The Effect of Increasing the Rate of Repetitions of Classical Reactions

Using quantum theory operator method, we discuss the general reversible classical reactions A ₁ + A ₁ + A _r B ₁ + B ₂ + + B _s, where r and s are arbitrary natural positive numbers. We show that if either direction of the reaction is repeated a large number of times N in a finite total times T then in the limit of very large N, keeping T constant, one remains with the initial reacting particles only. We also show that if the reaction evolves through different possible paths of evolution, each of them beginning at the same side of the reaction, proceeds through different intermediate consecutive reactions and ends at the other side, then one may realize any such path by performing in a dense manner the set of reactions along it. the same results are also numerically demonstrated for the specific reversible reaction A + B A + C. We note that similar results have been shown to hold also in the quantum regime.     

Off-shell effects inpp↔πd spin observables

We show that spin observables inppd are fairly sensitive to small changes in the off-shell N helicity amplitudes. This is illustrated at proton laboratory kinetic energies ofT _p=515 MeV andT _p=578 MeV. A reduction of the helicity-flip amplitude by 13% brings the predictions of the relativistic rescattering model much closer to experiment.     

Bimolecular annihilation reactions: Immobile reactants and multipolar interactions

We study the A + B 0 annihilation reaction via multipolar interactions wr^–s (r distance) in one and two dimensions. For equal numbers of immobile A and B particles we present computer simulations and numerical calculations of the decay. We find at large times that ind dimensions the particle concentration follows nt^–d/(2s–d)This work is dedicated to Prof. George H. Weiss.     

Frequency up-conversion He-Ne laser without inversion

A scheme for obtaining up-conversion lasing without inversion in the visible range is proposed using a Doppler-broadened He-Ne mixture as active medium. We consider a cascade scheme (2s₂2p₂1s₃) with a frequency up-conversion ratio of 1.91. The upper transition is inverted and driven by an external field and lasing without inversion occurs at 616.4 nm provided that the collisional decay rates of the 1s₃ and 1s₅ levels overcome a certain threshold. PACS 42.50.Gy; 32.80.Qk; 42.70.Hj     

Effect of nonequilibrium charge screening in A + B → 0 bimolecular reactions in condensed matter

The formalism of many-particle densities developed earlier by the present authors is applied to the study of the cooperative effects in the kinetics of bimolecular A + B 0 reactions between oppositely charged particles (reactants). It is shown that unlike the Debye-Hückel theory in statistical physics, here charge screening has essentially a nonequilibrium character. For the asymmetric mobility of reactants (D _A = 0,D _B 0 the joint spatial distribution of similar immobile reactants A reveals at short distances a singular character associated with their aggregation. The relevant reaction rate does not approach a steady state (as it does in the symmetric case,D _A =D _B, but increases infinitely in time, thus leading to a concentration decay which is quicker than the algebraic law generally accepted in chemical kinetics,n t _–1.     

Muon level crossing resonance in aluminium

Cross relaxation between implanted positive muons and²⁷Al nuclei in Al metal, lightly doped with Cu to impede the muon diffusion, shows weak resonances at 2.3 and 4.0 mT. Assignment of these to polarization transfervia the 1/2 3/2 and 3/2 5/2 transitions of the (J=5/2) spins leads to a quadrupole coupling constante ²qQ/h=1.8(1) MHz,i.e. an electric field gradient on Al nuclei immediately adjacent to the muon siteq=0.048(3) a.u., with a small departure from axial symmetry.     

Fluctuations and correlations in a diffusion-reaction system: Exact hydrodynamics

We present an exact closed formulation of the reversible diffusion-limited coagulation-growth reactions 2A A with irreversible input B A in one spatial dimension. The treatment here accommodates spatial as well as temporal variations in the particle density with a complete account of microscopic fluctuations and correlations. Moreover, spatial and/or temporal variations in the transport and reaction coefficients can be included in the model. A general solution to the reversible process is presented, and we explore the phenomenon of wavefront propagation.     

