Biomedical subjects

Karl-Fredrik Berggren

Publications and source records attributed to Karl-Fredrik Berggren.

4 recordsLinked to original sources

PubMed2005

Emulation of quantum mechanical billiards by electrical resonance circuits.

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 j omega method we find that the network is analogous to a discretized Schrödinger equation for quantum billiards and dots. Thus complex electric potentials play the role of quantum mechanical wave functions. Ways of realizing the electric network are discussed briefly. The role of symmetries is outlined, and a direct way of selecting states with a given symmetry is presented.

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PubMed2004

Current statistics for wave transmission through an open Sinai billiard: effects of net currents.

Transport through quantum and microwave cavities is studied by analytic and numerical techniques. In particular, we consider the statistics for a finite net probability current (Poynting vector) flowing through an open ballistic Sinai billiard to which two opposite leads/wave guides are attached. We show that if the net probability current is small, the scattering wave function inside the billiard is well approximated by a Gaussian random complex field. In this case, the current statistics are universal and obey simple analytic forms. For larger net currents, these forms still apply over several orders of magnitudes. However, small characteristic deviations appear in the tail regions. Although the focus is on electron and microwave billiards, the analysis is relevant also to other classical wave cavities as, for example, open planar acoustic reverberation rooms, elastic membranes, and water surface waves in irregularly shaped vessels.

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PubMed2002

Crossover from regular to irregular behavior in current flow through open billiards.

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 evaluated 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.

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PubMed1996

Quantum chaos in nano-sized billiards in layered two-dimensional semiconductor structures.

We consider two-dimensional, electron-rich cavities that can be created at a (AlGa)As-GaAs interface. In the modelling of such cavities we include features that are typical for small semiconductor structures or devices, i.e., soft walls representing electrostatic confinement and disorder due to ionized impurities. The introduction of soft walls is found to have a profound effect on the dynamic behaviour. There are situations in which there is a crossover from a Wigner distribution for the nearest level spacing to an effectively Poisson-like one as the confining walls are softened. The crossover occurs in a region which is accessible experimentally. A mechanism for the crossover is discussed in terms of groups of energy levels being separated from each other as walls become soft. The effects of disorder are found to be negligible for high-mobility samples, i.e., the motion of the particles is ballistic. These findings are of a general nature. Chaotic Robnik dots, circular dots with a special "dent," are also investigated. In this case there is no crossover from Wigner to Poisson distributions. An explanation for this difference is proposed. Finally, the effects of leads are investigated in an elementary way by simply attaching two stubs to a circular dot. For wide stubs, which in our simple model would correspond to open leads, we obtain Wigner statistics indicating a transition to irregular behaviour. A lead-induced transition of this kind appears consistent with recent measurements of the line-shape of the weak localization peak, observed in the low-temperature magnetoresistance of square semiconductor billiards. Finally, implications for conductance fluctuations are briefly commented on. (c) 1996 American Institute of Physics.

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