6,910 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
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
Interaction-induced harmonic frequency mixing in quantum dots
We show that harmonic frequency mixing in quantum dots coupled to two leads
under the influence of time-dependent voltages of different frequency is
dominated by interaction effects. This offers a unique and direct spectroscopic
tool to access correlations, and holds promise for efficient frequency mixing
in nano-devices. Explicit results are provided for an Anderson dot and for a
molecular level with phonon-mediated interactions.Comment: 4 pages, 2 figures, accepted for publication in Phys.Rev.Let
Engineering adiabaticity at an avoided crossing with optimal control
We investigate ways to optimize adiabaticity and diabaticity in the
Landau-Zener model with non-uniform sweeps. We show how diabaticity can be
engineered with a pulse consisting of a linear sweep augmented by an
oscillating term. We show that the oscillation leads to jumps in populations
whose value can be accurately modeled using a model of multiple,
photon-assisted Landau-Zener transitions, which generalizes work by Wubs et al.
[New J. Phys. 7, 218 (2005)]. We extend the study on diabaticity using methods
derived from optimal control. We also show how to preserve adiabaticity with
optimal pulses at limited time, finding a non-uniform quantum speed limit
Applying voltage sources to a Luttinger liquid with arbitrary transmission
The Landauer approach to transport in mesoscopic conductors has been
generalized to allow for strong electronic correlations in a single-channel
quantum wire. We describe in detail how to account for external voltage sources
in adiabatic contact with a quantum wire containing a backscatterer of
arbitrary strength. Assuming that the quantum wire is in the Luttinger liquid
state, voltage sources lead to radiative boundary conditions applied to the
displacement field employed in the bosonization scheme. We present the exact
solution of the transport problem for arbitrary backscattering strength at the
special Coulomb interaction parameter g=1/2.Comment: 9 pages REVTeX, incl 2 fig
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