M. A. Topinka, R. M. Westervelt,, et al. Imaging Coherent Electron Flow from a Quantum Point Contact.
Science 289, 5488, 2323-2326 (2000).
Publisher's VersionAbstractScanning a charged tip above the two-dimensional electron gas inside a gallium arsenide/aluminum gallium arsenide nanostructure allows the coherent electron flow from the lowest quantized modes of a quantum point contact at liquid helium temperatures to be imaged. As the width of the quantum point contact is increased, its electrical conductance increases in quantized steps of 2e 2/h, where e is the electron charge and h is Planck's constant. The angular dependence of the electron flow on each step agrees with theory, and fringes separated by half the electron wavelength are observed. Placing the tip so that it interrupts the flow from particular modes of the quantum point contact causes a reduction in the conductance of those particular conduction channels below 2e 2/h without affecting other channels.
Barnett, A., Cohen, D. & Heller, E.J. Deformations and dilations of chaotic billiards: Dissipation rate, and quasiorthogonality of the boundary wave functions.
Physical review letters 85, 1412 (2000).
Publisher's VersionAbstractWe consider chaotic billiards in d dimensions, and study the matrix elements Mnm corresponding to general deformations of the boundary. We analyze the dependence of |Mnm|2 on ω=(En−Em)/ħ using semiclassical considerations. This relates to an estimate of the energy dissipation rate when the deformation is periodic at frequency ω. We show that, for dilations and translations of the boundary, |Mnm|2 vanishes like ω4 as ω→0, for rotations such as ω2, whereas for generic deformations it goes to a constant. Such special cases lead to quasiorthogonality of the eigenstates on the boundary.
Cohen, D. & Heller, E.J. Unification of perturbation theory, random matrix theory, and semiclassical considerations in the study of parametrically dependent eigenstates.
Physical review letters 84, 2841 (2000).
Publisher's VersionAbstractWe consider a classically chaotic system that is described by a Hamiltonian H(Q,P;x), where x is a constant parameter. Specifically, we discuss a gas particle inside a cavity, where x controls a deformation of the boundary or the position of a "piston." The quantum eigenstates of the system are |n(x)>. We describe how the parametric kernel P(nmid R:m) = |<n(x)mid R:m(x(0))>|(2) evolves as a function of deltax = x-x(0). We explore both the perturbative and the nonperturbative regimes, and discuss the capabilities and the limitations of semiclassical as well as random waves and random-matrix-theory considerations.