High-mobility two-dimensional electron gas (2DEG) which resides at the interface between GaAs and AlGaAs layered semiconductors has been used experimentally and theoretically to study ballistic electron transport. The present paper is motivated by recent experiments in magnetic electron focusing. The proposed device consists of two quantum point contacts (QPCs) serving as electron injector and collector which are placed in the same semiconductor GaAs/AlGaAs heterostructure. Here we focus on a theoretical study of the injection of electrons via a quantum wire/QPC into an open two-dimensional (2D) reservoir. The transport is considered for non-interacting electrons at different transmission regimes using the mode-matching technique. The proposed mode-matching technique has been implemented numerically. Electron flow through the quantum wire with hard-wall rectangular, conical and rounded openings has been studied. We have found for these three cases that the geometry of the opening does not play a crucial role for the electron propagation. When a perpendicular magnetic field is applied the electron paths in the 2D reservoir are curved. We analyse this case both classically and quantum-mechanically. The effect of spin-splitting due to exchange interactions on the electron flow is also considered. The effect is clearly present for realistic choices of device parameters and consistent with observations. The results of this study may be applied in designing magnetic focusing devices and spin separation.

Using a Non-equilibrium Green’s function (NEGF) approach, a set of experiments is suggested which can provide indirect evidence of the fine and non-local electrostatic tuning of the onset of spin polarization in two closely spaced quantum point contacts (QPCs) with two sets of in-plane side gates (SGs) in the presence of lateral spin-orbit coupling (LSOC). The conductance of the two closely spaced QPCs or four-gate QPC is studied for different biasing conditions applied to two leftmost and rightmost SGs. When calculated as a function of the common sweep voltage Vsweep applied to two of the SGs, the conductance plots show several conductance anomalies, i.e., below G0 = 2e2/h, characterized by intrinsic bistability, i.e., hysteresis loops due to a difference in the conductance curves for up and down sweeps of the common gate voltage. The hysteresis loops are related to the co-existence of multistable spin textures in the narrow channel of the four-gate QPC and are very sensitive to the biasing conditions on the four SGs. The shape of the conductance anomalies and size of hysteresis loops are different when the biasing conditions on the leftmost and rightmost SGs are swapped. This rectifying behavior is an additional indirect evidence for the onset of spontaneous spin polarization in nanoscale devices made of QPCs. These results show that the onset and fine tuning of conductance anomalies in QPC structures are highly sensitive to the non-local action of closely spaced SGs. This effect must therefore be taken into account in the design of all electrical spin valves making use of middle gates to fine tune the spin precession between QPC based spin injector and detector contacts.

This review outlines an unconventional but timely formulation of quantum dynamics of systems in contact with an environment. This alternative approach to traditional quantum mechanics is generic and is currently gaining attention in a number of fields as, for example, quantum scattering and transport, optical waveguides, devices embedded in an environment, oscillatory classical systems, RLC circuits and other open systems with loss and gain. Here we briefly outline this formulation in which the condition of space-time reflection (PT-symmetry) plays a central role. If PT-symmetry is broken upon parametric change, real energy levels generally turn complex. At the onset of such a symmetry breaking levels coalesce at “Exceptional Points” (EP).

Faraday first characterised the behaviour of a fluid in a container subjected to vertical periodic oscillations. His study pertaining to hydrodynamic instability, the Faraday instability, has catalysed a myriad of experimental, theoretical, and numerical studies shedding light on the mechanisms responsible for the transition of a system at rest to a new state of well-ordered vibrational patterns at fixed frequencies. Here we study dual strata in a shallow vessel containing distilled water and high-viscosity lubrication oil on top of it. At elevated driving power, beyond the Faraday instability, the top stratum is found to freeze into a rigid pattern with maxima and minima. At the same time there is a dynamic crossover into a new state in the form of a lattice of recirculating vortices in the lower layer containing the water. Instrumentation and the physics behind are analysed in a phenomenological way together with a basic heuristic modelling of the wave field. The study, which is based on relatively low-budget equipment, stems from related art projects that have evolved over the years. The study is of value within basic research as well as in education, especially as more advanced collective project work in e.g. engineering physics, where it invites further studies of pattern formation, the emergence of vortex lattices and complexity.

The structure of scattered wave fields and currents is of interest in a variety of fields within physics such as quantum mechanics and optics. Traditionally two-dimensional structures have been investigated; here we focus on three-dimensional structures. We make a generic study of three dimensional quantum box cavities, and our main objective is to visualize the probability current. Visualizations are achieved for complex linear combinations of wave functions with different excitations and with boundary conditions: Dirichlet, Neumann, and mixed. By using different boundary conditions, the results reported here are relevant to many different wave analogues such as microwave billiards and acoustic cavities. Visualization was mainly done through animated images, but a chaotic state was visualized by 3D printing. Our results suggest that if the state of excitation is the same in the different boundary conditions, the current is the same, except at the boundaries of the box. Application to sort nanoparticles in acoustic cavities is considered.

