10,222 research outputs found
On the effects of irrelevant boundary scaling operators
We investigate consequences of adding irrelevant (or less relevant) boundary
operators to a (1+1)-dimensional field theory, using the Ising and the boundary
sine-Gordon model as examples. In the integrable case, irrelevant perturbations
are shown to multiply reflection matrices by CDD factors: the low-energy
behavior is not changed, while various high-energy behaviors are possible,
including ``roaming'' RG trajectories. In the non-integrable case, a Monte
Carlo study shows that the IR behavior is again generically unchanged, provided
scaling variables are appropriately renormalized.Comment: 4 Pages RevTeX, 3 figures (eps files
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
Nonlinear magnetotransport in interacting chiral nanotubes
Nonlinear transport through interacting single-wall nanotubes containing a
few impurities is studied theoretically. Extending the Luttinger liquid theory
to incorporate trigonal warping and chirality effects, we derive the current
contribution {\sl even} in the applied voltage and {\sl odd} in an
orbital magnetic field , which is non-zero only for chiral tubes and in the
presence of interactions.Comment: 4 pages, 1 figure, minor changes, to appear in PR
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
A Space-Time Discontinuous Galerkin Trefftz Method for time dependent Maxwell's equations
We consider the discretization of electromagnetic wave propagation problems
by a discontinuous Galerkin Method based on Trefftz polynomials. This method
fits into an abstract framework for space-time discontinuous Galerkin methods
for which we can prove consistency, stability, and energy dissipation without
the need to completely specify the approximation spaces in detail. Any method
of such a general form results in an implicit time-stepping scheme with some
basic stability properties. For the local approximation on each space-time
element, we then consider Trefftz polynomials, i.e., the subspace of
polynomials that satisfy Maxwell's equations exactly on the respective element.
We present an explicit construction of a basis for the local Trefftz spaces in
two and three dimensions and summarize some of their basic properties. Using
local properties of the Trefftz polynomials, we can establish the
well-posedness of the resulting discontinuous Galerkin Trefftz method.
Consistency, stability, and energy dissipation then follow immediately from the
results about the abstract framework. The method proposed in this paper
therefore shares many of the advantages of more standard discontinuous Galerkin
methods, while at the same time, it yields a substantial reduction in the
number of degrees of freedom and the cost for assembling. These benefits and
the spectral convergence of the scheme are demonstrated in numerical tests
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
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