Stability of Coulomb systems in a magnetic field.

I study N electrons and M protons in a magnetic field. It is shown that the total energy per particle is bounded below by a constant independent of M and N, provided the fine structure constant is small. Here, the total energy includes the energy of the magnetic field.

Theory of strongly correlated electron systems. I. Intersite coulomb interaction and the approximation of renormalized fermions in total energy calculations

The diagrammatic strong-coupling perturbation theory (SCPT) for correlated electron systems is developed for intersite Coulomb interaction and for a nonorthogonal basis set. The construction is based on iterations of exact closed equations for many - electron Green functions (GFs) for Hubbard operators in terms of functional derivatives with respect to external sources. The graphs, which do not contain the contributions from the fluctuations of the local population numbers of the ion states, play a special role: a one-to-one correspondence is found between the subset of such graphs for the many - electron GFs and the complete set of Feynman graphs of weak-coupling perturbation theory (WCPT) for single-electron GFs. This fact is used for formulation of the approximation of renormalized Fermions (ARF) in which the many-electron quasi-particles behave analogously to normal Fermions. Then, by analyzing: (a) Sham's equation, which connects the self-energy and the exchange- correlation potential in density functional theory (DFT); and (b) the Galitskii and Migdal expressions for the total energy, written within WCPT and within ARF SCPT, a way we suggest a method to improve the description of the systems with correlated electrons within the local density approximation (LDA) to DFT. The formulation, in terms of renormalized Fermions LIDA (RF LDA), is obtained by introducing the spectral weights of the many electron GFs into the definitions of the charge density, the overlap matrices, effective mixing and hopping matrix elements, into existing electronic structure codes, whereas the weights themselves have to be found from an additional set of equations. Compared with LDA+U and self-interaction correction (SIC) methods, RF LDA has the advantage of taking into account the transfer of spectral weights, and, when formulated in terms of GFs, also allows for consideration of excitations and nonzero temperature. Going beyond the ARF SCPT, as well as RF LIDA, and taking into account the fluctuations of ion population numbers would require writing completely new codes for ab initio calculations. The application of RF LDA for ab initio band structure calculations for rare earth metals is presented in part 11 of this study (this issue). (c) 2005 Wiley Periodicals, Inc.

Anisotropic viscous models of large-deformation Mohr-Coulomb failure

We have developed a way to represent Mohr-Coulomb failure within a mantle-convection fluid dynamics code. We use a viscous model of deformation with an orthotropic viscoplasticity (a different viscosity is used for pure shear to that used for simple shear) to define a prefered plane for slip to occur given the local stress field. The simple-shear viscosity and the deformation can then be iterated to ensure that the yield criterion is always satisfied. We again assume the Boussinesq approximation, neglecting any effect of dilatancy on the stress field. An additional criterion is required to ensure that deformation occurs along the plane aligned with maximum shear strain-rate rather than the perpendicular plane, which is formally equivalent in any symmetric formulation. We also allow for strain-weakening of the material. The material can remember both the accumulated failure history and the direction of failure. We have included this capacity in a Lagrangian-integration-point finite element code and show a number of examples of extension and compression of a crustal block with a Mohr-Coulomb failure criterion. The formulation itself is general and applies to 2- and 3-dimensional problems.

An anisotropic viscous representation of Mohr-Coulomb failure for use is modelling coupled mantle-continent dynamics

In mantle convection models it has become common to make use of a modified (pressure sensitive, Boussinesq) von Mises yield criterion to limit the maximum stress the lithosphere can support. This approach allows the viscous, cool thermal boundary layer to deform in a relatively plate-like mode even in a fully Eulerian representation. In large-scale models with embedded continental crust where the mobile boundary layer represents the oceanic lithosphere, the von Mises yield criterion for the oceans ensures that the continents experience a realistic broad-scale stress regime. In detailed models of crustal deformation it is, however, more appropriate to choose a Mohr-Coulomb yield criterion based upon the idea that frictional slip occurs on whichever one of many randomly oriented planes happens to be favorably oriented with respect to the stress field. As coupled crust/mantle models become more sophisticated it is important to be able to use whichever failure model is appropriate to a given part of the system. We have therefore developed a way to represent Mohr-Coulomb failure within a code which is suited to mantle convection problems coupled to large-scale crustal deformation. Our approach uses an orthotropic viscous rheology (a different viscosity for pure shear to that for simple shear) to define a prefered plane for slip to occur given the local stress field. The simple-shear viscosity and the deformation can then be iterated to ensure that the yield criterion is always satisfied. We again assume the Boussinesq approximation - neglecting any effect of dilatancy on the stress field. An additional criterion is required to ensure that deformation occurs along the plane aligned with maximum shear strain-rate rather than the perpendicular plane which is formally equivalent in any symmetric formulation. It is also important to allow strain-weakening of the material. The material should remember both the accumulated failure history and the direction of failure. We have included this capacity in a Lagrangian-Integration-point finite element code and will show a number of examples of extension and compression of a crustal block with a Mohr-Coulomb failure criterion, and comparisons between mantle convection models using the von Mises versus the Mohr-Coulomb yield criteria. The formulation itself is general and applies to 2D and 3D problems, although it is somewhat more complicated to identify the slip plane in 3D.

