89 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
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
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
Intersubband Electron Interaction in 1D-2D Junctions
We have shown that the electron transport through junctions of
one-dimensional and two-dimensional systems, as well as through quantum point
contacts, is considerably affected by the interaction of electrons of different
subbands. The interaction mechanism is caused by Friedel oscillations, which
are produced by electrons of the closed subbands even in smooth junctions.
Because of the interaction with these oscillations, electrons of the open
subbands experience a backscattering. The electron reflection coefficient,
which describes the backscattering, has a sharp peak at the energy equal to the
Fermi energy and may be as high as about 0.1. This result allows one to explain
a number of available experimental facts.Comment: 5 pages, 3 figure
Density-functional theory of inhomogeneous electron systems in thin quantum wires
Motivated by current interest in strongly correlated quasi-one-dimensional
(1D) Luttinger liquids subject to axial confinement, we present a novel
density-functional study of few-electron systems confined by power-low external
potentials inside a short portion of a thin quantum wire. The theory employs
the 1D homogeneous Coulomb liquid as the reference system for a Kohn-Sham
treatment and transfers the Luttinger ground-state correlations to the
inhomogeneous electron system by means of a suitable local-density
approximation (LDA) to the exchange-correlation energy functional. We show that
such 1D-adapted LDA is appropriate for fluid-like states at weak coupling, but
fails to account for the transition to a ``Wigner molecules'' regime of
electron localization as observed in thin quantum wires at very strong
coupling. A detailed analyzes is given for the two-electron problem under axial
harmonic confinement.Comment: 8 pages, 7 figures, submitte
Observation of a One-Dimensional Spin-Orbit Gap in a Quantum Wire
Understanding the flow of spins in magnetic layered structures has enabled an
increase in data storage density in hard drives over the past decade of more
than two orders of magnitude1. Following this remarkable success, the field of
'spintronics' or spin-based electronics is moving beyond effects based on local
spin polarisation and is turning its attention to spin-orbit interaction (SOI)
effects, which hold promise for the production, detection and manipulation of
spin currents, allowing coherent transmission of information within a device.
While SOI-induced spin transport effects have been observed in two- and
three-dimensional samples, these have been subtle and elusive, often detected
only indirectly in electrical transport or else with more sophisticated
techniques. Here we present the first observation of a predicted 'spin-orbit
gap' in a one-dimensional sample, where counter-propagating spins, constituting
a spin current, are accompanied by a clear signal in the easily-measured linear
conductance of the system.Comment: 10 pages, 5 figures, supplementary informatio
Manipulating the Tomonaga-Luttinger exponent by electric field modulation
We establish a theoretical framework for artificial control of the power-law
singularities in Tomonaga-Luttinger liquid states. The exponent governing the
power-law behaviors is found to increase significantly with an increase in the
amplitude of the periodic electric field modulation applied externally to the
system. This field-induced shift in the exponent indicates the tunability of
the transport properties of quasi-one-dimensional electron systems.Comment: 7 pages, 3 figure
Spin Echo Decay in a Stochastic Field Environment
We derive a general formalism with which it is possible to obtain the time
dependence of the echo size for a spin in a stochastic field environment. Our
model is based on ``strong collisions''. We examine in detail three cases
where: (I) the local field is Ising-like, (II) the field distribution is
continuous and has a finite second moment, and (III) the distribution is
Lorentzian. The first two cases show a T2 minimum effect and are exponential in
time cubed for short times. The last case can be approximated by a
phenomenological stretched exponential.Comment: 11 pages + 3 postscript figure
Tunneling effects on impurity spectral function in coupled asymmetric quantum wires
The impurity spectral function is studied in coupled double quantum wires at
finite temperatures. Simple anisotropy in the confinement direction of the
wires leads to finite non-diagonal elements of the impurity spectral function
matrix. These non-diagonal elements are responsible for tunneling effects and
result in pronounced extra peak in the impurity spectral function up to
temperatures as high as 20 K.Comment: Accepted in Phys. Rev.
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