Asymptotic orbits in a free Fermi gas

We consider the time evolution of local observables and physical states in an infinite system of non-interacting Fermi particles. The orbit of an observable in theC*-algebra of the canonical anticommutation relations is proved to be asymptotic to a set of observables consisting of sums of products of elements of grade two and lower with support in a family of separated cells in ³ (alacunary paving of ³) under time evolution. A space-factorization (clustering) property for primary, even, locally Fock states is established. A class of such states whose space-correlations decay as (logd)^–(1+a) witha positive andd the (space-) separation is, then, proved to be time-asymptotic to their associated quasi-free states.     

Force Relaxation in the q-Model for Granular Media

We study the relaxation of force distributions in the q-model, assuming a uniform q-distribution. We show that diffusion of correlations makes this relaxation very slow. On a d-dimensional lattice, the asymptotic state is approached as l ^(1–d)/2, where l is the number of layers from the top. Furthermore, we derive asymptotic modes of decay, along which an arbitrary short-range correlated initial distribution will decay towards the stationary state.     

Erratum: Renormalization group study of the A+B→Φ diffusion-limited reaction

A recent argument of Oerding shows that our calculation of the quantity , which determines the amplitude of the asymptotic decay of the particle density in 2<d<4, was in error. Instead it is simply given by =n ₀, the initial density, for uncorrelated initial conditions.     

Distinctive Features of the Absorption Spectra of Titanium and Iron Ions in α‐Al2O3:Ti,Fe Crystals

In the UV and visible radiation regions, the absorption spectra of Al₂O₃:Ti,Fe single crystals grown under oxidizing conditions by the Verneuil method are investigated. A considerable residual absorption in the regions 200–300 and 400–600 nm is revealed, which depends strongly on the conditions of growing (the growth rate and temperature drops) and which is caused by transitions in an impurityvacancy complex with charge transfer (IVC CT) O^2––Ti⁴⁺...Fe³⁺ and by conversion of the state of titanium ions Ti⁴⁺ Ti³⁺. The reversible conversion of the state of titanium ions Ti³⁺ Ti⁴⁺ on bending strain of specimens is established.     

Nonlinear chemical dynamics in low dimensions: An exactly soluble model

Restricting space to low dimensions can cause deviations from the mean-field behavior in certain statistical systems. We investigate, both numerically and analytically, the behavior of the chemical reaction A+2X3X in one and two dimensions. In one dimension, we produce exact results showing that the trimolecular reaction system stabilizes in a nonequilibrium, locally frozen, asymptotic state in which the ratior of A to X particles is a constant number,r=0.38, quite different from the mean-field ratio,r _MF=1. The same trimolecular model, however, reaches the mean-field limit in two dimensions. In contrast, the bimolecular chemical reaction A+X2X is shown to agree with the mean-field predictions in all dimensions. For both models, we show that the adoption of certain types of transition rules in the laws of evolution can lead to oscillatory steady states.     

Upper bound on total cross sections

It is shown, under certain assumptions, that if the Nth derivative of the absorptive part of an elastic scattering amplitude exists in the interval t ₁t0, then, the total cross section has the asymptotic upper bound      

Exactly Solvable Model of Reactions on a Random Catalytic Chain

In this paper we study a catalytically-activated A+A0 reaction taking place on a one-dimensional regular lattice which is brought in contact with a reservoir of A particles. The A particles have a hard-core and undergo continuous exchanges with the reservoir, adsorbing onto the lattice or desorbing back to the reservoir. Some lattice sites possess special, catalytic properties, which induce an immediate reaction between two neighboring A particles as soon as at least one of them lands onto a catalytic site. We consider three situations for the spatial placement of the catalytic sites: regular, annealed random, and quenched random. For all these cases we derive exact results for the partition function, and the disorder-averaged pressure per lattice site. We also present exact asymptotic results for the particles' mean density and the system's compressibility. The model studied here furnishes another example of a 1D Ising-type system with random multisite interactions which admits an exact solution.     

