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 $\alpha$ 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

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

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

Coulomb charging energy for arbitrary tunneling strength

The Coulomb energy of a small metallic island coupled to an electrode by a tunnel junction is investigated. We employ Monte Carlo simulations to determine the effective charging energy for arbitrary tunneling strength. For small tunneling conductance, the data agree with analytical results based on a perturbative treatment of electron tunneling, while for very strong tunneling recent semiclassical results for large conductance are approached. The data allow for an identification of the range of validity of various analytical predictions.Comment: 4 pages REVTeX, incl 3 figures, to appear in Europhys.Let

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 $0.01-0.1$ eV.Comment: 4 pages, 2 figure