Relaxation dynamics of multi-level tunneling systems

A quantum mechanical treatment of an asymmetric double-well potential (DWP) interacting with a heat bath is presented for circumstances where the contribution of higher vibrational levels to the relaxation dynamics cannot be excluded from consideration. The deep quantum limit characterized by a discrete energy spectrum near the barrier top is considered. The investigation is motivated by simulations on a computer glass which show that the considered parameter regime is ``typical'' for DWPs being responsible for the relaxation peak of sound absorption in glasses. Relaxation dynamics resembling the spatial- and energy-diffusion-controlled limit of the classical Kramers' problem, and Arrhenius-like behavior is found under specific conditions.Comment: 23 pages, RevTex, 2 figures can be received from the Authors upon reques

Kinetics of helium bubble formation in nuclear materials

The formation and growth of helium bubbles due to self-irradiation in plutonium has been modelled by a discrete kinetic equations for the number densities of bubbles having $k$ atoms. Analysis of these equations shows that the bubble size distribution function can be approximated by a composite of: (i) the solution of partial differential equations describing the continuum limit of the theory but corrected to take into account the effects of discreteness, and (ii) a local expansion about the advancing leading edge of the distribution function in size space. Both approximations contribute to the memory term in a close integrodifferential equation for the monomer concentration of single helium atoms. The present boundary layer theory for discrete equations is compared to the numerical solution of the full kinetic model and to previous approximation of Schaldach and Wolfer involving a truncated system of moment equations.Comment: 24 pages, 6 figures, to appear in Physica

Domain structure of epitaxial Co films with perpendicular anisotropy

Epitaxial hcp Cobalt films with pronounced c-axis texture have been prepared by pulsed lased deposition (PLD) either directly onto Al2O3 (0001) single crystal substrates or with an intermediate Ruthenium buffer layer. The crystal structure and epitaxial growth relation was studied by XRD, pole figure measurements and reciprocal space mapping. Detailed VSM analysis shows that the perpendicular anisotropy of these highly textured Co films reaches the magnetocrystalline anisotropy of hcp-Co single crystal material. Films were prepared with thickness t of 20 nm < t < 100 nm to study the crossover from in-plane magnetization to out-of-plane magnetization in detail. The analysis of the periodic domain pattern observed by magnetic force microscopy allows to determine the critical minimum thickness below which the domains adopt a pure in-plane orientation. Above the critical thickness the width of the stripe domains is evaluated as a function of the film thickness and compared with domain theory. Especially the discrepancies at smallest film thicknesses show that the system is in an intermediate state between in-plane and out-of-plane domains, which is not described by existing analytical domain models

Wave trains, self-oscillations and synchronization in discrete media

We study wave propagation in networks of coupled cells which can behave as excitable or self-oscillatory media. For excitable media, an asymptotic construction of wave trains is presented. This construction predicts their shape and speed, as well as the critical coupling and the critical separation of time scales for propagation failure. It describes stable wave train generation by repeated firing at a boundary. In self-oscillatory media, wave trains persist but synchronization phenomena arise. An equation describing the evolution of the oscillator phases is derived.Comment: to appear in Physica D: Nonlinear Phenomen

К вопросу о новых философских основаниях гуманизма

Представлено новое направление философских поисков для определения понятия "гуманизм". Новые философские основания гуманизма позволят выработать обновленное видение отношений человека, общества и природы

Random matrix theory for CPA: Generalization of Wegner's nn--orbital model

We introduce a generalization of Wegner's $n$-orbital model for the description of randomly disordered systems by replacing his ensemble of Gaussian random matrices by an ensemble of randomly rotated matrices. We calculate the one- and two-particle Green's functions and the conductivity exactly in the limit $n\to\infty$. Our solution solves the CPA-equation of the $(n=1)$-Anderson model for arbitrarily distributed disorder. We show how the Lloyd model is included in our model.Comment: 3 pages, Rev-Te

