The effect of dissipation on coherent quantum tunnelling in a double-well system: Two-level model using an adjoint equation approach

We examine the effect of dissipation on coherent quantum tunnelling between the two lowest levels of a double-well system using an adjoint equation approach developed previously in the treatment of quantum-optical problems. Dissipation is modelled by a linear coupling to a bath of harmonic oscillators. The high frequency portion of the bath is adiabatically eliminated using a cumulant expansion technique, which generates frequency renormalisation terms. Making a low temperature assumption, an approximate two-level model is developed in the form of three coupled stochastic differential equations. With a decorrelation approximation, the two-level equations can be solved to yield familiar results. However, the adjoint equation also permits the use of direct stochastic simulation as a means of solution, and simulations are carried out for a range of parameters. A comparison with the decorrelation approximation is made.     

Influence of heat treatment conditions on the porosity changes of sulfonated styrene/divinylbenzene copolymers

Sulfonic cation exchangers with two ion exchange group concentrations (0.5 and 2.4 mmol/g, samples A and B, respectively) were obtained by sulfonation of a porous styrene (S) and divinylbenzene (DVB) copolymer with chlorosulfonic acid. Strong thermal decomposition of the sulfonated copolymer A, accompanied by significant changes in its porous structure, starts at ca. 400°C. The char has no sulfonic groups. After heat treatment at 400°C in steam, a sorbent was obtained (yield 65%) that shows higher phenol sorption than the untreated sample when related to the bed volume. The chlorosulfonic derivatives of the initial copolymer were less thermally resistant than the sulfonic ones obtained by hydrolysis. Pyrolysis of the cation exchanger B, in its H+ and Ca²⁺ forms, was carried out at 900°C (yield of both chars close to 30%). By subsequent steam activation at 800°C to a 50% burn-off of the char, sorbents with well-developed, but distinctly different, porous structures were obtained. The activated char from the sulfonated copolymer in its hydrogen form was highly microporous and indicated an effective surface area of 1180 m²/g. However, because of a low contribution of mesopores, its ability to adsorb phenol from the liquid phase was not very high. The activated char from the calcium-doped copolymer, indicating a smaller surface area (580 m²/g) but characterized by a well-developed mesoporosity, was a better sorbent for phenol. © 1994 John Wiley & Sons, Inc.     

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Quantum Nonlocality of Photon Pairs in Interference in a Mach-Zehnder Interferometer

Nonlocal character of entangled photon pairs generated in spontaneous parametric downconversion is demonstrated. One photon from a pair propagates through a Mach-Zehnder interferometer and is detected in coincidence-count measurement with its twin. Width of the coincidence-count interference pattern (measured for various values of path difference in the Mach-Zehnder interferometer) depends on spectral width of the twin as a result of entanglement of photons in a pair. The experimental setup is analyzed for a Gaussian spectral filter and a Fabry-Perot resonator. It is shown that nonlocal interference is much stronger for cw pumping in comparison with femtosecond pulsed pumping for values of parameters commonly used in spontaneous parametric downconversion experiments.     

Densitometric Determination of Embelin in Lysimachia punctata

JPC – Journal of Planar Chromatography – Modern TLC - Athin layer chromatographic method with densitometric UV detection at λ = 285 nm has been developed for quantification of...     

States and Structure of von Neumann Algebras

We summarize and deepen recent results on the interplay between properties of states and the structure of von Neumann algebras. We treat Jauch–Piron states and the concept of independence in noncommutative probability theory.     

Crossover Critical Behavior in the Three-Dimensional Ising Model

The character of critical behavior in physical systems depends on the range of interactions. In the limit of infinite range of the interactions, systems will exhibit mean-field critical behavior, i.e., critical behavior not affected by fluctuations of the order parameter. If the interaction range is finite, the critical behavior asymptotically close to the critical point is determined by fluctuations and the actual critical behavior depends on the particular universality class. A variety of systems, including fluids and anisotropic ferromagnets, belongs to the three-dimensional Ising universality class. Recent numerical studies of Ising models with different interaction ranges have revealed a spectacular crossover between the asymptotic fluctuation-induced critical behavior and mean-field-type critical behavior. In this work, we compare these numerical results with a crossover Landau model based on renormalization-group matching. For this purpose we consider an application of the crossover Landau model to the three-dimensional Ising model without fitting to any adjustable parameters. The crossover behavior of the critical susceptibility and of the order parameter is analyzed over a broad range (ten orders) of the scaled distance to the critical temperature. The dependence of the coupling constant on the interaction range, governing the crossover critical behavior, is discussed.     

An iterative procedure for differential analysis of gene expression

Microarrays are a popular technology to study genes that are differentially expressed between two conditions. In this Note, we propose an iterative procedure to determine the biggest subset of non-differentially expressed genes. We prove a pseudo Markov relationship that allows practical computations. We obtain explicit expressions for FDR and the level of the proposed test at each step. To cite this article: A. Bar-Hen, S. Robin, C. R. Acad. Sci. Paris, Ser. I 337 (2003).