The long-time behavior of initially separated A+B→0 reaction-diffusion systems with arbitrary diffusion constants

We examine the long-time behavior of A+B0 reaction-diffusion systems with initially segregated species A and B. All of our analysis is carried out for arbitrary (positive) values of the diffusion constantsD _A andD _B and initial concentrationsa ₀ andb ₀ of A's and B's. We divide the domain of the partial differential equations describing the problem into several regions in which they can be reduced to simpler, solvable equations, and we merge the solutions. Thus we derive general formulas for the concentration profiles outside the reaction zone, the location of the reaction zone center, and the total reaction rate. An asymptotic condition for the reaction front to be stationary is also derived. The properties of the reaction layer are studied in the mean-field approximation, and we show that not only the scaling exponents, but also the scaling functions are independent ofD _A,D _B,a ₀ andb ₀.     

Mixed analytic-numerical solutions for a simple radiating system

A procedure is presented for dealing with fast radiating systems. It employs a method of matching a numerical solution in the source region to an analytic solution in the outer region. As a test of its effectiveness it is applied to a simple radiating system composed of a nonrelativistic harmonic oscillator coupled to a spherically symmetric scalar field. The effects of radiation damping on the oscillator are readily calculated and agree with the exact analytic predictions that one can derive. The accuracy of the monopole formula is checked and shown to fail in the fast-motion regime. It is also shown that the asymptotic damping of the system is independent of the initial conditions as long as the total energy is positive and constant. An instability of the system is also discussed.Work supported in part by NSF Grant No. PHY-8503879.     

Asymptotic behavior of densities for two-particle annihilating random walks

Consider the system of particles on ^d where particles are of two types—A andB—and execute simple random walks in continuous time. Particles do not interact with their own type, but when anA-particle meets aB-particle, both disappear, i.e., are annihilated. This system serves as a model for the chemical reactionA+B inert. We analyze the limiting behavior of the densities _A (t) and _B (t) when the initial state is given by homogeneous Poisson random fields. We prove that for equal initial densities _A (0)= _B (0) there is a change in behavior fromd4, where _A (t)= _B (t)C/t ^d /4, tod4, where _A (t)= _B (t)C/tast. For unequal initial densities _A (0)< _B (0), _A (t)e ^–cl ind=1, _A (t)e ^–Ct/logt ind=2, and _A (t)e ^–Ct ind3. The termC depends on the initial densities and changes withd. Techniques are from interacting particle systems. The behavior for this two-particle annihilation process has similarities to those for coalescing random walks (A+AA) and annihilating random walks (A+Ainert). The analysis of the present process is made considerably more difficult by the lack of comparison with an attractive particle system.     

Power law decay of correlations in stationary nonequilibrium lattice gases with conservative dynamics

We report computer simulations and high-temperature approximations of the pair correlation in a stationary nonequilibrium system, a lattice gas subject to a strong uniform driving fieldE. The dynamics of the system is given by hoppings of particles to adjacent empty sites with rates biased for jumps in the direction ofE. We study the anisotropic short-distance behavior as well as the long-distance decay properties of the two-point correlations along the principal axes. The simulations as well as the (approximate) expansion in strongly suggest that the correlations in this system have a power law decay,r ^–D for dimensionsD=2 and 3, even at high temperatures.     

Exact solutions of anisotropic diffusion-limited reactions with coagulation and annihilation

We report exact results for one-dimensional reaction-diffusion modelsA+Ainert,A+AA, andA+Binert, where in the latter case like particles coagulate on encounters and move as clusters. Our study emphasizes anisotropy of hopping rates; no changes in universal properties are found, due to anisotropy, in all three reactions. The method of solution employs mapping onto a model of coagulating positive integer charges. The dynamical rules are synchronous, cellular-automaton type. All the asymptotic large-time results for particle densities are consistent, in the framework of universality, with other model results with different dynamical rules, when available in the literature.     

Random walks in a random field of decaying traps

We study random walks on ^d (d 1) containing traps subject to decay. The initial trap distribution is random. In the course of time, traps decay independently according to a given lifetime distribution. We derive a necessary and sufficient condition under which the walk eventually gets trapped with probability 1. We prove bounds and asymptotic estimates for the survival probability as a function of time and for the average trapping time. These are compared with some well-known results for nondecaying traps.