing a normal conversion process. This penetration parameter agrees with a hindrance factorH _W(E1)=2.1 · 10^?3 for theE1 transition.     

On Vlasov–Manev Equations. I: Foundations, Properties, and Nonglobal Existence

We consider the classical stellar dynamic (Vlasov) equation with a so-called Manev correction (based on a pair potential γ/r + ε/r ²). For the pure Manev potential γ = 0 we discuss both the continuous case and the N-body problem and show that global solutions will not exist if the initial energy is negative. Certain global solutions can be constructed from local ones by a transformation which is peculiar for the ε/r ² law. Moreover, scaling arguments are used to show that Boltzmann collision terms are meaningful in conjunction with Manev force terms. In an appendix, a formal justification of the Manev correction based on the quasirelativistic Lagrangian formalism for the motion of a particle in a central force field is given.