Exact Eigenfunctions of a Chaotic System

The interest in the properties of quantum systems, whose classical dynamics are chaotic, derives from their abundance in nature. The spectrum of such systems can be related, in the semiclassical approximation (SCA), to the unstable classical periodic orbits, through Gutzwiller's trace formula. The class of systems studied in this work, tiling billiards on the pseudo-sphere, is special in this correspondence being exact, via Selberg's trace formula. In this work, an exact expression for Green's function (GF) and the eigenfunctions (EF) of tiling billiards on the pseudo-sphere, whose classical dynamics are chaotic, is derived. GF is shown to be equal to the quotient of two infinite sums over periodic orbits, where the denominator is the spectral determinant. Such a result is known to be true for typical chaotic systems, in the leading SCA. From the exact expression for GF, individual EF can be identified. In order to obtain a SCA by finite series for the infinite sums encountered, resummation by analytic continuation in $\hbar$ was performed. The result is similar to known results for EF of typical chaotic systems. The lowest EF of the Hamiltonian were calculated with the help of the resulting formulae, and compared with exact numerical results. A search for scars with the help of analytical and numerical methods failed to find evidence for their existence.Comment: 53 pages LaTeX, 10 Postscript figure

Viscous Decoupling Transitions for Individually Dragged Particles in Systems with Quenched Disorder

We show that when an individual particle is dragged through an assembly of other particles in the presence of quenched disorder, a viscous decoupling transition occurs between the dragged particle and the surrounding particles which is controlled by the quenched disorder. A counterintuitive consequence of this transition is that the velocity of the dragged particle can be increased by increasing the strength or density of the quenched disorder. The decoupling transition can also occur when the external drive on the dragged particle is increased, and is observable as a clear signature in the velocity-force response.Comment: 4 pages, 3 postscript figure

Finite-size effects in tunneling between parallel quantum wires

We present theoretical calculations and experimental measurements which reveal finite-size effects in the tunneling between two parallel quantum wires, fabricated at the cleaved edge of a GaAs/AlGaAs bilayer heterostructure. Observed oscillations in the differential conductance, as a function of bias voltage and applied magnetic field, provide direct information on the shape of the confining potential. Superimposed modulations indicate the existence of two distinct excitation velocities, as expected from spin-charge separation.Comment: Accepted to Phys. Rev. Lett. 7/200

Interference and zero-bias anomaly in tunneling between Luttinger-liquid wires

We present theoretical calculations and experimental measurements which reveal the Luttinger-liquid (LL) nature of elementary excitations in a system consisting of two quantum wires connected by a long narrow tunnel junction at the edge of a GaAs/AlGaAs bilayer heterostructure. The boundaries of the wires are important and lead to a characteristic interference pattern in measurements on short junctions. We show that the experimentally observed modulation of the conductance oscillation amplitude as a function of the voltage bias can be accounted for by spin-charge separation of the elementary excitations in the interacting wires. Furthermore, boundaries affect the LL exponents of the voltage and temperature dependence of the tunneling conductance at low energies. We show that the measured temperature dependence of the conductance zero-bias dip as well as the voltage modulation of the conductance oscillation pattern can be used to extract the electron interaction parameters in the wires.Comment: 17 pages, 12 figure

Many-body dispersions in interacting ballistic quantum wires

We have measured the collective excitation spectrum of interacting electrons in one-dimension. The experiment consists of controlling the energy and momentum of electrons tunneling between two clean and closely situated, parallel quantum wires in a GaAs/AlGaAs heterostructure while measuring the resulting conductance. We measure excitation spectra that clearly deviate from the non-interacting spectrum, attesting to the importance of Coulomb interactions. Notable is an observed 30% enhancement of the velocity of the main excitation branch relative to non-interacting electrons with the same density. In short wires, finite size effects resulting from broken translational invariance are observed. Spin - charge separation is manifested through moire patterns, reflecting different spin and charge excitation velocities.Comment: 14 pages, 6 eps figures. To be published in NANOWIRE, a special issue of Solid State Communication

Controlled Manipulation of Individual Vortices in a Superconductor

We report controlled local manipulation of single vortices by low temperature magnetic force microscope (MFM) in a thin film of superconducting Nb. We are able to position the vortices in arbitrary configurations and to measure the distribution of local depinning forces. This technique opens up new possibilities for the characterization and use of vortices in superconductors

Four-point measurements of n- and p-type two-dimensional systems fabricated with cleaved-edge overgrowth

We demonstrate a contact design that allows four-terminal magnetotransport measurements of cleaved-edge overgrown two-dimensional electron and hole systems. By lithographically patterning and etching a bulk-doped surface layer, finger-shaped leads are fabricated, which contact the two-dimensional systems on the cleave facet. Both n- and p-type two-dimensional systems are demonstrated at the cleaved edge, using Si as either donor or acceptor, dependent on the growth conditions. Four-point measurements of both gated and modulation-doped samples yield fractional quantum Hall features for both n- and p-type, with several higher-order fractions evident in n-type modulation-doped samples.Comment: 3 pages, 3 figure