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 $\alpha$ measured for the tunneling density of states in carbon nanotubes. We predict that further reduction of $\alpha$ 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 $I_e$ {\sl even} in the applied voltage $V$ and {\sl odd} in an orbital magnetic field $B$, 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