Long-time tails in a quantum Lorentz gas

The long-time behaviour of the velocity autocorrelation function (VACF) in a quantum Lorentz gas is investigated using both tetradic and double contour methods. The two classes of most divergent diagrams in the double contour analysis, called ladders and stars, are summed explicitly for the case of separable interactions. The ladders lead to the ringsum long-time tail. The stars give rise to a curious $\text{t}{}^{\mathrm{<mtext>?</mtext><mtext>d</mtext><mtext>2</mtext>}}$-tail which is of quantum-mechanical nature. Moreover these diagrams yield an additional contribution to the classical $\text{t}{}^{\mathrm{<mtext>?(</mtext><mtext>d</mtext><mtext>2</mtext><mtext>\; +\; 1)</mtext>}}$-tail which might explain the discrepancy between the observed and predicted long-time tail coefficient. Extending the star diagrams to the class of ladders of stars, the $\text{t}{}^{\mathrm{<mtext>?</mtext><mtext>d</mtext><mtext>2</mtext>}}$-tail is shown to be removed for the two-dimensional case. Quantum corrections to the long time tail coefficient arising from the tetradic ring diagrams are studied in two and three dimensions. A repeated ringsum expression for the VACF has been evaluated numerically for all times to study the cage effect and appearance of the algebraic long-time tail.     

Enhancedt −3/2 long-time tail for the stress-stress time correlation function

Nonequilibrium molecular dynamics is used to calculate the spectrum of shear viscosity for a Lennard-Jones fluid. The calculated zero-frequency shear viscosity agrees well with experimental argon results for the two state points considered. The low-frequency behavior of shear viscosity is dominated by an ^1/2 cusp. Analysis of the form of this cusp reveals that the stress-stress time correlation function exhibits at ^–3/2 long-time tail. It is shown that for the state points studied, the amplitude of this long-time tail is between 12 and 150 times larger than what has been predicted theoretically. If the low-frequency results are truly asymptotic, they imply that the cross and potential contributions to the Kubo-Green integrand for shear viscosity exhibit at ^–3/2 long-time tail. This result contradicts the established theory of such processes.     

Spatial correlation study of internal magnetic fields in magnets by μSR2-technique

It is shown that using position-sensitive detectors in μSR experiments to determine the muon stopping site in a target permits one to study correlation effects in μSR time histograms produced by the decay of muons stopping in the same domain, i.e. to obtain time correlators of μSR histograms of decays from a small region. These correlators contain information on the spatial correlation of magnetic fields in the sample under study. The proposed method (μSR²-technique) allows measuring correlation radii (r _c ) down to 10⁻⁵ cm in a bulk sample. Among interesting physical phenomena occuring overr _c≥3×10⁻⁶ cm are, for instance, long wavelength fluctuations of the order parameter near the phase transition point in ferromagnets and antiferromagnets and magnetic field correlations in magnet domains and spin glasses. One may use this method also on heavy-current accelerators producing pulsed muon beams to investigate the variation in time of spatial correlations in magnets, spin glasses and superconductors.     

Carmeli's Cosmology Fits Data for an Accelerating and Decelerating Universe Without Dark Matter or Dark Energy

A new relation for the density parameter Ω is derived as a function of expansion velocity υ based on Carmeli's cosmology. This density function is used in the luminosity distance relation D _L. A heretofore neglected source luminosity correction factor (1 − (υ/c)²)^−1/2 is now included in D _L. These relations are used to fit type Ia supernovae (SNe Ia) data, giving consistent, well-behaved fits over a broad range of redshift 0.1 < z < 2. The best fit to the data for the local density parameter is Ω_m = 0.0401 ± 0.0199. Because Ω_m is within the baryonic budget there is no need for any dark matter to account for the SNe Ia redshift luminosity data. From this local density it is determined that the redshift where the universe expansion transitions from deceleration to acceleration is z _t = 1.095^+0.264 _−0.155. Because the fitted data covers the range of the predicted transition redshift z _t, there is no need for any dark energy to account for the expansion rate transition. We conclude that the expansion is now accelerating and that the transition from a closed to an open universe occurred about 8.54 Gyr ago.     

