Statistical theory of finite Fermi systems with chaotic excited eigenstates

A theory of strongly interacting Fermi systems of a few particles is developed. At high excit at ion energies (a few times the single-parti cle level spacing) these systems are characterized by an extreme degree of complexity due to strong mixing of the shell-model-based many-part icle basis st at es by the residual two- body interaction. This regime can be described as many-body quantum chaos. Practically, it occurs when the excitation energy of the system is greater than a few single-particle level spacings near the Fermi energy. Physical examples of such systems are compound nuclei, heavy open shell atoms (e.g. rare earths) and multicharged ions, molecules, clusters and quantum dots in solids. The main quantity of the theory is the strength function which describes spreading of the eigenstates over many-part icle basis states (determinants) constructed using the shell-model orbital basis. A nonlinear equation for the strength function is derived, which enables one to describe the eigenstates without diagonalization of the Hamiltonian matrix. We show how to use this approach to calculate mean orbital occupation numbers and matrix elements between chaotic eigenstates and introduce typically statistical variable s such as t emperature in an isolated microscopic Fermi system of a few particles.

Attitudes, norms, identity and environmental behaviour: Using an expanded theory of planned behaviour to predict participation in a kerbside recycling programme

In an effort to contribute to greater understanding of norms and identity in the theory of planned behaviour, an extended model was used to predict residential kerbside recycling, with self-identity, personal norms, neighbourhood identification, and injunctive and descriptive social norms as additional predictors. Data from a field study (N = 527) using questionnaire measures of predictor variables and an observational measure of recycling behaviour supported the theory. Intentions predicted behaviour, while attitudes, perceived control, and the personal norm predicted intention to recycle. The interaction between neighbourhood identification and injunctive social norms in turn predicted personal norms. Self-identity and the descriptive social norm significantly added to the original theory in predicting intentions as well as behaviour directly. A replication survey on the self-reported recycling behaviours of a random residential sample (N = 264) supported the model obtained previously. These findings offer a useful extension of the theory of planned behaviour and some practicable suggestions for pro-recycling interventions. It may be productive to appeal to self-identity by making people feel like recyclers, and to stimulate both injunctive and descriptive norms in the neighbourhood.

Detailed analytical investigation of magnetic field line random walk in turbulent plasmas: II. Isotropic turbulence

The random walk of magnetic field lines in the presence of magnetic turbulence in plasmas is investigated from first principles. An isotropic model is employed for the magnetic turbulence spectrum. An analytical investigation of the asymptotic behavior of the field-line mean-square displacement is carried out. in terms of the position variable z. It is shown that varies as similar to z ln z for large distance z. This result corresponds to a superdiffusive behavior of field line wandering. This investigation complements previous work, which relied on a two-component model for the turbulence spectrum. Contrary to that model, quasilinear theory appears to provide an adequate description of the field line random walk for isotropic turbulence.

Random Regret Minimization: Exploration of a New Choice Model for Environmental and Resource Economics

This paper introduces the discrete choice model-paradigm of Random Regret Minimization (RRM) to the field of environmental and resource economics. The RRM-approach has been very recently developed in the context of travel demand modelling and presents a tractable, regret-based alternative to the dominant choice-modelling paradigm based on Random Utility Maximization-theory (RUM-theory). We highlight how RRM-based models provide closed form, logit-type formulations for choice probabilities that allow for capturing semi-compensatory behaviour and choice set-composition effects while being equally parsimonious as their utilitarian counterparts. Using data from a Stated Choice-experiment aimed at identifying valuations of characteristics of nature parks, we compare RRM-based models and RUM-based models in terms of parameter estimates, goodness of fit, elasticities and consequential policy implications.

Scattering theory of multilevel atoms interacting with arbitrary radiation fields

We present a generic transfer matrix approach for the description of the interaction of atoms possessing multiple ground state and excited state sublevels with light fields. This model allows us to treat multi-level atoms as classical scatterers in light fields modified by, in principle, arbitrarily complex optical components such as mirrors, resonators, dispersive or dichroic elements, or filters. We verify our formalism for two prototypical sub-Doppler cooling mechanisms and show that it agrees with the standard literature.

