Symmetry-breaking in local Lyapunov exponents

Integrable dynamical systems, namely those having as many independent conserved quantities as freedoms, have all Lyapunov exponents equal to zero. Locally, the instantaneous or finite time Lyapunov exponents are nonzero, but owing to a symmetry, their global averages vanish. When the system becomes nonintegrable, this symmetry is broken. A parallel to this phenomenon occurs in mappings which derive from quasiperiodic Schr?dinger problems in 1-dimension. For values of the energy such that the eigenstate is extended, the Lyapunov exponent is zero, while if the eigenstate is localized, the Lyapunov exponent becomes negative. This occurs by a breaking of the quasiperiodic symmetry of local Lyapunov exponents, and corresponds to a breaking of a symmetry of the wavefunction in extended and critical states. Received 25 October 2001 / Received in final form 8 December 2001 Published online 2 October 2002 RID="a" ID="a"e-mail: r.ramaswamy@mail.jnu.ac.in     

Generic structure of externally driven tearing modes instabilities

A major limit to steady state and advanced high operation of tokamaks of reactor class is due to the onset of tearing modes that develop magnetic and may cause loss of energy confinement or a major disruption. Here the structure of a classical problem about the effects of external control helical fields is analysed and it is shown to offer a general paradigm of response of low order classical and neoclassical tearing modes to a wide class of external perturbations. New results of principle on the structural stability of the response model are obtained, leading to a clear interpretation of the role of “seed islands" in the onset of neo-classical tearing modes and the role of finite ion larmor radius corrections to Ohm's law. Received 12 November 2001 and Received in final form 4 January 2002     

Radiation inhibition effects in the coherent-state many-atom Jaynes-Cummings model

Summary Radiation inhibition in the many-atom Jaynes-Cummings model being a consequence of cooperative as well as cavity detuning effects is examined. Numerical solutions for the time evolution of the atomic population inversion exhibiting quasi-stationary behaviour are presented. Furthermore, the cooperative energy shift of these quasi-stationary states is numerically computed by using a special projection operator. The authors of this paper have agreed to not receive the proofs for correction.     

Probing buried interfaces with non-linear optical spectroscopy

The importance of buried interfaces in our everyday lives and in current scientific research is highlighted, along with experimental difficulty associated with studying such systems. We present an overview of the application of second harmonic generation and sum-frequency spectroscopy to the study of buried interfaces. Several examples from the current literature are presented, ranging from chemical and biological, to electrical and magnetic interfaces. The importance of this work in the context of ongoing research in these areas is discussed. Finally, we provide a snapshot of the state of the art in non-linear optical spectroscopy by mentioning several new directions that are likely to have a large impact on future research into the physics and chemistry of buried interfaces.     

Tailoring magnetism in artificially structured materials: the new frontier

The current standard of electronic devices and data storage media has reached a level such that magnetic materials have to be fabricated on a nanometer scale. In particular, the emerging concept of spintronics, which is based on fact that current carriers have not only charge but also spin, requires the assembling of nanometer-sized magnetic structures with desired magnetic properties. It is this background that motivates scientists and engineers to attempt to grow and characterize magnetic objects at smaller and smaller length scales, from 2D films and multilayers to 1D wires and eventually to 0D dots. In this article, some of the most significant progress in recent years in the effort of growing artificially structured magnetic materials are reviewed. The new structural and magnetic properties of these materials are discussed, with an emphasis on the correlation between structure and magnetism, which also serves as guidance for improving their magnetic properties. The emerging emphasis is on converting the existing knowledge into growing and studying low-dimensional complex materials, which promise to have considerably higher “tuning” ability for desired properties.     

The possible role of intermediate NH species in oscillations of the NO+H2 reaction on noble metal surfaces

A comparative study of the thermodynamic properties of adsorbed NH_n species (n = 0, 1, 2, 3) on transition metal surfaces is performed by using the semi-empirical method of interacting bonds. The principal difference between single crystal surfaces exhibiting oscillatory behavior in the NO+H₂ reaction, and those surfaces which do not show such a behavior is that the combination reaction of NH species can easily proceed in the former case, whereas it is substantially endothermic on the latter surfaces.A trigger-like route for the oscillatory behavior is considered where the combination reaction of NH species operates as a temporary reaction pathway. This pathway practically does not contribute to the N₂ formation until the nitrogen coverage reaches some critical value, which ensures a sufficiently close distance between adjacent NH particles. The trigger pathway starts upon reaching that stage initiating the surface wave propagation, and stops immediately when the wave propagation is completed. The surface becomes then nearly clean and ready for the next oscillatory cycle. In this way, the feedback mechanism and the critical point of the regular wave initiation can be understood without any further assumptions. An alternative key reaction is also considered.     

