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This^{ }paper reports on a joint theoretical and experimental study of^{ }the Pauli quantum-mechanical stress tensor T_{}(x,y) for open two-dimensional chaotic^{ }billiards. In the case of a finite current flow through^{ }the system the interior wave function is expressed as =u+iv.^{ }With the assumption that u and v are Gaussian random^{ }fields we derive analytic expressions for the statistical distributions for^{ }the quantum stress tensor components T_{}. The Gaussian random field^{ }model is tested for a Sinai billiard with two opposite^{ }leads by analyzing the scattering wave functions obtained numerically from^{ }the corresponding Schrödinger equation. Two-dimensional quantum billiards may be emulated^{ }from planar microwave analogs. Hence we report on microwave measurements^{ }for an open two-dimensional cavity and how the quantum stress^{ }tensor analog is extracted from the recorded electric field. The^{ }agreement with the theoretical predictions for the distributions for T_{}(x,y)^{ }is quite satisfactory for small net currents. However, a distinct^{ }difference between experiments and theory is observed at higher net^{ }flow, which could be explained using a Gaussian random field,^{ }where the net current was taken into account by an^{ }additional plane wave with a preferential direction and amplitude.
On 28 May 2009, at a closed meeting in Brussels, ministers and state secretaries of education and science from several EU countries decided to build the European Spallation Source (ESS) in Lund, Sweden. Or did they?It is common for big European science projects to be surrounded by secrecy and political deceit, but the ESS is extraordinary in its elusiveness. There is a remarkable lack of concrete economic, political, technical and scientific underpinnings to the project but a boasting certainty in the promises of future paybacks.The ESS is an accelerator-based neutron spallation facility that will cost billions of Euros to build and run. It is expected to bring new knowledge in several fields including materials science, energy research, and the life sciences. But its financing is not yet certain, and future returns hard to predict. How then could the decision to build ESS occur? Why was there so little organized resistance?This book places the ESS project in its political and scientific context. It links the decisions taken to the history of Big Science in Europe and in Sweden. It looks at the dynamic political processes of establishing this megaproject in a small town in the south of Sweden. The eight chapters start from a paradoxical state of affairs: The ESS is not funded, and not formally decided in any binding agreements yet it is treated as a future reality, locally and nationally, loaded with promises of scientific, economic and social returns.The book makes a much-needed first contribution to the analysis of the ESS project and its political, environmental, and social ramifications. It should be read by scholars of science and technology studies, politicians and the interested general public.
A basic model for particle states and current flow in open quantum dots/billiards are investigated. The model is unconventional and extends the use of complex potentials first introduced in phenomenological nuclear inelastic scattering theory (the optical model). Attached leads/source drain are represented by complex potentials. Probability densities and currents flows for open 2D quantum dots/billiards are calculated and the results are compared with microwave measurements used to emulate the dot. We also apply the model to a recangular enclosure and report on helical flows guided by nodal lines and disc-like accumulations of flow lines. The model is of conceptual as well as practical and educational interest.
Recent experimental studies of Zeeman-split one-dimensional subbands in ballistic quantum wires in an in-plane magnetic field show that additional nonquantized conductance structures occur as subbands cross at low electron densities [A. C. Graham et al., Phys. Rev.Lett. 91, 136404 (2003)]. These structures are called 0.7 analogs. We analyze the experimental transconductance data within the Kohn-Sham spin-density-functional method, including exchange and correlation effects for an infinite split-gate quantum wire in a parallel, in-plane magnetic field B∥. Energy levels are found to rearrange abruptly as they cross due to polarization effects driven by exchange and Coulomb interactions. Experimental qualitative features are explained well by this model. ©2005 The American Physical Society.
We propose that a two-dimensional electric network may be used for fundamental studies of wave function properties, transport, and related statistics. Using Kirchhoff 's current law and the jw-method we find that the network is analogous to a discretized Schrodinger equation for quantum billiards and clots. Thus the complex electric potentials play the role of quantum rnechanical wave functions.
We explore preliminary a 3D wave cavity in which the interior complex wave functions are of Berry-type. Streamlines and novel disc-like features are uncovered by means of selective and interactive visualization.
Level statistics are nodal point distribution in a rectangular semiconductor quantum dot are studies for different degrees of spin-orbit coupling. The chaotic features occurring from the spin-orbit coupling have no classical counterpart. Using experimental values of GaSb/InAs/GaSb semiconductor quantum wells we find that level repulsion can lead to the semi-Poisson distribution for nearest level separations. Nodal lines and nodal points are also investigated. Comparison is made with nodal point distributions for fully chaotic states.