Nonlinear Field Line Random Walk and Generalized Compound Diffusion of Charged Particles

A new nonlinear theory for the perpendicular transport of charged particles is presented. This approach is based on an improved nonlinear treatment of field line random walk in combination with a generalized compound diffusion model. The generalized compound diffusion model is much more systematic and reliable, in comparison to previous theories. Furthermore, the new theory shows remarkably good agreement with test-particle simulations and heliospheric observations.

Construction of Drug–Polymer Thermodynamic Phase Diagrams Using Flory–Huggins Interaction Theory: Identifying the Relevance of Temperature and Drug Weight Fraction to Phase Separation within Solid Dispersions

Amorphous drug-polymer solid dispersions have the potential to enhance the dissolution performance and thus bioavailability of BCS class II drug compounds. The principle drawback of this approach is the limited physical stability of amorphous drug within the dispersion. Accurate determination of the solubility and miscibility of drug in the polymer matrix is the key to the successful design and development of such systems. In this paper, we propose a novel method, based on Flory-Huggins theory, to predict and compare the solubility and miscibility of drug in polymeric systems. The systems chosen for this study are (1) hydroxypropyl methylcellulose acetate succinate HF grade (HPMCAS-HF)-felodipine (FD) and (2) Soluplus (a graft copolymer of polyvinyl caprolactam-polyvinyl acetate-polyethylene glycol)-FD. Samples containing different drug compositions were mixed, ball milled, and then analyzed by differential scanning calorimetry (DSC). The value of the drug-polymer interaction parameter ? was calculated from the crystalline drug melting depression data and extrapolated to lower temperatures. The interaction parameter ? was also calculated at 25 °C for both systems using the van Krevelen solubility parameter method. The rank order of interaction parameters of the two systems obtained at this temperature was comparable. Diagrams of drug-polymer temperature-composition and free energy of mixing (?G mix) were constructed for both systems. The maximum crystalline drug solubility and amorphous drug miscibility may be predicted based on the phase diagrams. Hyper-DSC was used to assess the validity of constructed phase diagrams by annealing solid dispersions at specific drug loadings. Three different samples for each polymer were selected to represent different regions within the phase diagram

A multi-fibre multi-layer representative volume element (M2RVE) for prediction of matrix and interfacial damage in composite laminates

Multiscale micro-mechanics theory is extensively used for the prediction of the material response and damage analysis of unidirectional lamina using a representative volume element (RVE). Th is paper presents a RVE-based approach to characterize the materi al response of a multi-fibre cross-ply laminate considering the effect of matrix damage and fibre-matrix interfacial strength. The framework of the homogenization theory for periodic media has been used for the analysis of a 'multi-fibre multi-layer representative volume element' (M2 RVE) representing cross-ply laminate. The non-homogeneous stress-strain fields within the M2RVE are related to the average stresses and strains by using Gauss theorem and the Hill-Mandal strain energy equivalence principle. The interfacial bonding strength affects the in-plane shear stress-strain response significantl y. The material response predicted by M2 RVE is in good agreement with the experimental results available in the literature. The maximum difference between the shear stress predicted using M2 RVE and the experimental results is ~15% for the bonding strength of 30MPa at the strain value of 1.1%

Implementation and testing of Lanczos-based algorithms for Random-Phase Approximation eigenproblems

The treatment of the Random-Phase Approximation Hamiltonians, encountered in different frameworks, like time-dependent density functional theory or Bethe-Salpeter equation, is complicated by their non-Hermicity. Compared to their Hermitian Hamiltonian counterparts, computational methods for the treatment of non-Hermitian Hamiltonians are often less efficient and less stable, sometimes leading to the breakdown of the method. Recently [Gruning et al. Nano Lett. 8 (2009) 28201, we have identified that such Hamiltonians are usually pseudo-Hermitian. Exploiting this property, we have implemented an algorithm of the Lanczos type for Random-Phase Approximation Hamiltonians that benefits from the same stability and computational load as its Hermitian counterpart, and applied it to the study of the optical response of carbon nanotubes. We present here the related theoretical grounds and technical details, and study the performance of the algorithm for the calculation of the optical absorption of a molecule within the Bethe-Salpeter equation framework. (C) 2011 Elsevier B.V. All rights reserved.

