Multiwalled carbon nanotubes are shown to be ballistic conductors at room temperature, with mean free paths of the order of tens of microns. The measurements are performed both in air and in high vacuum in the transmission electron microscope on nanotubes that protrude from unprocessed arc-produced nanotube containing fibers which contact with a liquid metal surface. These experiments follow and extend the original experiments by Frank et al (Science, 280 1744 1998) that demonstrated for the first time the large current carrying capability, very low intrinsic resistivities, and evidence for quantized conductance. This indicated 1D transport, that only the surface layer contributes to the transport, and ballistic conduction at room temperature. Here we follow up on the original experiment including in-situ electron microscopy experiments and a detailed analysis of the length dependence of the resistance. The per unit length resistance ρ < 100 Ω/µm, indicating free paths l > 65 µm, unambiguously demonstrate ballistic conduction at room temperature up to macroscopic distances. The nanotube-metal contact resistances are in the range 0.1-1 kΩµm. Contact scattering can explain why the measured conductances are about half the expected theoretical value of 2 G 0 . For V>0.1V the conductance rises linearly (dG/dV~0.3 G 0 /V) reflecting the linear increase in the density-of-states in a metallic nanotube above the energy gap. Increased resistances (ρ =2-10 kΩ/µm) and anomalous I-V dependences result from impurities and surfactants on the tubes. Evidence is presented that ballistic transport occurs in undoped and undamaged tubes for which the top layer is metallic and the next layer is semiconducting. The diffusive properties of lithographically contacted multiwalled nanotubes most likely result from purification and other processing steps that damage and dope the nanotubes thereby making them structurally and electronically different than the pristine nanotubes investigated here.

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The electrical transport in multiwalled carbon nanotubes is shown to be ballistic at room temperature with mean free paths on the order of tens of microns. The measurements are performed both in air and in the transmission electron microscope by contacting the free end of a nanotube pointing out of a fiber to a liquid metal and measuring the dependence of the nanotube resistance between the contacts. For a specific representative nanotube the resistance per unit length is found to be Rt = 31 +/- 61 omega/micron and the contact resistance with the liquid metal, Rc = 165 +/- 55 omega microns, corresponding to a mean free path l = 200 microns. Current-to-voltage characteristics are in accord with the electronic structure. The nanotubes survive high currents (up to 1 mA, i.e., current density on the order of 10(9) A/cm2). In situ electron microscopy shows that a relatively large fraction of the nanotubes do not conduct (even at high bias), consistent with the existence of semiconducting nanotubes. Discrepancies with other measurements are most likely due to damage caused to the outer layer(s) of the nanotubes during processing. The measured mean free path of clean, undamaged arc-produced multiwalled carbon nanotubes is several orders of magnitude greater than that for metals, making this perhaps the most significant property of carbon nanotubes.

Authors' note: We rephrased the abstract. We employ KAM theory to rigorously investigate quasiperiodic dynamics in cigar-shaped Bose-Einstein condensates (BEC) in periodic lattices and superlattices. Toward this end, we apply a coherent structure ansatz to the GrossPitaevskii equation to obtain a parametrically forced Duffing equation describing the spatial dynamics of the condensate. For shallow-well, intermediatewell, and deep-well potentials, we find KAM tori and Aubry-Mather sets to prove that one obtains mostly quasiperiodic dynamics for condensate wave functions of sufficiently large amplitude, where the minimal amplitude depends on the experimentally adjustable BEC parameters. We show that this threshold scales with the square root of the inverse of the two-body scattering length, whereas the rotation number of tori above this threshold is proportional to the amplitude. As a consequence, one obtains the same dynamical picture for lattices of all depths, as an increase in depth essentially only affects scaling in phase space. Our approach is applicable to periodic superlattices with an arbitrary number of rationally dependent wave numbers.MSC: 37J40, 70H99, 37N20