Exhaustion of Nucleation in a Closed System

We determine the distribution of cluster sizes that emerges from an initial phase of homogeneous aggregation with conserved total particle density. The physical ingredients behind the predictions are essentially classical: Super-critical nuclei are created at the Zeldovich rate, and before the depletion of monomers is significant, the characteristic cluster size is so large that the clusters undergo diffusion limited growth. Mathematically, the distribution of cluster sizes satisfies an advection PDE in "size-space". During this creation phase, clusters are nucleated and then grow to a size much larger than the critical size, so nucleation of super-critical clusters at the Zeldovich rate is represented by an effective boundary condition at zero size. The advection PDE subject to the effective boundary condition constitutes a "creation signaling problem" for the evolving distribution of cluster sizes during the creation era. Dominant balance arguments applied to the advection signaling problem show that the characteristic time and cluster size of the creation era are exponentially large in the initial free-energy barrier against nucleation, G_*. Specifically, the characteristic time is proportional to exp(2 G_*/ 5 k_B T) and the characteristic number of monomers in a cluster is proportional to exp(3G_*/5 k_B T). The exponentially large characteristic time and cluster size give a-posteriori validation of the mathematical signaling problem. In a short note, Marchenko obtained these exponentials and the numerical pre-factors, 2/5 and 3/5. Our work adds the actual solution of the kinetic model implied by these scalings, and the basis for connection to subsequent stages of the aggregation process after the creation era.Comment: Greatly shortened paper. Section on growth model removed. Added a section analyzing the error in the solution of the integral equation. Added reference

Rigorous mean field model for CPA: Anderson model with free random variables

A model of a randomly disordered system with site-diagonal random energy fluctuations is introduced. It is an extension of Wegner's $n$-orbital model to arbitrary eigenvalue distribution in the electronic level space. The new feature is that the random energy values are not assumed to be independent at different sites but free. Freeness of random variables is an analogue of the concept of independence for non-commuting random operators. A possible realization is the ensemble of at different lattice-sites randomly rotated matrices. The one- and two-particle Green functions of the proposed hamiltonian are calculated exactly. The eigenstates are extended and the conductivity is nonvanishing everywhere inside the band. The long-range behaviour and the zero-frequency limit of the two-particle Green function are universal with respect to the eigenvalue distribution in the electronic level space. The solutions solve the CPA-equation for the one- and two-particle Green function of the corresponding Anderson model. Thus our (multi-site) model is a rigorous mean field model for the (single-site) CPA. We show how the Llyod model is included in our model and treat various kinds of noises.Comment: 24 pages, 2 diagrams, Rev-Tex. Diagrams are available from the authors upon reques

Reply to Comment on "Cosmic rays, carbon dioxide, and climate"

In our analysis [Rahmstorf et al., 2004], we arrived at two main conclusions: the data of Shaviv and Veizer [2003] do not show a significant correlation of cosmic ray flux (CRF) and climate, and the authors' estimate of climate sensitivity to CO2 based on a simple regression analysis is questionable. After careful consideration of Shaviv and Veizer's comment, we want to uphold and reaffirm these conclusions. Concerning the question of correlation, we pointed out that a correlation arose only after several adjustments to the data, including shifting one of the four CRF peaks and stretching the time scale. To calculate statistical significance, we first need to compute the number of independent data points in the CRF and temperature curves being correlated, accounting for their autocorrelation. A standard estimate [Quenouille, 1952] of the number of effective data points is urn:x-wiley:00963941:media:eost14930:eost14930-math-0001 where N is the total number of data points and r1, r2 are the autocorrelations of the two series. For the curves of Shaviv and Veizer [2003], the result is NEFF = 4.8. This is consistent with the fact that these are smooth curves with four humps, and with the fact that for CRF the position of the four peaks is determined by four spiral arm crossings or four meteorite clusters, respectively; that is, by four independent data points. The number of points that enter the calculation of statistical significance of a linear correlation is (NEFF− 2), since any curves based on only two points show perfect correlation; at least three independent points are needed for a meaningful result