Surface reactions of monoethylgermane on Si(100)-(2×1)

The adsorption and decomposition of monoethylgermane (GeH₃Et) on the Si(100)-(2×1) surface was investigated with the intent of elucidating the surface processes leading to the deposition of germanium. The low-temperature adsorption of the molecule was explored, as well as its thermal decomposition. H₂ and C₂H₄ are observed as the desorption products in temperature-programmed desorption experiments. The ethylene is produced by a hydride elimination reaction within the adsorbed ethyl groups. The amount of Ge which can be deposited in a reaction cycle is correlated with the number of sites occupied by the ethyl groups upon the dissociation of GeH₃Et.     

Asymptotic behavior of fluctuations for the 1D Ising model in zero-temperature limit

Fluctuation of the average spin for one-dimensional Ising spins with nearest neighbor interactions are studied. The distribution function for the average spin is calculated for a finite volume, finite temperature, and finite magnetic field. As the volume increases and the temperature diminishes at zero magnetic field, there are two limits in which the probability distribution shows quite different behaviors: in the thermodynamic limit as the volume goes to infinity for finite temperature, small deviations of the fluctuations are described by a Gaussian distribution, and in the limit as the temperature vanishes for a finite volume, the ground states are realized with probability one. The crossover between these limits is analyzed via a ratio of the correlation length to the volume. The helix-coil transition in a polypeptide is discussed as an application.     

Synthese arylsubstituierter 2-Pyrimidinamine,Dihydro-2-pyrimidinamine und Pyrimido[1,2-a]pyrimidine durch Reaktion von Guanidin mit Chalkonen

4- and 4-methoxy-, 4-hydroxy- and 2-hydroxychalcone4 e,k,f andg, respectively, are transformed by action of guanidine in benzene to yield 4-(4-methoxyphenyl)-6-phenyl-2-pyrimidinamine (6 e=6 k) and hydroxyphenylpyrimidinamines6 f andg, respectively. In contrast, 4- and 4-chlor-, 4-brom- and 4-phenylchalcone4 h,l–n resp. react with guanidine under analogous conditions to give 4,6-diaryl-1,4-dihydro-2-pyrimidinamines5 h,l–n. The bases5 h,l–n also tend to aromatize, but they can be stabilized by transformation into salts5 h,l–n · HCl with hydrochloric acid. Heating of5 n inDMF under atmospheric oxygen yields 4-(4-biphenyl)-6-phenyl-2-pyrimidinamine (6 n). Action of guanidine on 4-nitrochalcone4 o in chloroform affords 2-amino-4-nitrophenyl-6-phenyl-tetrahydro-4-pyrimidinol8 o, which is transformed by hydrochloric acid into 6-nitrophenyl-dihydropyrimidinamine-hydrochloride5 o · HCl. Treating of the latter with sodiummethylat in methanol yields the very stable dihydropyrimidinamine5 o. Action of guanidine on 4-chlor- and 4-bromchalcone4 h andm respectively (in addition to5 h andm) yields 2,4,6,8-tetraaryl-1,4-dihydro-2H-pyrimido[1,2-a]pyrimidines7 h andm, respectively.

Herrn Prof. Dr.Erwin Schauenstein mit den besten Wünschen zum 65. Geburtstag gewidmet.     

Brownian diffusion in a nonuniform gas

An analysis is made of the effects on the diffusion of Brownian particles whose Knudsen number is large compared to unity, of nonuniformities in the host gas. As examples, in one type of nonuniformity of the host gas, the Chapman-Enskog velocity distribution function for the gas molecules is used; in the other, the host gas is a free-molecule Couette flow. In both cases, a new force on the Brownian particles appears. Two techniques are used (extending Kramers' method and utilizing the Chapman-Enskog method) to transform the new Fokker-Planck equation into generalized Smoluchowski and convective diffusion equations. In these equations, the diffusion coefficient appears as a second-order tensor. Thus, it is demonstrated that Brownian diffusion in a nonuniform gas is anisotropic.The work of Slinn was financially supported in part by Battelle Memorial Institute and in part by U.S. Atomic Energy Commission Contract AT(45-1)-1830. The work of Shen was supported in part by U.S. Air Force Office of Scientific Research Contract 49(638)-1346.