In this article, we present a summary of the current status of the study of the transport of electrons confined to one dimension in very low disorder GaAs–AlGaAs heterostructures. By means of suitably located gates and application of a voltage to ‘electrostatically squeeze’ the electronic wave functions, it is possible to produce a controllable size quantization and a transition from two-dimensional transport. If the length of the electron channel is sufficiently short, then transport is ballistic and the quantized subbands each have a conductance equal to the fundamental quantum value 2e^{2}/h, where the factor of 2 arises from the spin degeneracy. This mode of conduction is discussed, and it is shown that a number of many-body effects can be observed. These effects are discussed as in the spin-incoherent regime, which is entered when the separation of the electrons is increased and the exchange energy is less than kT. Finally, results are presented in the regime where the confinement potential is decreased and the electron configuration relaxes to minimize the electron–electron repulsion to move towards a two-dimensional array. It is shown that the ground state is no longer a line determined by the size quantization alone, but becomes two distinct rows arising from minimization of the electrostatic energy and is the precursor of a two-dimensional Wigner lattice.
We trace signatures of quantum chaos in the distribution of nodal points and streamlines for coherent electron transport through different types of quantum dots (chaotic and regular). We have calculated normalized distribution functions for the nearest distances between nodal points and found that this distribution may be used as a signature of quantum chaos for electron transport in open systems. Different chaotic billiards show the same characteristic distribution function for nodal points. This signature of quantum chaos is well reproduced using well known approaches for chaotic wavefunctions. We have also investigated the quantum flows which display some remarkable features.
We discuss signatures of quantum chaos in terms of distributions of nodal points, saddle points, and streamlines for coherent electron transport through two-dimensional billiards, which are either nominally integrable or chaotic. As typical examples of the two cases we select rectangular and Sinai billiards. We have numerically evaluted distribution functions for nearest distances between nodal points and found that there is a generic form for open chaotic billiards through which a net current is passed. We have also evaluated the distribution functions for nodal points with specific vorticity (winding number) as well as for saddle points. The distributions may be used as signatures of quantum chaos in open systems. All distributions are well reproduced using random complex linear combinations of nearly monochromatic states in nominally closed billiards. In the case of rectangular billiards with simple sharp-cornered leads the distributions have characteristic features related to order among the nodal points. A flaring or rounding of the contact regions may, however, induce a crossover to nodal point distributions and current flow typical for quantum chaos. For an irregular arrangement of nodal points, as for example in the Sinai billiard, the quantum flow lines become very complex and volatile, recalling chaos among classical trajectories. Similarities with percolation are pointed out. ©2002 The American Physical Society.
The spontaneous magnetization of a quantum point contact (QPC) formed between two large quantum dots by a lateral confinement of a high-mobility two-dimensional electron gas is studied for a realistic GaAs/AlxGa1-xAs heterostructure. The model of the device incorporates the contributions from a patterned gate, doping, surface states, and mirror charges. To explore the magnetic properties, the Kohn-Sham local spin-density formalism is used with exchange and correlation potentials that allows for local spin polarization. Exchange is the dominant mechanism behind local magnetization within the QPC, while the correlation part is less prominent. However, the correlation potential gives rise to an important correction in the QPC potential. Below the first conduction plateau we thus find a magnetized regime corresponding approximately to a single electron spin. Using an approximate separable saddle potential we compute the conductance and recover the so-called similar to0.7 (2e(2)/h) conduction anomaly plus an additional anomaly at similar to0.4 (2e(2)/h) below which the magnetization collapses.
Spontaneous magnetization of single and coupled quantum dots formed by lateral confinement of a high-mobility two-dimensional electron gas is studied for a realistic GaAs/AlGaAs heterostructure. The modelling of the device takes into account contributions from a patterned gate, doping, surface states, and mirror charges. To explore the magnetic properties we use the Kohn-Sham local spin-density formalism including the contributions from electron correlation and exchange. We show by explicit calculations that the exchange is the dominant mechanism driving a spontaneous magnetization of a dot. The correlation potential reduces the amount of level splitting and usually affects the electron content in the dot at a given gate voltage. These effects are, however, small and may be neglected under present circumstances. Single dots with up to 50 electrons have been studied.
A heuristic model for particle states and current flow in open ballistictwo-dimensional (2D) quantum dots/wave billiards is proposed. The modelmakes use of complex potentials first introduced in phenomenological nuclearinelastic scattering theory (the optical model). Here we assume that externalinput and output leads connecting the system to the source and the drain regionsmay be represented by complex potentials. In this way, a current may be set upbetween the two ‘pseudo-leads’. Probability densities and current flows for anopen quantum dot are analyzed here numerically and the results are comparedwith the microwave measurements used to emulate the system. The model isof conceptual as well as practical interest. In addition to quantum billiards, itmay be used as a tool per se to analyze transport in classical wave analogues,such as microwave resonators, acoustic resonators, effects of leakage on suchsystems, etc.