Effects of randomly distributed impurities on conductance, spin polarization and electronlocalization in realistic gated semiconductor quantum point contacts (QPCs) have beensimulated numerically. To this end density functional theory in the local spin-densityapproximation has been used. In the case when the donor layer is embedded far from thetwo-dimensional electron gas (2DEG) the electrostatic confinement potential exhibits theconventional parabolic form, and thus the usual ballistic transport phenomena take place bothin the devices with split gates alone and with an additional metallic gate on the top.In the opposite case, i.e. when the randomly distributed donors are placed not far away fromthe 2DEG layer, there are drastic changes like the localization of electrons in the vicinity ofconfinement potential minima which give rise to fluctuations in conductance and resonances.The conductance as a function of the voltage applied to the top gate for asymmetricallycharged split gates has been calculated. In this case resonances in conductance caused byrandomly distributed donors are shifted and decrease in amplitude while the anomaliescaused by interaction effects remain unmodified. It has been also shown that for a wide QPCthe polarization can appear in the form of stripes. The importance of partial ionization ofthe random donors and the possibility of short range order among the ionized donors areemphasized. The motivation for this work is to critically evaluate the nature of impurities andhow to guide the design of high-mobility devices.

We study effects of randomly distributed impurities on spin polarization and electronlocalization in realistic semiconductor quantum point contacts (QPCs). To this end we usedensity functional theory in local spin-density approximation (LSDA). Previous studies (as,for example, in [1]) have been restricted to the Thomas-Fermi approximation, and thus theeffects of electron correlation and realistic confinement potentials were beyond the subject.Our studies have been performed for the two geometries of the gates, the first one with onlysplit gates, and the other one with an additional top gate situated over the split gates. In thelatter case there is a possibility to vary electron density within a fixed confinement whichgives an opportunity to separate the effects on conductance caused by impurities and electronelectroninteractions in a more distinct way. In both cases we recover the conventionalfluctuation free parabolic electrostatic potential when the distance between the donor layerand the two-dimensional electron gas (2DEG) exceeds ~50 nm. In the opposite case, i.e.,when the randomly distributed donors are placed more close to the 2DEG layer, there aredrastic changes like the localization of electrons in the vicinity of the confinement potentialminima which gives rise to fluctuation in conductance and resonances. At the same time theusual conductance steps vanish. By charging asymmetrically the split gates voltage wecalculate the conductance as a function of the voltage applied to the top gate. In this way wefind that resonances in conductance caused by randomly distributed donors are shifted anddescreased in amplitude while the anomalies caused by interaction effects remain unmodified.Resonance peaks in the conductance derive from localized states within the QPC due torandom fluctuations. The nature of electron localization has been discussed in our previousstudy [2] where we stress the crucial role of the shape of confinement potential on theformation of electron localization. In the present study we have shown that electronlocalization may be caused by randomly distributed donors and play an important role inelectron transport, especially near the pinch-off regime. The results of our numericalsimulations agree qualitatively with experimental studies [3-4]. We have also shown that fora wide QPC spin polarization appears in the form of stripes. This finding may be interesting inview of experimental study in [5] where it has been shown that the structure of such kind canbe responsible for the anomalous behavior of the quantized conductance of a quantum wire inthe shallow confinement limit. We also discuss the diminished effect of partially ionizedrandom donors on the electronic potentials and the appearance of short-range order among thedonors. The results of the present study is important for applications. For example,homogeneity and order of an assembly of nanostructures are crucial for their use in largescaleelectronic and optical systems.[1] J.A. Nixon, J.H. Davies, and H.U. Baranger, Phys. Rev. B 43, 12638 (1991)[2] I. I. Yakimenko, V. S. Tsykunov and K.-F. Berggren, J. Phys. Condens. Matter 25, 072201 (2013)[3] L.W. Smith, K. J. Thomas, M. Pepper, D. A. Ritchie, I. Farrer, J.P. Griffiths, G.A.C. Jones, J. ofPhys.: Conf. Series 376, 012018, (2012)[4] L. W. Smith, H. Al-Taie, F. Sfigakis, P. See, A. A. J. Lesage, B. Xu, J. P. Griffiths, H. E. Beere, G.A. C. Jones, D. A. Ritchie, M. J. Kelly, and C. G. Smith, Phys. Rev. B 90, 045426 (2014).

A basic quantum-mechanical model for wave functions and current flow in open quantum dots or billiards is investigated. The model involves non-Hertmitian quantum mechanics, parity-time (PT) symmetry, and PT-symmetry breaking. Attached leads are represented by positive and negative imaginary potentials. Thus probability densities, currents flows, etc., for open quantum dots or billiards may be simulated in this way by solving the Schrödinger equation with a complex potential. Here we consider a nominally open ballistic quantum dot emulated by a planar microwave billiard. Results for probability distributions for densities, currents (Poynting vector), and stress tensor components are presented and compared with predictions based on Gaussian random wave theory. The results are also discussed in view of the corresponding measurements for the analogous microwave cavity. The model is of conceptual as well as of practical and educational interest.

We analyze the occurrence of local  magnetization and the effects of electron localization in different models of quantum point contacts (QPCs) using spin-relaxed density functional theory (DFT/LSDA) by means of numerical simulations. In the case of soft confinement potentials the degree of localization is weak and we therefore observe only traces of partial electron localization in the middle of the QPC. In the pinch-off regime there is, however, distinct accumulation at the QPC edges. At the other end, strong confinement potential, low-electron density in the leads and top or implant gates favor electron localization. In such cases one may create a variety of electron configurations from a single localized electron to more complex structures with multiple rows and Wigner lattices.