205 research outputs found
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 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
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