Quantum Lissajous Scars.

A quantum scar-an enhancement of a quantum probability density in the vicinity of a classical periodic orbit-is a fundamental phenomenon connecting quantum and classical mechanics. Here we demonstrate that some of the eigenstates of the perturbed two-dimensional anisotropic (elliptic) harmonic oscillator are strongly scarred by the Lissajous orbits of the unperturbed classical counterpart. In particular, we show that the occurrence and geometry of these quantum Lissajous scars are connected to the anisotropy of the harmonic confinement, but unlike the classical Lissajous orbits the scars survive under a small perturbation of the potential. This Lissajous scarring is caused by the combined effect of the quantum (near) degeneracies in the unperturbed system and the localized character of the perturbation. Furthermore, we discuss experimental schemes to observe this perturbation-induced scarring.

Effects of scarring on quantum chaos in disordered quantum wells.

The suppression of chaos in quantum reality is evident in quantum scars, i.e. in enhanced probability densities along classical periodic orbits. They provide opportunities in controlling quantum transport in nanoscale quantum systems. Here, we study energy level statistics of perturbed two-dimensional quantum systems exhibiting recently discovered, strong perturbation-induced quantum scarring. In particular, we focus on the effect of local perturbations and an external magnetic field on both the eigenvalue statistics and scarring. Energy spectra are analyzed to investigate the chaoticity of the quantum system in the context of the Bohigas-Giannoni-Schmidt conjecture. We find that in systems where strong perturbation-induced scars are present, the eigenvalue statistics are mostly mixed, i.e. between Wigner-Dyson and Poisson pictures in random matrix theory. However, we report interesting sensitivity of both the eigenvalue statistics to the perturbation strength, and analyze the physical mechanisms behind this effect.

Finite-size effects and interactions in artificial graphene formed by repulsive scatterers.

We carry out a numerical real-space study on electrons confined in a two-dimensional triangular lattice of repulsive scattering centres. The system represents a qualitative model of molecular graphene, where the electron gas is confined between the scattering molecules in a hexagonal configuration. Our main interest is, on one hand, in the comparability of a finite system (flake) and a fully periodic one, and, on the other hand, in the role of the Coulombic electron-electron interactions and the relative strength of the scattering centres. Our real-space study shows in detail how the density of states of the fully periodic system-containing the Dirac point-is gradually formed as the size of the flake is increased. Good qualitative agreement with the experimental density of states is obtained. Our study confirms the minor role of the electron-electron interactions with selected system parameters, and shows in detail that large scattering amplitudes are required to obtain a distinctive Dirac point in the density of states.

Prediction of quantum dot characteristics through universal scaling relations.

We derive scaling relations for the electrochemical potential and addition energy of 2D quantum dots charged with N electrons. In the derivation we apply the Thomas-Fermi theory for the harmonic model of a quantum dot in the effective mass approximation. We demonstrate that the resulting scaling relations yield excellent agreement with measured chemical potentials and addition energies for both lateral and vertical quantum dots. Moreover, we show that the scaling relation has predictive power in estimating the confinement strength and the number of electrons trapped in the quantum dot.

Construction of the B88 Exchange-Energy Functional in Two Dimensions.

We construct a generalized-gradient approximation for the exchange-energy density of finite two-dimensional systems. Guided by nonempirical principles, we include the proper small-gradient limit and the proper tail for the exchange-hole potential. The observed performance is superior to that of the two-dimensional local-density approximation, which underlines the usefulness of the approach in practical applications.

Fractal dynamics in chaotic quantum transport.

Despite several experiments on chaotic quantum transport in two-dimensional systems such as semiconductor quantum dots, corresponding quantum simulations within a real-space model have been out of reach so far. Here we carry out quantum transport calculations in real space and real time for a two-dimensional stadium cavity that shows chaotic dynamics. By applying a large set of magnetic fields we obtain a complete picture of magnetoconductance that indicates fractal scaling. In the calculations of the fractality we use detrended fluctuation analysis-a widely used method in time-series analysis-and show its usefulness in the interpretation of the conductance curves. Comparison with a standard method to extract the fractal dimension leads to consistent results that in turn qualitatively agree with the previous experimental data.

Stability of spin droplets in realistic quantum Hall devices.

