10,403 research outputs found
Partial Isometries of a Sub-Riemannian Manifold
In this paper, we obtain the following generalisation of isometric
-immersion theorem of Nash and Kuiper. Let be a smooth manifold of
dimension and a rank subbundle of the tangent bundle with a
Riemannian metric . Then the pair defines a sub-Riemannian
structure on . We call a -map into a Riemannian
manifold a {\em partial isometry} if the derivative map restricted
to is isometric; in other words, . The main result states that
if then a smooth -immersion satisfying
can be homotoped to a partial isometry which is
-close to . In particular we prove that every sub-Riemannian manifold
admits a partial isometry in provided .Comment: 13 pages. This is a revised version of an earlier submission (minor
revision
Electron transport through an interacting region: The case of a nonorthogonal basis set
The formula derived by Meir and Wingreen [Phys. Rev. Lett. {\bf 68}, 2512
(1992)] for the electron current through a confined, central region containing
interactions is generalized to the case of a nonorthogonal basis set. As in the
original work, the present derivation is based on the nonequilibrium Keldysh
formalism. By replacing the basis functions of the central region by the
corresponding elements of the dual basis, the lead- and central
region-subspaces become mutually orthogonal. The current formula is then
derived in the new basis, using a generalized version of second quantization
and Green's function theory to handle the nonorthogonality within each of the
regions. Finally, the appropriate nonorthogonal form of the perturbation series
for the Green's function is established for the case of electron-electron and
electron-phonon interactions in the central region.Comment: Added references. 8 pages, 1 figur
Effect of gas flow on electronic transport in a DNA-decorated carbon nanotube
We calculate the two-time current correlation function using the experimental
data of the current-time characteristics of the Gas-DNA-decorated carbon
nanotube field effect transistor. The pattern of the correlation function is a
measure of the sensitivity and selectivity of the sensors and suggest that
these gas flow sensors may also be used as DNA sequence detectors. The system
is modelled by a one-dimensional tight-binding Hamiltonian and we present
analytical calculations of quantum electronic transport for the system using
the time-dependent nonequilibrium Green's function formalism and the adiabatic
expansion. The zeroth and first order contributions to the current
and are calculated, where is the Landauer formula. The formula for the time-dependent current
is then used to compare the theoretical results with the experiment.Comment: 14 pages, 5 figures and 2 table
Weak coupling approximations in non-Markovian Transport
We study the transport properties of the Fano-Anderson model with a
Lorentzian-shaped density of states in one of the electronic reservoirs. We
explicitly show that the energy dependence of the density of states can cause
non-Markovian effects and that the non-Markovian master equation may fail if
these effects are strong. We evaluate the stationary current, the zero
frequency current noise and the occupation dynamics of the resonant level by
means of a quantum master equation approach within different approximation
schemes and compare the results to the exact solution obtained by scattering
theory and Green's functions.Comment: 9 pages, 6 figures; due to suggestions of a referee we have added an
appendix where our kernel is derived in detail; a few typos are correcte
Ballistic-Ohmic quantum Hall plateau transition in graphene pn junction
Recent quantum Hall experiments conducted on disordered graphene pn junction
provide evidence that the junction resistance could be described by a simple
Ohmic sum of the n and p mediums' resistances. However in the ballistic limit,
theory predicts the existence of chirality-dependent quantum Hall plateaus in a
pn junction. We show that two distinctively separate processes are required for
this ballistic-Ohmic plateau transition, namely (i) hole/electron Landau states
equilibration and (ii) valley iso-spin dilution of the incident Landau edge
state. These conclusions are obtained by a simple scattering theory argument,
and confirmed numerically by performing ensembles of quantum magneto-transport
calculations on a 0.1um-wide disordered graphene pn junction within the
tight-binding model. The former process is achieved by pn interface roughness,
where a pn interface disorder with a root-mean-square roughness of 10nm was
found to suffice under typical experimental conditions. The latter process is
mediated by extrinsic edge roughness for an armchair edge ribbon and by
intrinsic localized intervalley scattering centers at the edge of the pn
interface for a zigzag ribbon. In light of these results, we also examine why
higher Ohmic type plateaus are less likely to be observable in experiments.Comment: 9 pages, 6 figure
Enhancement of shot noise due to the fluctuation of Coulomb interaction
We have developed a theoretical formalism to investigate the contribution of
fluctuation of Coulomb interaction to the shot noise based on Keldysh
non-equilibrium Green's function method. We have applied our theory to study
the behavior of dc shot noise of atomic junctions using the method of
nonequilibrium Green's function combined with the density functional theory
(NEGF-DFT). In particular, for atomic carbon wire consisting 4 carbon atoms in
contact with two Al(100) electrodes, first principles calculation within
NEGF-DFT formalism shows a negative differential resistance (NDR) region in I-V
curve at finite bias due to the effective band bottom of the Al lead. We have
calculated the shot noise spectrum using the conventional gauge invariant
transport theory with Coulomb interaction considered explicitly on the Hartree
level along with exchange and correlation effect. Although the Fano factor is
enhanced from 0.6 to 0.8 in the NDR region, the expected super-Poissonian
behavior in the NDR regionis not observed. When the fluctuation of Coulomb
interaction is included in the shot noise, our numerical results show that the
Fano factor is greater than one in the NDR region indicating a super-Poissonian
behavior
Relevance of Induced Gauge Interactions in Decoherence
Decoherence in quantum cosmology is shown to occur naturally in the presence
of induced geometric gauge interactions associated with particle production.A
new 'gauge '-variant form of the semiclassical Einstein equations is also
presented which makes the non-gravitating character of the vacuum polarisation
energy explicit.Comment: 10 pages, LATEX, IC/94/16
Hall of Mirrors Scattering from an Impurity in a Quantum Wire
This paper develops a scattering theory to examine how point impurities
affect transport through quantum wires. While some of our new results apply
specifically to hard-walled wires, others--for example, an effective optical
theorem for two-dimensional waveguides--are more general. We apply the method
of images to the hard-walled guide, explicitly showing how scattering from an
impurity affects the wire's conductance. We express the effective cross section
of a confined scatterer entirely in terms of the empty waveguide's Green's
function, suggesting a way in which to use semiclassical methods to understand
transport properties of smooth wires. In addition to predicting some new
phenomena, our approach provides a simple physical picture for previously
observed effects such as conductance dips and confinement-induced resonances.Comment: 19 pages, 8 figures. Accepted for publication in Physical Review B.
Minor additions to text, added reference
New Asymptotic Expanstion Method for the Wheeler-DeWitt Equation
A new asymptotic expansion method is developed to separate the Wheeler-DeWitt
equation into the time-dependent Schr\"{o}dinger equation for a matter field
and the Einstein-Hamilton-Jacobi equation for the gravitational field including
the quantum back-reaction of the matter field. In particular, the nonadiabatic
basis of the generalized invariant for the matter field Hamiltonian separates
the Wheeler-DeWitt equation completely in the asymptotic limit of
approaching infinity. The higher order quantum corrections of the gravity to
the matter field are found. The new asymptotic expansion method is valid
throughout all regions of superspace compared with other expansion methods with
a certain limited region of validity. We apply the new asymptotic expansion
method to the minimal FRW universe.Comment: 24 pages of Latex file, revte
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