Erratum to “Master equation for structured reservoirs” [Photonics Nanostruct.: Fundam. Appl. 2/3 (2004) 167]

In this work we generalize the formalism developed in our previous work [D. Mogilevtsev, S. Kilin, S.B. Cavalcanti, PNFA (2–3) (2004) 161]. We derive a master equation suitable to describe atom-field interaction in structured reservoirs, particulary those that exhibit ‘freezing’ of spontaneous decay as well as atom-field bound states. For a wide range of reservoir densities-of-states, this equation can be reduced to the Markovian form. In this work we extend the range of applicability of the method to times comparable to those of the atom-field bound state formation. We discuss novel features that such an extension brings forth and confirm predictions made in our previous work, namely, the stationary positive atomic inversion, a possibility of in-reservoir coherent control of the atom-field bound state and bipartite character of such a state in the absence of external perturbations.     

Master Equation and Fokker–Planck Equation: Comparison of Entropy and of Rate Constants

A usual approximation of the master equation is provided by the Fokker–Planck equation. For chemical systems with one species, we prove generally that the prediction of the rate constant of the metastable state given by the Master equation and the Fokker–Planck approximation differ exponentially with respect to the size of the system. We show that this is related to the fact that the entropy of the metastable state is not described correctly by the Fokker–Planck equation. We prove that the rate given by the Fokker–Planck equation overestimates that rate given by the Master equation.     

Systematic analysis of the multivariate master equation for a reaction-diffusion system

The multivariate master equation for a reaction-diffusion system is analyzed using a singular perturbation approach. It is shown that in the vicinity of a bifurcation leading to two simultaneously stable steady states, the steady-state probability distribution reduces asymptotically to the exponential of the Landau-Ginzburg functional. On the other hand, for a system displaying quadratic nonlinearities and an absorbing state, critical behavior is ruled out.Supported in part by the Actions de Recherche Concertées of the Belgian government under convention no. 76/81 II 3.     

Gas‐phase reactions of Cl atoms with hydrochloroethers: relative rate constants and their correlation with substituents' electronegativities

Rate constants for the reactions of Cl atoms with CH₃OCHCl₂ and CH₃OCH₂CH₂Cl were determined at (296 ± 2) K and atmospheric pressure using synthetic air as bath gas. Decay rates of these organic compounds were measured relative to the following reference compounds: CH₂ClCH₂Cl and n‐C₅H₁₂. Using rate constants of 1.33 × 10^?12 and 2.52 × 10^?10 cm³ molecule^?1 sec^?1 for the reaction of Cl atoms with CH₂ClCH₂Cl and n‐C₅H₁₂, respectively, the following rate coefficients were derived: k(Cl + CH₃OCHCl₂) = (1.05 ± 0.11) × 10^?12 and k(Cl + CH₃OCH₂CH₂Cl) = (1.14 ± 0.10) × 10^?10, in units of cm³ molecule^?1 s^?1. The rate constants obtained were compared with previous literature data and a correlation was found between the rate coefficients of some CH₃OCHR¹R² + Cl reactions and ΔElectronegativity of ? CHR¹R². Copyright © 2008 John Wiley & Sons, Ltd.     

Stochastic analysis of symmetry-breaking bifurcations: Master equation approach

The multivariate master equation for a general reaction-diffusion system is solved perturbatively, in the vicinity of a bifurcation point leading to symmetry-breaking transitions. The possibility to express the result through a Brazovskii type of potential is examined, and a comparison with the Langevin analysis of Walgraefet al. [Adv. Chem. Phys. 49:311 (1982)] is performed.     

The effect of pressure on the elastic constants of Cu, Ag and Au: a molecular dynamics study

This paper describes the effect of pressure on some the mechanical properties of transition metals Cu, Ag, and Au, such as elastic constants and bulk modulus. Using molecular dynamics (MD) simulation, the present study was carried out using the modified many-body Morse potential function expression in the framework of the Embedded Atom Method (EAM). The effect of pressure on equilibrium volume, elastic constants, and bulk modulus were determined, and found to be in agreement with other theoretical calculations and experimental data.     

A rate equation of the laser that reflects the coherence of light

This paper presents a kind of rate equation of a laser governed by Feigenbaum's geometric relation of bifurcate gaps. New rate equations can not only describe the changing action of the laser output strength qualitatively, but can also reflect the coherence of light, and therefore reflect the relaxation of the equilibrium process of a laser to a certain degree.     

Stochastic analysis of a Hopf bifurcation: Master equation approach

The effect of inhomogeneous fluctuations in a reaction-diffusion system exhibiting a Hopf bifurcation is analyzed using the master equation approach. A Taylor expansion of the logarithm of the stationary probability, known as the stochastic potential, is calculated. This procedure displays marked analogies with the theory of normal forms. The critical potential, reduced to its local expansion around an arbitrary point of the limit cycle, brings out the essential role played by the phase of the oscillating variables. A comparison with the Langevin analysis of Walgraefet al. [J. Chem. Phys. 78(6):3043 (1983)] is performed.     