We study the formation and characteristics of 'spin droplets', i.e. compact spin-polarized configurations in the highest occupied Landau level, in an etched quantum Hall device at filling factors 2 ≤ ν ≤ 3. The confining potential for electrons is obtained with self-consistent electrostatic calculations on a GaAs/AlGaAs heterostructure with experimental system parameters. Real-space spin-density-functional calculations for electrons confined in the obtained potential show the appearance of stable spin droplets at ν ~ 5/2. The qualitative features of the spin droplet are similar to those in idealized (parabolic) quantum-dot systems. The universal stability of the state against geometric deformations underlines the applicability of spin droplets in, for example, spin-transport through quantum point contacts.

Electron-electron interactions in artificial graphene.

Recent advances in the creation and modulation of graphenelike systems are introducing a science of "designer Dirac materials". In its original definition, artificial graphene is a man-made nanostructure that consists of identical potential wells (quantum dots) arranged in an adjustable honeycomb lattice in the two-dimensional electron gas. As our ability to control the quality of artificial graphene samples improves, so grows the need for an accurate theory of its electronic properties, including the effects of electron-electron interactions. Here we determine those effects on the band structure and on the emergence of Dirac points.

Many-particle dynamics and intershell effects in Wigner molecules.

We apply classical molecular dynamics within the velocity Verlet algorithm to examine the formation dynamics of Wigner crystals in two-dimensional harmonic oscillators. Using a large ensemble of initial conditions as well as different freezing mechanisms, we obtain reliable information on the energies and probabilities of stable and metastable configurations, their formation dynamics, and their stability. Wigner-crystal configurations of up to 30 particles are presented and the dynamics of transition processes, e.g., intershell effects, are analyzed.

Interaction-induced spin polarization in quantum dots.

The electronic states of lateral many-electron quantum dots in high magnetic fields are analyzed in terms of energy and spin. In a regime with two Landau levels in the dot, several Coulomb-blockade peaks are measured. A zigzag pattern is found as it is known from the Fock-Darwin spectrum. However, only data from Landau level 0 show the typical spin-induced bimodality, whereas features from Landau level 1 cannot be explained with the Fock-Darwin picture. Instead, by including the interaction effects within spin-density-functional theory a good agreement between experiment and theory is obtained. The absence of bimodality on Landau level 1 is found to be due to strong spin polarization.

Billiards in magnetic fields: a molecular dynamics approach.

We present a computational scheme based on classical molecular dynamics to study chaotic billiards in static external magnetic fields. The method allows us to treat arbitrary geometries and several interacting particles. We test the scheme for rectangular single-particle billiards in magnetic fields and find a sequence of regularity islands at integer aspect ratios. In the case of two Coulomb-interacting particles the dynamics is dominated by chaotic behavior. However, signatures of quasiperiodicity can be identified at weak interactions, as well as regular trajectories at strong magnetic fields. Our scheme provides a promising tool to monitor the classical limit of many-electron semiconductor nanostructures and transport systems up to high magnetic fields.

Universal correction for the Becke-Johnson exchange potential.

The Becke-Johnson exchange potential [A. D. Becke and E. R. Johnson, J. Chem. Phys. 124, 221101 (2006)] has been successfully used in electronic structure calculations within density-functional theory. However, in its original form, the potential may dramatically fail in systems with non-Coulombic external potentials, or in the presence of external magnetic or electric fields. Here, we provide a system-independent correction to the Becke-Johnson approximation by (i) enforcing its gauge-invariance and (ii) making it exact for any single-electron system. The resulting approximation is then better designed to deal with current-carrying states and recovers the correct asymptotic behavior for systems with any number of electrons. Tests of the resulting corrected exchange potential show very good results for a hydrogen chain in an electric field and for a four-electron harmonium in a magnetic field.

Lower bounds on the exchange-correlation energy in reduced dimensions.

Bounds on the exchange-correlation energy of many-electron systems are derived and tested. By using universal scaling properties of the electron-electron interaction, we obtain the exponent of the bounds in three, two, one, and quasione dimensions. From the properties of the electron gas in the dilute regime, the tightest estimate to date is given for the numerical prefactor of the bound, which is crucial in practical applications. Numerical tests on various low-dimensional systems are in line with the bounds obtained and give evidence of an interesting dimensional crossover between two and one dimensions.

Microscale granulation in a fluid bed powder processor using electrostatic atomisation.

The aim of this study was to use the electrostatic atomisation in miniaturised fluid bed granulation process and define the effect of process parameters. The process parameters included in the study were granulation liquid flow rate, atomisation voltage and binder concentration in the granulation liquid. Altogether 22 batches were granulated in Multichamber Microscale Fluid bed powder Processor (MMFP). Granule size distributions were measured with both sieves and image analyses. With these process conditions, the atomisation liquid flow rate had a strong positive correlation with the granule size. Increasing the atomisation voltage increased the granule size, which is contradictory with the expectations. The effect of the binder concentration remained unclear. Although it is challenging to model the fluid bed granulation process in micro-scale, multivariate methods such as principal component analysis (PCA) are helpful in studying the most important phenomena.

