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

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

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

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

Field emission from Luttinger liquids and single-wall carbon nanotubes

We develop a theory for the field emission effect in Luttinger liquids and single-wall carbon nanotubes at the level of the energy resolved current distribution. We generalise Fowler-Nordheim relations. Just below the Fermi edge, we find a power-law vanishing current distribution with the density of states exponent. The current distribution above the Fermi edge owes its existence to a peculiar interplay of interactions and correlated tunnelling. It displays a non-trivial power-law divergence just above the Fermi energy.Comment: 4 pages, 2 figures (eps files

Form-factors computation of Friedel oscillations in Luttinger liquids

We show how to analytically determine for $g\leq 1/2$ the "Friedel oscillations" of charge density by a single impurity in a 1D Luttinger liquid of spinless electrons.Comment: Revtex, epsf, 4pgs, 2fig

Interaction Constants and Dynamic Conductance of a Gated Wire

We show that the interaction constant governing the long-range electron-electron interaction in a quantum wire coupled to two reservoirs and capacitively coupled to a gate can be determined by a low frequency measurement. We present a self-consistent, charge and current conserving theory of the full conductance matrix. The collective excitation spectrum consists of plasma modes with a relaxation rate which increases with the interaction strength and is inversely proportional to the length of the wire. The interaction parameter is determined by the first two coefficients of the out-of-phase component of the dynamic conductance measured at the gate.Comment: 4 pages, LaTeX, 2 figure

Multi-particle effects in non-equilibrium electron tunnelling and field emission

We investigate energy resolved electric current from various correlated host materials under out-of-equilibrium conditions. We find that, due to a combined effect of electron-electron interactions, non-equilibrium and multi-particle tunnelling, the energy resolved current is finite even above the Fermi edge of the host material. In most cases, the current density possesses a singularity at the Fermi level revealing novel manifestations of correlation effects in electron tunnelling. By means of the Keldysh non-equilibrium technique, the current density is calculated for one-dimensional interacting electron systems and for two-dimensional systems, both in the pure limit and in the presence of disorder. We then specialise to the field emission and provide a comprehensive theoretical study of this effect in carbon nanotubes.Comment: 22 pages, 8 figures (eps files

RKKY interaction and Kondo screening cloud for correlated electrons

The RKKY law and the Kondo screening cloud around a magnetic impurity are investigated for correlated electrons in 1D (Luttinger liquid). We find slow algebraic distance dependences, with a crossover between both types of behavior. Monte Carlo simulations have been developed to study this crossover. In the strong coupling regime, the Knight shift is shown to increase with distance due to correlations.Comment: 5 pages REVTeX, incl two figures, to appear in Phys.Rev.