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.     

Properties of the asymptotic nA + mB → C reaction-diffusion fronts

We discuss, at the mean-field level, the asymptotic shape of the reaction fronts in the general nA + mB → Creaction-diffusion processes with initially separated reactants, thereby generalizing to arbitrary reaction-order kinetics the work done by Gálfi and Rácz for the case n = m =1. The obtained information allows us to calculate the asymptotic density of Cparticles deposited by the moving reaction front, a quantity that plays an important role in the theories of Liesegang patterns formation. Received 12 April 2000     

Stochastic simulation of the reaction-diffusion systemA+B→inert in integer and fractal dimensions

We present a stochastic simulation of the reaction-diffusion systemA+Binert based upon the algorithm of the minimal process method. In order to overcome the well known problems of this algorithm when selecting a reaction or diffusion event according to its rate contribution we introduce the concept of logarithmic classes which accelerates the algorithm by an order of magnitude. We simulate the systemA+Binert for integer dimensionsd=1,2,3,4 and confirm the predictions of the scaling theory by Kang and Redner. We extend our simulations to fractal structures, namely the Sierpinski carpet, triangle, the Menger sponge and HLA-clusters. Again we find agreement with the scaling theory if the fractal dimensions are defined as the spectral dimension.     

Fluctuation-dominated kinetics in the a+b→0 reaction between immobile particles

We consider the accumulation of immobile particles landing on a one-dimensional lattice and annihilating via the A + B 0 bimolecular reaction. Here we focus on short-range interactions with cutoff. We investigate through computer simulations both the kinetics of the particles' accumulation and also their spatial distribution. The relation between the exponents describing the growth of the particles' concentration and the correlation length of their distribution shows that the kinetics of accumulation is fluctuation-dominated.This work is dedicated to Prof. George H. Weiss.     

Some properties of the Alday–Maldacena minimum

The Alday–Maldacena solution, relevant to the n=4$n=4$ gluon amplitude in N=4$N=4$ SYM at strong coupling, was recently identified as a minimum of the regularized action in the moduli space of solutions of the AdS₅${\mathit{AdS}}_5$σ  -model equations of motion. Analogous solutions of the Nambu–Goto equations for the n=4$n=4$ case are presented and shown to form (modulo the reparametrization group) an equally large but different moduli space, with the Alday–Maldacena solution at the intersection of the σ  -model and Nambu–Goto moduli spaces. We comment upon the possible form of the regularized action for n=5$n=5$. A function of moduli parameters za$z_a$ is written, whose minimum reproduces the BDDK one-loop five-gluon amplitude. This function may thus be considered as some kind of Legendre transform of the BDDK formula and has its own value independently of the Alday–Maldacena approach.     

Decay π → + ν in the field of a plane electromagnetic wave with allowance for the polarizability of the pion

The process + in the field of a plane electromagnetic wave is investigated with allowance for the complex structure of the pion. Exact values are obtained for the probability of pion decay in circularly and elliptically polarized fields. Pion structure effects become observable for 5, where .Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 12, pp. 65–68, December, 1991.     

Absorption properties of a driven Doppler—broadened ladder system with hyperfine structure

We have studied the absorption spectrum of a Doppler-broadened ladder system,where the highest level is coupled into two middle hyperfine sublevels by a strong coherent field.We find that,when the system is considered as homogeneous,either two or three spectral components are observed,depending on the detuning of the coherent field.but when the velocity distribution of atoms is considered,we can always observe one electromagnetically induced transparency (EIT) window with high dispersion.So the atomic hyperfine structure cannot be an impediment for obtaining EIT.     

Effects of charged Higgs bosons on the processes b→sγ, b→sg1 and b→sℓ+ℓ−

Effects of charged Higgs bosons (H⁺) on various loop-induced processes in the B-meson system are discussed, within the framework of two Higgs doublet models (2HDMs). The H⁺ contribution to the magnetic moment form factor turns out to be very significant and it can distinguish between the two types of 2HDMs. Even with constraints from B_d mixing, both strong enhancements or strong suppressions (in b→sγ) of decay rates are possible. Thus, information from these modes is competitive with, and may soon surpass, restrictions on 2HDMs from B_d mixing. Since (inclusive) b→sγ and b→sg¹ at current limits are not excluded, continued effort to detect them is encouraged.     

Λ b →Λ c +a 1 decay in the heavy quark effective theory

Using the heavy quark approximation, we have studied the nonleptonic decay mode Λ _b →Λ _c a ₁. We have included nonfactorizable contributions as well as factorizable ones in our analysis. The estimated branching ratio for this process is (1.4±0.1)% and the asymmetry parameter α found to be −0.8.     

Entropy evolution properties in a system of two entangled atoms interacting with light field

In this paper, we use the field entropy as a measurement of the degree of entanglement between the light field and the atoms of the system which is composed of two dipole—dipole interacting two-level atoms initially in an entangled state interacting with the single mode coherent field in a Kerr medium. The influence of the coupling constant of dipole—dipole interaction between atoms and the coupling strength of the Kerr medium with the light field and the intensity of the light field on the field entropy are discussed by numerical calculations. It is shown that when the coupling strength of the Kerr medium with the light field is large enough, and the light field is strong, the degree of entanglement between the atoms with the light field becomes weaker. The degree of entanglement only changes slightly with the change of the coupling constant of dipole—dipole interaction between atoms.     

Peculiarities of α → β transformation in the Pd-In-Ru-H system

A precise X-ray diffractometry method is employed to investigate a Pd-In-Ru alloy foil subjected to electrolytic hydrogenation. It is revealed that an increase in the scattering volume of the sample and its multiphase disintegration are caused by the α → β transformation. The basic characteristics of the given transformation are established.     

WKB properties of the time-dependent Schrödinger system

It is shown that the time-dependent WKB expansion highlights some of the hidden properties of the Schrödinger equation and forms a natural bridge between that equation and the functional integral formulation of quantum mechanics. In particular it is shown that the leading (zero- and first-order in ) terms in the WKB expansion are essentially classical, and the relationship of this result to the classical nature of the WKB partition function, and of the anomalies in quantum field theory, is discussed.     

Some unexpected proportionalities between components of the spin—other-orbit interaction in the f shell

The reduced matrix elements of the component z _i of the inter-electronic spin-other-orbit interaction have been calculated for all the states of the atomic f shell. Three of the z _i , each of which belongs to the irreducible representation (30) of Racah's group G₂, are found to exhibit matrix elements that are often related to one another in ways that go beyond what the Wigner-Eckart theorem, generalized to G₂, would predict. Examples are presented for matrix elements whose bras belong to the IR (20) of G₂ and whose kets belong to (31). The challenges to current theory are discussed.