Macroscopic limit of time-dependent density-functional theory for adiabatic local approximations of the exchange-correlation kernel

Time-dependent density-functional theory is a rather accurate and efficient way to compute electronic excitations for finite systems. However, in the macroscopic limit (systems of increasing size), for the usual adiabatic random-phase, local-density, or generalized-gradient approximations, one recovers the Kohn-Sham independent-particle picture, and thus the incorrect band gap. To clarify this trend, we investigate the macroscopic limit of the exchange-correlation kernel in such approximations by means of an algebraical analysis complemented with numerical studies of a one-dimensional tight-binding model. We link the failure to shift the Kohn-Sham spectrum of these approximate kernels to the fact that the corresponding operators in the transition space act only on a finite subspace.

Density functionals from many-body perturbation theory: The band gap for semiconductors and insulators

Theoretically the Kohn-Sham band gap differs from the exact quasiparticle energy gap by the derivative discontinuity of the exchange-correlation functional. In practice for semiconductors and insulators the band gap calculated within any local or semilocal density approximations underestimates severely the experimental energy gap. On the other hand, calculations with an "exact" exchange potential derived from many-body perturbation theory via the optimized effective potential suggest that improving the exchange-correlation potential approximation can yield a reasonable agreement between the Kohn-Sham band gap and the experimental gap. The results in this work show that this is not the case. In fact, we add to the exact exchange the correlation that corresponds to the dynamical (random phase approximation) screening in the GW approximation. This accurate exchange-correlation potential provides band structures similar to the local density approximation with the corresponding derivative discontinuity that contributes 30%-50% to the energy gap. Our self-consistent results confirm substantially the results for Si and other semiconductors obtained perturbatively [R. W. Godby , Phys. Rev. B 36, 6497 (1987)] and extend the conclusion to LiF and Ar, a wide-gap insulator and a noble-gas solid. (c) 2006 American Institute of Physics.

Optimization through quantum annealing: theory and some applications

Quantum annealing is a promising tool for solving optimization problems, similar in some ways to the traditional ( classical) simulated annealing of Kirkpatrick et al. Simulated annealing takes advantage of thermal fluctuations in order to explore the optimization landscape of the problem at hand, whereas quantum annealing employs quantum fluctuations. Intriguingly, quantum annealing has been proved to be more effective than its classical counterpart in many applications. We illustrate the theory and the practical implementation of both classical and quantum annealing - highlighting the crucial differences between these two methods - by means of results recently obtained in experiments, in simple toy-models, and more challenging combinatorial optimization problems ( namely, Random Ising model and Travelling Salesman Problem). The techniques used to implement quantum and classical annealing are either deterministic evolutions, for the simplest models, or Monte Carlo approaches, for harder optimization tasks. We discuss the pro and cons of these approaches and their possible connections to the landscape of the problem addressed.

Disturbance, neutral theory and patterns of beta diversity in soil communities

Beta diversity describes how local communities within an area or region differ in species composition/abundance. There have been attempts to use changes in beta diversity as a biotic indicator of disturbance, but lack of theory and methodological caveats have hampered progress. We here propose that the neutral theory of biodiversity plus the definition of beta diversity as the total variance of a community matrix provide a suitable, novel, starting point for ecological applications. Observed levels of beta diversity (BD) can be compared to neutral predictions with three possible outcomes: Observed BD equals neutral prediction or is larger (divergence) or smaller (convergence) than the neutral prediction. Disturbance might lead to either divergence or convergence, depending on type and strength. We here apply these ideas to datasets collected on oribatid mites (a key, very diverse soil taxon) under several regimes of disturbances. When disturbance is expected to increase the heterogeneity of soil spatial properties or the sampling strategy encompassed a range of diverging environmental conditions, we observed diverging assemblages. On the contrary, we observed patterns consistent with neutrality when disturbance could determine homogenization of soil properties in space or the sampling strategy encompassed fairly homogeneous areas. With our method, spatial and temporal changes in beta diversity can be directly and easily monitored to detect significant changes in community dynamics, although the method itself cannot inform on underlying mechanisms. However, human-driven disturbances and the spatial scales at which they operate are usually known. In this case, our approach allows the formulation of testable predictions in terms of expected changes in beta diversity, thereby offering a promising monitoring tool.