242 research outputs found
A Strong Szego Theorem for Jacobi Matrices
We use a classical result of Gollinski and Ibragimov to prove an analog of
the strong Szego theorem for Jacobi matrices on . In particular, we
consider the class of Jacobi matrices with conditionally summable parameter
sequences and find necessary and sufficient conditions on the spectral measure
such that and lie in
, the linearly-weighted space.Comment: 26 page
Acoustoelectric pumping through a ballistic point contact in the presence of magnetic fields
The acoustoelectric current, J, induced in a ballistic point contact (PC) by
a surface acoustic wave is calculated in the presence of a perpendicular
magnetic field, B. It is found that the dependence of the current on the Fermi
energy in the terminals is strongly correlated with that of the PC conductance:
J is small at the conductance plateaus, and is large at the steps. Like the
conductance, the acoustoelectric current has the same functional behavior as in
the absence of the field, but with renormalized energy scales, which depend on
the strength of the magnetic field, | B|.Comment: 7 page
Hall Coefficient in an Interacting Electron Gas
The Hall conductivity in a weak homogeneous magnetic field, , is calculated. We have shown that to leading order in
the Hall coefficient is not renormalized by the
electron-electron interaction. Our result explains the experimentally observed
stability of the Hall coefficient in a dilute electron gas not too close to the
metal-insulator transition. We avoid the currently used procedure that
introduces an artificial spatial modulation of the magnetic field. The problem
of the Hall effect is reformulated in a way such that the magnetic flux
associated with the scattering process becomes the central element of the
calculation.Comment: 23 pages, 15 figure
How backscattering off a point impurity can enhance the current and make the conductance greater than e^2/h per channel
It is well known that while forward scattering has no effect on the
conductance of one-dimensional systems, backscattering off a static impurity
suppresses the current. We study the effect of a time-dependent point impurity
on the conductance of a one-channel quantum wire. At strong repulsive
interaction (Luttinger liquid parameter g<1/2), backscattering renders the
linear conductance greater than its value e^2/h in the absence of the impurity.
A possible experimental realization of our model is a constricted quantum wire
or a constricted Hall bar at fractional filling factors nu=1/(2n+1) with a
time-dependent voltage at the constriction.Comment: 7 pages, 2 figure
Quantized adiabatic charge pumping and resonant transmission
Adiabatically pumped charge, carried by non-interacting electrons through a
quantum dot in a turnstile geometry, is studied as function of the strength of
the two modulating potentials (related to the conductances of the two
point-contacts to the leads) and of the phase shift between them. It is shown
that the magnitude and sign of the pumped charge are determined by the relative
position and orientation of the closed contour traversed by the system in the
parameter plane, and the transmission peaks (or resonances) in that plane.
Integer values (in units of the electronic charge ) of the pumped charge
(per modulation period) are achieved when a transmission peak falls inside the
pumping contour. The integer value is given by the winding number of the
pumping contour: double winding in the same direction gives a charge of 2,
while winding around two opposite branches of the transmission peaks or winding
in opposite directions can give a charge close to zero.Comment: 7 pages, 12 figure
AR and MA representation of partial autocorrelation functions, with applications
We prove a representation of the partial autocorrelation function (PACF), or
the Verblunsky coefficients, of a stationary process in terms of the AR and MA
coefficients. We apply it to show the asymptotic behaviour of the PACF. We also
propose a new definition of short and long memory in terms of the PACF.Comment: Published in Probability Theory and Related Field
Resonance approximation and charge loading/unloading in adiabatic quantum pumping
Quantum pumping through mesoscopic quantum dots is known to be enhanced by
resonant transmission. The pumped charge is close to an integer number of
electrons when the pumping contour surrounds a resonance, but the transmission
remains small on the contour. For non-interacting electrons, we give a
quantitative account of the detailed exchange of electrons between the dot and
the leads (to the electron reservoirs) during a pumping cycle. Near isolated
distinct resonances, we use approximate Breit-Wigner expressions for the dot's
Green function to discuss the loading/unloading picture of the pumping: the
fractional charge exchanged between the dot and each lead through a single
resonance point is related to the relative couplings of the dot and the leads
at this resonance. If each resonance point along the pumping contour is
dominated by the coupling to a single lead (which also implies a very small
transmission), then the crossing of each such resonance results in a single
electron exchange between the dot and that lead, ending up with a net quantized
charge. When the resonance approximation is valid, the fractional charges can
also be extracted from the peaks of the transmissions between the various
leads.Comment: 10 pages, 4 figure
Dissipation and noise in adiabatic quantum pumps
We investigate the distribution function, the heat flow and the noise
properties of an adiabatic quantum pump for an arbitrary relation of pump
frequency and temperature. To achieve this we start with the
scattering matrix approach for ac-transport. This approach leads to expressions
for the quantities of interest in terms of the side bands of particles exiting
the pump. The side bands correspond to particles which have gained or lost a
modulation quantum . We find that our results for the pump
current, the heat flow and the noise can all be expressed in terms of a
parametric emissivity matrix. In particular we find that the current
cross-correlations of a multiterminal pump are directly related a to a
non-diagonal element of the parametric emissivity matrix. The approach allows a
description of the quantum statistical correlation properties (noise) of an
adiabatic quantum pump
Magnetoluminescence
Pulsar Wind Nebulae, Blazars, Gamma Ray Bursts and Magnetars all contain
regions where the electromagnetic energy density greatly exceeds the plasma
energy density. These sources exhibit dramatic flaring activity where the
electromagnetic energy distributed over large volumes, appears to be converted
efficiently into high energy particles and gamma-rays. We call this general
process magnetoluminescence. Global requirements on the underlying, extreme
particle acceleration processes are described and the likely importance of
relativistic beaming in enhancing the observed radiation from a flare is
emphasized. Recent research on fluid descriptions of unstable electromagnetic
configurations are summarized and progress on the associated kinetic
simulations that are needed to account for the acceleration and radiation is
discussed. Future observational, simulation and experimental opportunities are
briefly summarized.Comment: To appear in "Jets and Winds in Pulsar Wind Nebulae, Gamma-ray Bursts
and Blazars: Physics of Extreme Energy Release" of the Space Science Reviews
serie
Pauli blocking factors in quantum pumps
We investigate the Pauli blocking factor in quantum pumps using Floquet
formalism. Even though the time dependent potentials in quantum pumping can not
only cause inelastic scatterings but also break the micro-reversibility, i.e.
, the Pauli blocking factor is unnecessary when the
scattering process through the scatterer is coherent. The well defined
scattering states extending from one reservoir to the others form a complete
non-orthogonal set. Regardless of the non-orthogonality one can obtain the
pumped currents using the field operator formalism. The current expression
finally obtained do not contain Pauli blocking factor.Comment: 4 pages, 2 figure
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