Semiconductor quantum dots in high magnetic fields

We review and extend the composite fermion theory for semiconductor quantum dots in high magnetic fields. The mean-field model of composite fermions is unsatisfactory for the qualitative physics at high angular momenta. Extensive numerical calculations demonstrate that the microscopic CF theory, which incorporates interactions between composite fermions, provides an excellent qualitative and quantitative account of the quantum dot ground state down to the largest angular momenta studied, and allows systematic improvements by inclusion of mixing between composite fermion Landau levels (called Λ levels).     

Variational derivation of improved KP-type of equations

The Kadomtsev-Petviashvili equation describes nonlinear dispersive waves which travel mainly in one direction, generalizing the Korteweg-de Vries equation for purely uni-directional waves. In this Letter we derive an improved KP-equation that has exact dispersion in the main propagation direction and that is accurate in second order of the wave height. Moreover, different from the KP-equation, this new equation is also valid for waves on deep water. These properties are inherited from the AB-equation (E. van Groesen, Andonowati, 2007 [1]) which is the unidirectional improvement of the KdV equation. The derivation of the equation uses the variational formulation of surface water waves, and inherits the basic Hamiltonian structure.     

液态水微观结构研究的新进展

液态水有很多奇异特性.近年来,对液态水以何种微观结构形式存在的问题争议激烈.文章介绍了当前对水的微观结构的一些研究及其进展,讨论了液态水中的氢键模式与水的结构关系,进而用一个简化模型探讨了氢键的取向性与强弱性对水的异常行为的作用.     

Structured water chains in external electric fields

ABSTRACT

We study the structural, energetic and electronic properties of the structured water chain clusters within the density functional theory. We refer the structured water chains to those water clusters that have specific geometric patterns stretched along one direction. External electric field required to keep the structures open chain, thereby preventing them to form closed structures, is applied along the length of the chain. The structures are essentially periodic with basic repeating unit consisting of the corner- or edge-sharing 4-, 5- or 6-membered ring water clusters. Our calculations underscore the possible existence of such structured water clusters in the electrostatic environments, which we simulate in its simplicity employing a dipolar, uniform and static electric field. Analysis reveals that the 5-membered ring water chain clusters, i.e. the pentamer chain clusters have the lowest average dipole moment per water molecule while the threshold field, that marks the onset of the field-induced closure of the HOMO (highest occupied molecular orbital)-LUMO (lowest unoccupied molecular orbital) energy gap, is highest, followed by that for the tetramer and hexamer chains. The results suggest that the pentamer chains are the most stable clusters over a wide range of electric fields.     

Orbital contribution to the magnetic properties of nanowires: is the orbital polarization ansatz justified?

We show that considerable orbital magnetic moments and magneto-crystalline anisotropy energies are obtained for a Fe monatomic wire described in a tight-binding method with intra-atomic electronic interactions treated in a full Hartree Fock (HF) decoupling scheme. Even though the use of the orbital polarization ansatz with simplified Hamiltonians leads to fairly good results when the spin magnetization is saturated this is not the case of unsaturated systems. We conclude that the full HF scheme is necessary to investigate low dimensional systems.     

A nonextensive approach to the dynamics of financial observables

We present results about financial market observables, specifically returns and traded volumes. They are obtained within the current nonextensive statistical mechanical framework based on the entropy . More precisely, we present stochastic dynamical mechanisms which mimic probability density functions empirically observed. These mechanisms provide possible interpretations for the emergence of the entropic indices q in the time evolution of the corresponding observables. In addition to this, through multi-fractal analysis of return time series, we verify that the dual relation q_stat+q_sens=2 is numerically satisfied, q_stat and q_sens being associated to the probability density function and to the sensitivity to initial conditions respectively. This type of simple relation, whose understanding remains ellusive, has been empirically verified in various other systems.     

Dynamics of the infinitely-thin kink

We consider the dynamics of the domain-wall kink soliton, in particular we study the zero mode of translation. In the infinitely-thin kink limit, we show that the zero mode is almost completely frozen out, the only remnant being a dynamically constrained four-dimensional mode of a single but arbitrary frequency. In relation to this result, we show that the usual mode expansion for dealing with zero modes - implicit collective coordinates - is not in fact a completely general expansion, and that one must use instead a traditional generalised Fourier analysis.     

Miscibility in poly(L-lactide)- b -poly( $ \upvarepsilon$ -caprolactone) double crystalline diblock copolymers

Thermally stimulated depolarization currents, TSDC, wide-angle X-ray scattering, WAXS, differential scanning calorimetry, DSC, and polarized light optical microscopy, PLOM, have been used to examine poly(L-lactide)-b -poly( -caprolactone) diblock copolymers in a wide composition range. Both components are crystallizable and the miscibility in the amorphous phase has been determined from the behavior of the primary relaxations which are the dielectric manifestation of the glass transition, and also from the superstructural morphology revealed by PLOM and the compositional dependence of the melting points as determined by DSC. Distinct segmental mobilities in the amorphous phase which can be well resolved by TSDC are present; the mode of the slower component shifts to lower temperatures as the PCL content increases while the glass transition of neat PCL is present for all compositions. A relaxation times bimodal distribution is apparent for PCL-rich copolymers. The composition dependence of the multiple glass transitions detected in these weakly segregated copolymers are predicted by the self-concentration model for a miscible blend made of components with a large T_g contrast.     

Correlation functions from a unified variational principle: Trial Lie groups

Time-dependent expectation values and correlation functions for many-body quantum systems are evaluated by means of a unified variational principle. It optimizes a generating functional depending on sources associated with the observables of interest. It is built by imposing through Lagrange multipliers constraints that account for the initial state (at equilibrium or off equilibrium) and for the backward Heisenberg evolution of the observables. The trial objects are respectively akin to a density operator and to an operator involving the observables of interest and the sources. We work out here the case where trial spaces constitute Lie groups. This choice reduces the original degrees of freedom to those of the underlying Lie algebra, consisting of simple observables; the resulting objects are labeled by the indices of a basis of this algebra. Explicit results are obtained by expanding in powers of the sources. Zeroth and first orders provide thermodynamic quantities and expectation values in the form of mean-field approximations, with dynamical equations having a classical Lie–Poisson structure. At second order, the variational expression for two-time correlation functions separates–as does its exact counterpart–the approximate dynamics of the observables from the approximate correlations in the initial state. Two building blocks are involved: (i) a commutation matrix which stems from the structure constants of the Lie algebra; and (ii) the second-derivative matrix of a free-energy function. The diagonalization of both matrices, required for practical calculations, is worked out, in a way analogous to the standard RPA. The ensuing structure of the variational formulae is the same as for a system of non-interacting bosons (or of harmonic oscillators) plus, at non-zero temperature, classical Gaussian variables. This property is explained by mapping the original Lie algebra onto a simpler Lie algebra. The results, valid for any trial Lie group, fulfill consistency properties and encompass several special cases: linear responses, static and time-dependent fluctuations, zero- and high-temperature limits, static and dynamic stability of small deviations.     

Oscillatory zoning caused by oscillating surface relaxations

Oscillatory zoning is a spatial variation in the composition of minerals. It has been observed in many different minerals and a variety of mechanisms have been proposed to explain it. We propose an equilibrium model of oscillatory zoning in which the variations in composition stabilise a ferroelastic phase. This results in a sinusoidal variation in composition. We expect that this mechanism could account for oscillatory zoning found in minerals with oscillatory surface relaxations. Received 9 March 1999