Theoretical investigation on H abstraction reaction mechanisms and rate constants of Isoflurane with the OH radical

The mechanism of H abstraction reactions for Isoflurane with the OH radical was investigated using density functional theory and G3(MP2) duel theory methods. The geometrical structures of all the species were fully optimised at B3LYP/6-311++G** level of theory. Thermochemistry data were obtained by utilising the high accurate model chemistry method G3(MP2) combined with the standard statistical thermodynamic calculations. Gibbs free energies were used for the reaction channels analysis. All the reaction channels were confirmed throughout the intrinsic reaction coordinate analysis. The results show that two channels were obtained, which correspond to P(1) and P(2) with the respective activation barriers of 63.03 and 54.82 kJ/mol. The rate constants for the two channels over a wide temperature range of 298.15–2000 K were predicted and the calculated data are in agreement with the experimental one. The results show that P(2) is the dominant reaction channel under 800 K and above 800 K, it can be found that P(1) will be more preferable reaction channel.     

On phase separation in the spherical model of a ferromagnet: Quasiaverage approach

The spherical model of a ferromagnet is investigated in the framework of the generalized quasiaverage approach where an external field positive in one half of a square lattice and negative in the other half is used. It is shown that in addition to the well-known critical point, a second one can be produced by the field. Although the main asymptotic of the free energy is analytic at this point, the next-to-leading asymptotic possesses a singularity here, as well as at the point where the free energy per site is nonanalytic. An order parameter of the model also has singularities at both critical points. The magnetization profile is studied at different scales. It is shown that (in an appropriate regime), below the new critical temperature the magnetization profile freezes, that is, becomes temperature independent.     

Reaction mechanism and rate constants of the CH+CH4 reaction: a theoretical study

Ab initio and density functional calculations have been performed to elucidate the mechanism of CH radical insertion into methane. The results show that the reaction can be viewed to occur via two stages. On the first stage, the CH radical approaches methane without large structural changes to acquire proper positioning for the subsequent stage, where H-migration occurs from CH₄ to CH, along with a C–C bond formation. Where the first stage ends and the second begins, a tight transition state was located using the B3LYP/6-311G(d,p) and MP4(SDQ)/6-311++G(d,p) methods. Using a rigid rotor – harmonic oscillator approach within transition state theory, we show that at the MP5/6-311++G(d,p)//MP4(SDQ)/6-311++G(d,p) level the calculated rate constants are in a reasonably good agreement with experiment in a broad temperature range of 145–581 K. Even at low temperatures, the insertion reaction bottleneck is found about the location of the tight transition state, rather than at long separations between the CH and CH₄ reactants. In addition, high level CCSD(T)-F12/CBS calculations of the remainder of the C₂H₅ potential energy surface predict the CH+CH₄ reaction to proceed via the initial insertion step to the ethyl radical which then can emit a hydrogen atom to form highly exothermic C₂H₄+H products.     

On full rate of reconnection in the nonstationary vortex tangle: A master equation approach

The expression for the reconnection frequency in the nonstationary vortex tangle is obtained. An approach based on the master equation for the length distribution of vortex loops is developed.     

A nonperturbative quantum electrodynamic approach to the theory of laser induced high harmonic generation

Using nonperturbative quantum electrodynamics, we develop a scattering theory for high harmonic generation (HHG). A transition rate formula for HHG is obtained. Applying this formula, we calculate the spectra of high harmonics generated from different noble gases shined by strong laser light. We study the cutoff property of the spectra. The data show that the cutoff orders of high harmonics are greater than that predicted by the “3.17” cutoff law. As a numerical experiment, the data obtained from our repeated calculations support the newly derived theoretical expression of the cutoff law. The cutoff energy of high harmonics described by the new cutoff law, in terms of the ponderomotive energy U_p and the ionization potential energy I_p, is 3.34U_p+ 1.83I_p. The higher cutoff orders predicted by this theory are due to the absorption of the extra photons, which participate only the photon-mode up-conversion and do nothing in the photoionization process.     

Heike Kamerlingh Onnes: Master of Experimental Technique and Quantitative Research

Heike Kamerlingh Onnes (1853-1926), born a century and a half ago, was a major protagonist in the so-called Second Golden Age of Dutch Science. He devoted his career to the emerging field of low-temperature physics. His particular concern was to test the theories of his older compatriot Johannes Diderik van der Waals (1837-1923) by creating a style of research that was characterized by meticulous planning, precise measurement, and constant improvement of techniques and instruments. He made numerous contributions to low-temperature physics, but I focus on his liquefaction of helium, for which he received the Nobel Prize in Physics for 1913, and on his discovery of superconductivity. He became known internationally as le gentleman du zéro absolu.     

Formation of Cs molecules via Feshbach resonances stabilized by spontaneous emission: theoretical treatment with the Fourier grid method

This paper proposes a general method to investigate Feshbach resonances in atomic collisions similar to Cs(6 s ) + Cs(6 p ) in the thermal or cold regime. In order to compute the predissociation widths of the C ¹ Π _u (6 s + 5 d ) bound vibrational levels of Cs₂, coupled both with the (2) ³ Σ ⁺ _u (6 s + 6 p ) continuum and with the (2) ³ Π _u (6 s + 5 d ) vibrational series, a Fourier grid method is implemented, with an optical potential. A convenient way of optimizing the latter is proposed. A large number of resonances are found and calculations of their cross-sections for stabilization into ground state molecules show that the rate may be important. This confirms the interpretation of Lintz and Bouchiat [Phys. Rev. Lett. 80, 2570 (1998)] who observed dimer formation in cell experiments. Possible generalization to the cold regime relies on the possibility to tune the position of a resonance to coincide with the maximum of the collisional energy distribution. Received 14 February 2002 Published online 28 June 2002