3,962 research outputs found
Parameter identification in a semilinear hyperbolic system
We consider the identification of a nonlinear friction law in a
one-dimensional damped wave equation from additional boundary measurements.
Well-posedness of the governing semilinear hyperbolic system is established via
semigroup theory and contraction arguments. We then investigte the inverse
problem of recovering the unknown nonlinear damping law from additional
boundary measurements of the pressure drop along the pipe. This coefficient
inverse problem is shown to be ill-posed and a variational regularization
method is considered for its stable solution. We prove existence of minimizers
for the Tikhonov functional and discuss the convergence of the regularized
solutions under an approximate source condition. The meaning of this condition
and some arguments for its validity are discussed in detail and numerical
results are presented for illustration of the theoretical findings
Doping- and size-dependent suppression of tunneling in carbon nanotubes
We study the effect of doping in the suppression of tunneling observed in
multi-walled nanotubes, incorporating as well the influence of the finite
dimensions of the system. A scaling approach allows us to encompass the
different values of the critical exponent measured for the tunneling
density of states in carbon nanotubes. We predict that further reduction of
should be observed in multi-walled nanotubes with a sizeable amount
of doping. In the case of nanotubes with a very large radius, we find a
pronounced crossover between a high-energy regime with persistent
quasiparticles and a low-energy regime with the properties of a one-dimensional
conductor.Comment: 4 pages, 2 figures, LaTeX file, pacs: 71.10.Pm, 71.20.Tx, 72.80.R
Coulomb drag shot noise in coupled Luttinger liquids
Coulomb drag shot noise has been studied theoretically for 1D interacting
electron systems, which are realized e.g. in single-wall nanotubes. We show
that under adiabatic coupling to external leads, the Coulomb drag shot noise of
two coupled or crossed nanotubes contains surprising effects, in particular a
complete locking of the shot noise in the tubes. In contrast to Coulomb drag of
the average current, the noise locking is based on a symmetry of the underlying
Hamiltonian and is not limited to asymptotically small energy scales.Comment: 4 pages Revtex, accepted for publication in PR
Regularization independent of the noise level: an analysis of quasi-optimality
The quasi-optimality criterion chooses the regularization parameter in
inverse problems without taking into account the noise level. This rule works
remarkably well in practice, although Bakushinskii has shown that there are
always counterexamples with very poor performance. We propose an average case
analysis of quasi-optimality for spectral cut-off estimators and we prove that
the quasi-optimality criterion determines estimators which are rate-optimal
{\em on average}. Its practical performance is illustrated with a calibration
problem from mathematical finance.Comment: 18 pages, 3 figure
Transport theory of carbon nanotube Y junctions
We describe a generalization of Landauer-B\"uttiker theory for networks of
interacting metallic carbon nanotubes. We start with symmetric starlike
junctions and then extend our approach to asymmetric systems. While the
symmetric case is solved in closed form, the asymmetric situation is treated by
a mix of perturbative and non-perturbative methods. For N>2 repulsively
interacting nanotubes, the only stable fixed point of the symmetric system
corresponds to an isolated node. Detailed results for both symmetric and
asymmetric systems are shown for N=3, corresponding to carbon nanotube Y
junctions.Comment: submitted to New Journal of Physics, Focus Issue on Carbon Nanotubes,
15 pages, 3 figure
Electroneutrality and the Friedel sum rule in a Luttinger liquid
Screening in one-dimensional metals is studied for arbitrary
electron-electron interactions. It is shown that for finite-range interactions
(Luttinger liquid) electroneutrality is violated. This apparent inconsistency
can be traced to the presence of external screening gates responsible for the
effectively short-ranged Coulomb interactions. We also draw attention to the
breakdown of linear screening for wavevectors close to 2 K_f.Comment: 4 pages REVTeX, incl one figure, to appear in Phys.Rev.Let
Electronic Properties of Armchair Carbon Nanotubes : Bosonization Approach
The phase Hamiltonian of armchair carbon nanotubes at half-filling and away
from it is derived from the microscopic lattice model by taking the long range
Coulomb interaction into account. We investigate the low energy properties of
the system using the renormalization group method. At half-filling, the ground
state is a Mott insulator with spin gap, in which the bound states of electrons
at different atomic sublattices are formed. The difference from the recent
results [Phys. Rev. Lett. 79, 5082 (1997)] away half-filling is clarified.Comment: 4 pages, 1 figure, Revte
Universality of electron correlations in conducting carbon nanotubes
Effective low-energy Hamiltonian of interacting electrons in conducting
single-wall carbon nanotubes with arbitrary chirality is derived from the
microscopic lattice model. The parameters of the Hamiltonian show very weak
dependence on the chiral angle, which makes the low energy properties of
conducting chiral nanotubes universal. The strongest Mott-like electron
instability at half filling is investigated within the self-consistent harmonic
approximation. The energy gaps occur in all modes of elementary excitations and
estimate at eV.Comment: 4 pages, 2 figure
Low-temperature dynamical simulation of spin-boson systems
The dynamics of spin-boson systems at very low temperatures has been studied
using a real-time path-integral simulation technique which combines a
stochastic Monte Carlo sampling over the quantum fluctuations with an exact
treatment of the quasiclassical degrees of freedoms. To a large degree, this
special technique circumvents the dynamical sign problem and allows the
dynamics to be studied directly up to long real times in a numerically exact
manner. This method has been applied to two important problems: (1) crossover
from nonadiabatic to adiabatic behavior in electron transfer reactions, (2) the
zero-temperature dynamics in the antiferromagnetic Kondo region 1/2<K<1 where K
is Kondo's parameter.Comment: Phys. Rev. B (in press), 28 pages, 6 figure
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