An observation on the effect of fluctuations far from equilibrium: The Lotka-Volterra model

Spontaneous fluctuations in the Lotka-Volterra model of chemical reactions are known to grow in an unbounded way when species held in excess are neglected. This result is obtained in a simple way using generalized fluctuation-dissipation principles but appears to be an artifact of ignoring fluctuations in the variables that are held fixed. When fluctuations in the other concentrations are included in the model, the spontaneous fluctuations become bounded.This work was supported by the National Science Foundation through Research Grant No. MPS 74-00483 AO1.     

Generalized nonlinear master equations for local fluctuations: Dimensionality expansions and augmented mean field theory

By application of a projection operator technique we derive a formally exact generalization of the nonlinear mean field master equation introduced recently for the study of local fluctuations in a reacting medium. Our starting point is a phenomenological cell master equation. The results of our theory are applicable to the theory of a fluctuating hydrodynamic reacting system. The mean field equation is placed on a firm theoretical foundation by showing it to be the lowest order approximation in an expansion in the dimensionality of the physical space keeping the product of the number of nearest neighbors (an increasing function of dimensionality) and the typical diffusion coefficient constant. A more accurate nonlinear master equation that allows for the correlation and fluctuations in the environment of a given volume element is derived in the form of an augmented mean field equation.Work supported in part by a grant from the National Science Foundation.     

Generalizations of Quantum Mechanics Induced by Classical Statistical Field Theory

No Heading We show that the Dirac-von Neumann formalism for quantum mechanics can be obtained as an approximation of classical statistical field theory. This approximation is based on the Taylor expansion (up to terms of the second order) of classical physical variables – maps f : Ω → R, where Ω is the infinite-dimensional Hilbert space. The space of classical statistical states consists of Gaussian measures ρ on Ω having zero mean value and dispersion σ²(ρ) ≈ h. This viewpoint to the conventional quantum formalism gives the possibility to create generalized quantum formalisms based on expansions of classical physical variables in the Taylor series up to terms of nth order and considering statistical states ρ having dispersion σ²(ρ) = hⁿ (for n = 2 we obtain the conventional quantum formalism).     

Turbulence investigations during ergodic divertor operation with induced 2/1 tearing mode

Within the last year of TEXTOR operation a major part of the experiments were dedicated to the interaction of the ergodized plasma edge, induced by the dynamic ergodic divertor (DED), with the core plasma. Systematic experiments are performed in the 3/1 configuration of the DED. Depending on , the DED generates a locked 2/1 mode in the plasma at a critical current in the DED coils. Different diagnostics were used to measure the plasma response in the core and edge. The investigations in this paper are focused on the measurement of density fluctuation and the analysis of the coherent-mode structure outside the q = 2 surface using O-mode poloidal correlation reflectometry. A reduction of the quasi-coherent mode amplitude and frequency is observed, caused by the 2/1 mode together with a decrease of the density scale length. Moreover, the deduced poloidal rotation velocity at the q = 3 surface changes from the electron to the ion diamagnetic drift direction with the onset of the 2/1 island. Also a reduction of the density fluctuations is observed as well as a decrease in the poloidal correlation length. From Ar-injection a delayed inward propagation of the emission maximum is observed for different Ar ionization stages when the 2/1 mode is generated.Similar experiments with a slowly rotating DED show that the steepened density gradients are spatially localized and confirm the hypothesis that the 2/1 mode is responsible for the observations.Presented at the Workshop Electric Fields Structures and Relaxation in Edge Plasmas, Nice, France, October 26–27, 2004.     

An experimental study of a turbulent shear layer at a clean and contaminated free-surface

An experimental study was performed to measure the flow properties of a vertically-orientated shear layer in the vicinity of a free-surface. The effect of surface contamination on the near surface flow field was also determined. Digital Particle Image Velocimetry was used to measure instantaneous and averaged velocity, vorticity, and Reynolds stresses. Results show that the presence of surfactants can cause directional shifts of the shear layer, as well as an overall damping of the turbulence in the vicinity of the free-surface, except in the vicinity of a Reynolds ridge where an increase in Reynolds stress was observed.     