Tunnelling density of states at Coulomb-blockade peaks

We calculate the tunnelling density of states (TDoS) for a quantum dot in the Coulomb-blockade regime, using a functional integral representation with allowing correctly for the charge quantisation. We show that in addition to the well-known gap in the TDoS in the Coulomb-blockade valleys, there is a suppression of the TDoS at the peaks. We show that such a suppression is necessary in order to get the correct result for the peak of the differential conductance through an almost close quantum dot.

Coulomb dissociation of N-20,N-21

Neutron-rich light nuclei and their reactions play an important role in the creation of chemical elements. Here, data from a Coulomb dissociation experiment on N-20,N-21 are reported. Relativistic N-20,N-21 ions impinged on a lead target and the Coulomb dissociation cross section was determined in a kinematically complete experiment. Using the detailed balance theorem, the N-19(n,gamma)N-20 and N-20(n,gamma)N-21 excitation functions and thermonuclear reaction rates have been determined. The N-19(n,gamma)N-20 rate is up to a factor of 5 higher at T < 1 GK with respect to previous theoretical calculations, leading to a 10% decrease in the predicted fluorine abundance.

Fluctuations in and out of equilibrium: Thermalization, quantum measurements and Coulomb disorder

This purely theoretical thesis covers aspects of two contemporary research fields: the non-equilibrium dynamics in quantum systems and the electronic properties of three-dimensional topological insulators. In the first part we investigate the non-equilibrium dynamics in closed quantum systems. Thanks to recent technologies, especially from the field of ultracold quantum gases, it is possible to realize such systems in the laboratory. The focus is on the influence of hydrodynamic slow modes on the thermalization process. Generic systems in equilibrium, either classical or quantum, in equilibrium are described by thermodynamics. This is characterized by an ensemble of maximal entropy, but constrained by macroscopically conserved quantities. We will show that these conservation laws slow down thermalization and the final equilibrium state can be approached only algebraically in time. When the conservation laws are violated thermalization takes place exponential in time. In a different study we calculate probability distributions of projective quantum measurements. Newly developed quantum microscopes provide the opportunity to realize new measurement protocols which go far beyond the conventional measurements of correlation functions. The second part of this thesis is dedicated to a new class of materials known as three-dimensional topological insulators. Also here new experimental techniques have made it possible to fabricate these materials to a high enough quality that their topological nature is revealed. However, their transport properties are not fully understood yet. Motivated by unusual experimental results in the optical conductivity we have investigated the formation and thermal destruction of spatially localized electron- and hole-doped regions. These are caused by charged impurities which are introduced into the material in order to make the bulk insulating. Our theoretical results are in agreement with the experiment and can explain the results semi-quantitatively. Furthermore, we study emergent lengthscales in the bulk as well as close to the conducting surface.

Inhomogeneous cloud coverage through the Coulomb explosion of dust in substellar atmospheres

Context. Recent observations of brown dwarf spectroscopic variability in the infrared infer the presence of patchy cloud cover. Aims. This paper proposes a mechanism for producing inhomogeneous cloud coverage due to the depletion of cloud particles through the Coulomb explosion of dust in atmospheric plasma regions. Charged dust grains Coulomb-explode when the electrostatic stress of the grain exceeds its mechanical tensile stress, which results in grains below a critical radius a < a Coul crit being broken up. Methods. This work outlines the criteria required for the Coulomb explosion of dust clouds in substellar atmospheres, the effect on the dust particle size distribution function, and the resulting radiative properties of the atmospheric regions. Results. Our results show that for an atmospheric plasma region with an electron temperature of Te = 10 eV (≈105 K), the critical grain radius varies from 10−7 to 10−4 cm, depending on the grains’ tensile strength. Higher critical radii up to 10−3 cm are attainable for higher electron temperatures. We find that the process produces a bimodal particle size distribution composed of stable nanoscale seed particles and dust particles with a ≥ a Coul crit , with the intervening particle sizes defining a region devoid of dust. As a result, the dust population is depleted, and the clouds become optically thin in the wavelength range 0.1–10 μm, with a characteristic peak that shifts to higher wavelengths as more sub-micrometer particles are destroyed. Conclusions. In an atmosphere populated with a distribution of plasma volumes, this will yield regions of contrasting radiative properties, thereby giving a source of inhomogeneous cloud coverage. The results presented here may also be relevant for dust in supernova remnants and protoplanetary disks.

A further step in the modelling of the mechanical behaviour of bagasse

A better understanding of the behaviour of prepared cane and bagasse during the crushing process is believed to be an essential prerequisite for further improvements to the crushing process. Improvements could be made, for example, in throughput, sugar extraction, and bagasse moisture. The ability to model the mechanical behaviour of bagasse as it is squeezed in a milling unit to extract juice would help identify how to improve the current process to reduce final bagasse moisture. However an adequate mechanical model for bagasse is currently not available. Previous investigations have proven with certainty that juice flow through bagasse obeys Darcy’s permeability law, that the grip of the rough surface of the grooves on the bagasse can be represented by the Mohr- Coulomb failure criterion for soils, and that the internal mechanical behaviour of the bagasse is critical state behaviour similar to that for sand and clay. Current Finite Element Models (FEM) available in commercial software have adequate permeability models. However, the same commercial software do not contain an adequate mechanical model for bagasse. Progress has been made in the last ten years towards implementing a mechanical model for bagasse in finite element software code. This paper builds on that progress and carries out a further step towards obtaining an adequate material model.