A Construction of Blow up Solutions for Co-rotational Wave Maps

The existence of co-rotational finite time blow up solutions to the wave map problem from ${\mathbb{R}^{2+1} \to N}The existence of co-rotational finite time blow up solutions to the wave map problem from \mathbbR²⁺¹ ? N{\mathbb{R}^{2+1} \to N} , where N is a surface of revolution with metric d ρ ² + g(ρ)² dθ², g an entire function, is proven. These are of the form u(t,r)=Q(l(t)t)+R(t,r){u(t,r)=Q(\lambda(t)t)+\mathcal{R}(t,r)} , where Q is a time independent solution of the co-rotational wave map equation −u _tt  + u _rr  + r ⁻¹ u _r  = r ⁻² g(u)g′(u), λ(t) = t ^−1-ν, ν > 1/2 is arbitrary, and R{\mathcal{R}} is a term whose local energy goes to zero as t → 0.     

Quasi-long-range order in the random anisotropy Heisenberg model

The random field and random anisotropy N-vector models are studied with the functional renormalization group in 4−ε dimensions. The random anisotropy Heisenberg (N=3) model has a phase with an infinite correlation length at low temperatures and weak disorder. The correlation function of the magnetization obeys a power law 〈m(r ₁)m(r ₂)〉∼|r ₁−r ₂|^{− 0.62ε}. The magnetic susceptibility diverges at low fields as χ∼H ^−1+0.15ε. In the random field N-vector model the correlation length is finite at arbitrarily weak disorder for any N>3. Pis’ma Zh. éksp. Teor. Fiz. 70, No. 2, 130–135 (25 July 1999) Published in English in the original Russian journal. Edited by Steve Torstveit.     

Collective diffusion in a lattice gas automaton

We report on non-mean-field and ring-kinetic-theory calculations of both the momentum autocorrelation function and the collective diffusion coefficient in a diffusive lattice gas automaton. For both quantities the ring approximation is calculated exactly. A saddle point method yields a leadingt ^–2 and a subleadingt ^–5/2 long-time tail in the momentum autocorrelation function. The ring kinetic corrections to the mean field value of the diffusion coefficient are in good agreement with computer simulations.     

Transport Theory and Collective Modes II: Long-Time Tail and Green-Kubo Formalism

The long-time tail effect (i.e., a non-Markovian effect) in a velocity autocorrelation function for moderately dense classical gases in d-dimensional space is estimated for arbitray n-mode coupling by superposition of the Markov equations for the collective modes which has been introduced through the complex spectral representation of the Liouville operator in the previous paper. Taking into account intermediate nonhydrodynamic modes in a transition between hydrodynamic states, we found slower decay processes in the long-time tail. These new processes lead to a critical dimension at d = 4 as in the renormalization group, that is, higher modes processes lead to slower decay process in the autocorrelation function for d = 4, while they lead to quicker decay process for d > 4. This conclusion clashes with the traditional point of view, which leads to the critical dimension d = 2. These slower processes invalidate the traditional kinetic equations for bare distribution functions obtained by a truncation of the BBGKY hierarchy for d < 4, as well as the Green-Kubo formalism, as there appear contributions of order t^–1, t^–1/2, ... coming from multiple mode-mode couplings even for d = 3.     

Distribution function for large velocities of a two-dimensional gas under shear flow

The high-velocity distribution of a two-dimensional dilute gas of Maxwell molecules under uniform shear flow is studied. First we analyze the shear-rate dependence of the eigenvalues governing the time evolution of the velocity moments derived from the Boltzmann equation. As in the three-dimensional case discussed by us previously, all the moments of degreek⩾4 diverge for shear rates larger than a critical valuea _c ^(k) , which behaves for largek asa _c ^(k) ∼k ⁻¹. This divergence is consistent with an algebraic tail of the formf(V) ∼V ^−4-σ(a), where σ is a decreasing function of the shear rate. This expectation is confirmed by a Monte Carlo simulation of the Boltzmann equation far from equilibrium.     