Large quantum rings in the ν > 1 quantum Hall regime.

We study computationally the ground-state properties of large quantum rings in the filling-factor ν>1 quantum Hall regime. We show that the arrangement of electrons into different Landau levels leads to clear signatures in the total energies as a function of the magnetic field. In this context, we discuss possible approximations for the filling factor ν in the system. We are able to characterize integer-ν states in quantum rings in an analogy with conventional quantum Hall droplets. We also find a partially spin-polarized state between ν = 2 and 3. Despite the specific topology of a quantum ring, this state is strikingly reminiscent of the recently found ν = 5/2 state in a quantum dot.

Optimal control of quantum rings by terahertz laser pulses.

Complete control of single-electron states in a two-dimensional semiconductor quantum-ring model is established, opening a path into coherent laser-driven single-gate qubits. The control scheme is developed in the framework of optimal-control theory for laser pulses of two-component polarization. In terms of pulse lengths and target-state occupations, the scheme is shown to be superior to conventional control methods that exploit Rabi oscillations generated by uniform circularly polarized pulses. Current-carrying states in a quantum ring can be used to manipulate a two-level subsystem at the ring center. Combining our results, we propose a realistic approach to construct a laser-driven single-gate qubit that has switching times in the terahertz regime.

Half-integer filling-factor states in quantum dots.

The emergence of half-integer filling-factor states, such as upsilon=5/2 and 7/2, is found in quantum dots by using numerical many-electron methods. These states have interesting similarities and differences with their counterstates found in the two-dimensional electron gas. The upsilon=1/2 states in quantum dots are shown to have high overlaps with the composite fermion states. The lower overlap of the Pfaffian state indicates that electrons might not be paired in quantum dot geometry. The predicted upsilon=5/2 state has a high spin polarization, which may have an impact on the spin transport through quantum dot devices.

Determination of tackiness of chitosan film-coated pellets exploiting minimum fluidization velocity.

The tackiness of aqueous chitosan film coatings and effects of anti-sticking agents on sticking tendency, were evaluated. A novel rapid method exploiting minimum fluidization velocity to determine tackiness was introduced and tested. The pressure difference over the miniaturized fluidized-bed was precisely recorded as a function of velocity of fluidization air. High molecular weight chitosan plasticized with glycerol was used as a film-forming agent. Magnesium stearate, titanium dioxide, colloidal silicon dioxide and glyceryl-1-monostearate (GMS) were studied as anti-sticking agents. Film coatings were performed in a miniaturized top-spray coater. The incorporation of anti-sticking agents led to a clear decrease in tackiness of the chitosan films, and magnesium stearate and GMS were shown the most effective. Film-coated pellets containing magnesium stearate and GMS as an anti-sticking agent were very easily fluidized (showing very low values of minimum fluidization velocity) and were thus classified as the best flowing and the least sticking samples. Both these additives were found anti-sticking agents of choice for aqueous chitosan film coatings. Determination of the experimental minimum fluidization velocity in a fluidized bed, is a useful and sensitive method of measuring the tackiness tendency of film-coated pellets.

Poor sleep and psychiatric symptoms at school: an epidemiological study.

The objective of this study was to evaluate associations between sleep problems and psychiatric symptoms at school. A random sample consisting of 5813 eight- to nine-year-old children was selected from ordinary schools. Both parents' and children's reports of sleep problems were taken into account. The psychiatric symptoms were addressed according to the teachers' reports (the Rutter Scale B). Children with severe sleep problems were more likely to have a psychiatric disturbance according to the Rutter B Scale (OR 2.45, 95% CI 1.85-3.25). Logistic regression models showed that severe sleep problems were highly associated with emotional problems (OR 2.74, 95% CI 1.84-4.13), school attendance problems (OR 2.53, 95% OR 1.45-4.41), behavioural problems (OR 2.44, 95% CI 1.59-3.75) and hyperactivity (OR 2.02, 95% CI 1.30-3.13). Over 95% of severe sleep problems were reported only by the children themselves. In conclusion, children with severe sleep problems have substantially more teacher-reported psychiatric symptoms than those with no or mild sleep complaints. In diagnosing sleep disorders, it is important to include children as informants because relevant information may be overlooked when only parents are questioned.