Surface diffusion of dysprosium on the W(1 1 1) facet

Diffusion of dysprosium on the (1 1 1) facet of a tungsten micromonocrystal was investigated by means of spectral analysis of field emission current fluctuations. The experimental spectral density functions of the current fluctuations were analysed by using Gesley and Swanson’s theoretical spectral density function, which enables to determine the surface diffusion coefficient D for dysprosium. Derived from the temperature dependence of D, the diffusion activation energy E is presented for some Dy coverages θ_(1 1 1). In the temperature range 400–600 K, the E first drops from 1.25 eV per atom at θ₍₁₁₁₎≈0.25 ML to 0.48 eV per atom at θ₍₁₁₁₎≈1 ML (corresponding to the minimum of the work function of the system), then increases to 1.03 eV per atom at θ₍₁₁₁₎≈1.3 ML. The results are discussed from the aspects of the substrate structure and interaction in the adsorbed layer.     

Persistent currents in a lattice correlated electron ring with a magnetic impurity

The behavior of charge and spin persistent currents in an integrable lattice ring of strongly correlated electrons with a magnetic impurity is exactly studied. Our results manifest that the oscillations of charge and spin persistent currents are similar to the ones, earlier obtained for integrable continuum models with a magnetic impurity. The difference is due to two (instead of one) Fermi velocities of low-lying excitations. The form of oscillations in the ground state is “saw-tooth”-like, generic for any multi-particle coherent one-dimensional models. The integrable magnetic impurity introduces net charge and spin chiralities in the generic integrable lattice system, which determine the initial phase shifts of charge and spin persistent currents. We show that the magnitude of the charge persistent current in the generic Kondo situation does not depend on the parameters of the magnetic impurity, unlike the (magneto)resistivity of transport currents. Received 30 January 2003 / Received in final form 12 March 2003 Published online 11 April 2003 RID="a" ID="a"e-mail: zvyagin@fy.chalmers.se     

Macroscopic Determinism in Noninteracting Systems Using Large Deviation Theory

We consider a general system of n noninteracting identical particles which evolve under a given dynamical law and whose initial microstates are a priori independent. The time evolution of the n-particle average of a bounded function on the particle microstates is then examined in the large-n limit. Using the theory of large deviations, we show that if the initial macroscopic average is constrained to be near a given value, y, then the macroscopic average at time t converges in probability as n to a value _t(y) given explicitly in terms of a canonical expectation. Some general features of the graph of _t(y) versus t are examined, particularly in regard to continuity, symmetry, and convergence.     

Quantum n-Vector Anharmonic Crystal II: Displacement Fluctuations

Based on the 1/n-expansion derived in a previous paper, the displacement fluctuations are analyzed in a quantum n-vector model of anharmonic crystal in the large n regime. It is shown that in the ferroelectric phase the n limit of the local fluctuation field has faster large-distance correlation decay than its Hartree–Fock approximation. Also, the critical exponent of the global displacement fluctuation is strictly smaller there than the Hartree–Fock exponent. In particular, the displacement fluctuations may be normal in the ferroelectric phase in spite of the Hartree–Fock prediction.     

Scalar Domination and Normal Fluctuations in N-Vector Quantum Anharmonic Crystals

A lattice model of N-dimensional quantum anharmonic oscillators with a polynomial anharmonicity and a ferroelectric pair interaction is considered. For arbitrary N , correlation inequalities, showing that the temperature Green functions of this model are dominated by the corresponding Green functions of the scalar (N=1) model, are proven. These inequalities are then used to prove that the fluctuations of displacements of particles remain normal at all temperatures provided the model parameters obey a certain condition. In particular this means that the smallest distance between the energy levels of the corresponding one-dimensional isolated oscillator should be large enough or its mass should be small enough.