Excess 1/f noise in systems with an exponentially wide spectrum of resistances and dual universality of the percolation-like noise exponent

The excess 1/f noise in a random lattice with bond resistances r∼exp(−λx), where x is a random variable and λ≪1, is studied theoretically. It is shown that if the correlation function {δr ²}∼r r ^θ+2, then the relative spectral density of the noise in the system is expressed as C _e∼λ^m exp(−λ(1−p _c)), where p _c is the percolation threshold and m=νd (ν is the critical exponent of the correlation length and d is the dimensionality of the problem). It is hypothesized that the exponent m possesses a dual universality: It is independent of 1) the geometry of the lattice and 2) the θ-mechanism responsible for the generation of the local noise. Numerical modeling in a three-dimensional lattice gives m=52.3 for θ=1 and θ=0, in agreement with the hypothesis. Pis’ma Zh. éksp. Teor. Fiz. 63, No. 8, 614–618 (25 April 1996)     

Experimental study of optical gas-dynamic processes of polymeric material ablation by ultrashort laser pulses

Optical gas-dynamic processes occurring in polymeric targets ((CH₂O) _n , (C₂F₄) _n ) exposed to ultrashort laser pulses (τ _0.5 ∼ 45 − 70 fs; λ _I,II,III = 266, 400, 800 nm; and E/S ∼ 0.1 − 40 J/cm² at r ₀ ∼ 20 μm) were studied under normal conditions and in vacuum (p ∼ 10⁻² Pa). The dynamics of the mass flow from the target surface (m′ ∼ 10⁻⁵ − 10⁻⁴ g/J) was studied and the spectral-energy thresholds of laser ablation, the electron density distribution (n _e ∼ 10¹⁴ − 10¹⁸ cm⁻³), the mass-averaged velocity of the material flow from the target surface (∼ 10³ m/s), and the chemical composition and average temperature in the near-surface plasma formation (T ∼ 5000 K) were determined using interference microscopy, emission spectroscopy, and shadowgraphy.     

Long-time tails of the velocity autocorrelation functions for the triangular periodic Lorentz gas

We present numrical results on the velocity autocorrelation function (VACF)C(t)=<ν(t)·ν(0)> for the periodic Lorentz gas on a two-dimensional triangular lattice as a function of the radiusR of the hard disk scatterers on the lattice. Our results for the unbounded horizon case confirm 1/t decay of the VACF for long times (out to 100 times the mean free time between collisions) and provide strong support for the conjecture by Friedman and Martin that the 1/t decay is due to long free paths along which a moving particle does not scatter up to timet. Even after new sets of long free paths become available forR<1/4, we continue to find good agreement between numerical results and an analytically estimated 1/t decay. For the bounded horizon case , our numerical VACFs decay exponentially, although it is difficult to discriminate among pure exponential decay, exponential decay with prefactor, and stretched exponential decay.     

Hypervirial perturbation theory for eigenenergies for two types of atomic potentials

Eigenenergies are calculated for the potentialsV ₁(r)=−(a/r)[1+(1+br)e^−2br ] andV ₂(r)=−(v/r)[1 −λr(1−Z ⁻¹)(1+λr)⁻¹], using renormalized series technique. Accurate results produced here for various eigenstates agree with those available in the literature.     

Long-time tail in velocity correlations in a one-dimensional Rayleigh gas

The markovian Boltzmann equation for a newtonian gas consisting of two kinds of particles (test and host species) is evaluated analytically by means of systematic scaling methods for the one-dimensional system in the Rayleigh limit of heavy test particles. In the spatially uniform situation the velocity autocorrelation function of the test particles obeys a remarkably simple differential-integral equation. Elementary Laplace analysis reveals an exact t^-3 long-time tail.     

Thermal Conductivity for a Momentum Conservative Model

We introduce a model whose thermal conductivity diverges in dimension 1 and 2, while it remains finite in dimension 3. We consider a system of oscillators perturbed by a stochastic dynamics conserving momentum and energy. We compute thermal conductivity via Green-Kubo formula. In the harmonic case we compute the current-current time correlation function, that decay like t ^−d/2 in the unpinned case and like t ^−d/2–1 if an on-site harmonic potential is present. This implies a finite conductivity in d ≥ 3 or in pinned cases, and we compute it explicitly. For general anharmonic strictly convex interactions we prove some upper bounds for the conductivity that behave qualitatively as in the harmonic cases.     

Reacting polymers with highly correlated initial conditions

We propose and theoretically study an experiment designed to measure short-time polymer reaction kinetics in melts or dilute solutions. The photolysis of groups centrally located along chain backbones, one group per chain, creates pairs of spatially highly correlated macroradicals. We calculate time-dependent rate coefficients κ(t) governing their first-order recombination kinetics, which are novel on account of the far-from-equilibrium initial conditions. In dilute solutions (good solvents) reaction kinetics are intrinsically weak, despite the highly reactive radical groups involved. This leads to a generalised mean-field kinetics in which the rate of radical density decay - ∼S(t), where S(t) ∼t ^{- (1 + g/3)} is the equilibrium return probability for 2 reactive groups, given initial contact. Here g≈ 0.27 is the correlation hole exponent for self-avoiding chain ends. For times beyond the longest coil relaxation time τ, - ∼S(t) remains true, but center of gravity coil diffusion takes over with rms displacement of reactive groups x(t) ∼t ^1/2 and S(t) ∼ 1/x ³(t). At the shortest times ( t 10^-6s), recombination is inhibited due to spin selection rules and we find ∼tS(t). In melts, kinetics are intrinsically diffusion-controlled, leading to entirely different rate laws. During the regime limited by spin selection rules, the density of radicals decays linearly, n(0) - n(t) ∼t. At longer times the standard result - ∼d ³(t)/d (for randomly distributed ends) is replaced by ∼d2x ³(t)/d ² for these correlated initial conditions. The long-time behavior, t > τ, has the same scaling form in time as for dilute solutions. Received 18 May 2000     

Determination of low-energy parameters of neutron-proton scattering in the the shape-parameter approximation from present-day experimental data

On the basis of the total cross sections for neutron-proton scattering in the region of laboratory energies below 150 keV, the value of σ₀ = 20.4288(146) b was obtained for the total cross sections for neutron-proton scattering at zero energy. This value is in very good agreement with the experimental cross sections obtained by Houke and Hurst, but it is at odds with Dilg’s experimental cross section. By using the value that we found for σ₀ and the experimental values of the neutron-proton coherent scattering length f, the deuteron binding energy ɛ _t , the deuteron effective radius ρ _t (−ɛ _t , −ɛ _t ), and the total cross section in the region of energies below 5 MeV, the following values were found in the shape-parameter approximation for the low-energy parameters of neutron-proton scattering in the spin-triplet and spin-singlet states: a _t = 5.4114(27) fm, r _0t = 1.7606(35) fm, v _2t = 0.157 fm³, a _s = −23.7154(80) fm, r _0s = 2.706(67) fm, and v _2s = 0.491 fm³.     

Hyperfine interaction of111Cd in antiferromagnetic cobalt oxide

The temperature dependence of the hyperfine field of substitutional¹¹¹Cd in antiferromagnetic CoO has been measured by means of the perturbed angular correlation technique. The Larmor frequency ω_L is found to obey a power law ω_L(t=ω₀ t ^β) up tot _max=0.4 wheret=1−T/T _N is the reduced temperature withT _N=291.2(3) K and β=0.393 (5) the critical exponent. The results are discussed and compared with PAC experiments on¹¹¹Cd in NiO and Ni and with results obtained by other methods.     

Coulomb correlation effects in LaFeAsO: An LDA + DMFT(QMC) study

Effects of Coulomb correlation on the LaFeAsO electronic structure are investigated by the LDA + DMFT(QMC) method (combination of the local density approximation with the dynamic mean-field theory; impurity solver is a quantum Monte Carlo algorithm). The calculation results show that LaFeAsO is in the regime of intermediate correlation strength with a significant part of the spectral density moved from the Fermi energy to the Hubbard bands and far from the edge of the metal-insulator transition. Correlations affect iron d-orbitals differently. The t _2g states (xz, yz and x ² − y ² orbitals) have a higher energy due to crystal field splitting and are nearly half-filled. Their spectral functions have a pseudogap with the Fermi level position on the higher subband slope. The lower energy e _g set (xy and 3z ² − r ² orbitals) have occupancies significantly larger than 1/2 with typically metallic spectral functions. The article is published in the original.     

Brownian motion in a critical fluid; A critical long time tail

The frictioncoefficient of a Brownian particle in a critical fluid was evaluated, taking into account the finite correlation length of density fluctuations. A $\text{t}{}^{\mathrm{<mtext>?3</mtext><mtext>2</mtext>}}$ tail of the Brownian particle velocity autocorrelation function exists close to the critical point whose amplitude is 10²–10³ times the amplitude of the usual long time tail found far from the critical point.