Stability of 1-D Excitons in Carbon Nanotubes under High Laser Excitations

Through ultrafast pump-probe spectroscopy with intense pump pulses and a wide continuum probe, we show that interband exciton peaks in single-walled carbon nanotubes (SWNTs) are extremely stable under high laser excitations. Estimates of the initial densities of excitons from the excitation conditions, combined with recent theoretical calculations of exciton Bohr radii for SWNTs, suggest that their positions do not change at all even near the Mott density. In addition, we found that the presence of lowest-subband excitons broadens all absorption peaks, including those in the second-subband range, which provides a consistent explanation for the complex spectral dependence of pump-probe signals reported for SWNTs.Comment: 4 pages, 4 figure

Anomalous heat conduction and anomalous diffusion in nonlinear lattices, single walled nanotubes, and billiard gas channels

We study anomalous heat conduction and anomalous diffusion in low dimensional systems ranging from nonlinear lattices, single walled carbon nanotubes, to billiard gas channels. We find that in all discussed systems, the anomalous heat conductivity can be connected with the anomalous diffusion, namely, if energy diffusion is $\sigma^2(t)\equiv =2Dt^{\alpha} (0<\alpha\le 2)$, then the thermal conductivity can be expressed in terms of the system size $L$ as $\kappa = cL^{\beta}$ with $\beta=2-2/\alpha$. This result predicts that a normal diffusion ($\alpha =1$) implies a normal heat conduction obeying the Fourier law ($\beta=0$), a superdiffusion ($\alpha>1$) implies an anomalous heat conduction with a divergent thermal conductivity ($\beta>0$), and more interestingly, a subdiffusion ($\alpha <1$) implies an anomalous heat conduction with a convergent thermal conductivity ($\beta<0$), consequently, the system is a thermal insulator in the thermodynamic limit. Existing numerical data support our theoretical prediction.Comment: 15 Revtex pages, 16 figures. Invited article for CHAOS focus issue commemorating the 50th anniversary of the Fermi-Pasta-Ulam (FPU) mode

Thermodynamic formalism for the Lorentz gas with open boundaries in dd dimensions

A Lorentz gas may be defined as a system of fixed dispersing scatterers, with a single light particle moving among these and making specular collisions on encounters with the scatterers. For a dilute Lorentz gas with open boundaries in $d$ dimensions we relate the thermodynamic formalism to a random flight problem. Using this representation we analytically calculate the central quantity within this formalism, the topological pressure, as a function of system size and a temperature-like parameter \ba. The topological pressure is given as the sum of the topological pressure for the closed system and a diffusion term with a \ba-dependent diffusion coefficient. From the topological pressure we obtain the Kolmogorov-Sinai entropy on the repeller, the topological entropy, and the partial information dimension.Comment: 7 pages, 5 figure

Hall viscosity, orbital spin, and geometry: paired superfluids and quantum Hall systems

The Hall viscosity, a non-dissipative transport coefficient analogous to Hall conductivity, is considered for quantum fluids in gapped or topological phases. The relation to mean orbital spin per particle discovered in previous work by one of us is elucidated with the help of examples, using the geometry of shear transformations and rotations. For non-interacting particles in a magnetic field, there are several ways to derive the result (even at non-zero temperature), including standard linear response theory. Arguments for the quantization, and the robustness of Hall viscosity to small changes in the Hamiltonian that preserve rotational invariance, are given. Numerical calculations of adiabatic transport are performed to check the predictions for quantum Hall systems, with excellent agreement for trial states. The coefficient of k^4 in the static structure factor is also considered, and shown to be exactly related to the orbital spin and robust to perturbations in rotation invariant systems also.Comment: v2: Now 30 pages, 10 figures; new calculation using disk geometry; some other improvements; no change in result

Polarization dependence of coherent phonon generation and detection in highly-aligned single-walled carbon nanotubes

We have investigated the polarization dependence of the generation and detection of radial breathing mode (RBM) coherent phonons (CP) in highly-aligned single-walled carbon nanotubes. Using polarization-dependent pump-probe differential-transmission spectroscopy, we measured RBM CPs as a function of angle for two different geometries. In Type I geometry, the pump and probe polarizations were fixed, and the sample orientation was rotated, whereas, in Type II geometry, the probe polarization and sample orientation were fixed, and the pump polarization was rotated. In both geometries, we observed a very nearly complete quenching of the RBM CPs when the pump polarization was perpendicular to the nanotubes. For both Type I and II geometries, we have developed a microscopic theoretical model to simulate CP generation and detection as a function of polarization angle and found that the CP signal decreases as the angle goes from 0 degrees (parallel to the tube) to 90 degrees (perpendicular to the tube). We compare theory with experiment in detail for RBM CPs created by pumping at the E44 optical transition in an ensemble of single-walled carbon nanotubes with a diameter distribution centered around 3 nm, taking into account realistic band structure and imperfect nanotube alignment in the sample

Direct Observation of Sub-Poissonian Number Statistics in a Degenerate Bose Gas

We report the direct observation of sub-Poissonian number fluctuation for a degenerate Bose gas confined in an optical trap. Reduction of number fluctuations below the Poissonian limit is observed for average numbers that range from 300 to 60 atoms.Comment: 5 pages, 4 figure

Collective Antenna Effects in the Terahertz and Infrared Response of Highly Aligned Carbon Nanotube Arrays

We study macroscopically-aligned single-wall carbon nanotube arrays with uniform lengths via polarization-dependent terahertz and infrared transmission spectroscopy. Polarization anisotropy is extreme at frequencies less than $\sim$3 THz with no sign of attenuation when the polarization is perpendicular to the alignment direction. The attenuation for both parallel and perpendicular polarizations increases with increasing frequency, exhibiting a pronounced and broad peak around 10 THz in the parallel case. We model the electromagnetic response of the sample by taking into account both radiative scattering and absorption losses. We show that our sample acts as an effective antenna due to the high degree of alignment, exhibiting much larger radiative scattering than absorption in the mid/far-infrared range. Our calculated attenuation spectrum clearly shows a non-Drude peak at $\sim$10 THz in agreement with the experiment.Comment: 5 pages, 5 figure

Condensation of Ideal Bose Gas Confined in a Box Within a Canonical Ensemble

We set up recursion relations for the partition function and the ground-state occupancy for a fixed number of non-interacting bosons confined in a square box potential and determine the temperature dependence of the specific heat and the particle number in the ground state. A proper semiclassical treatment is set up which yields the correct small-T-behavior in contrast to an earlier theory in Feynman's textbook on Statistical Mechanics, in which the special role of the ground state was ignored. The results are compared with an exact quantum mechanical treatment. Furthermore, we derive the finite-size effect of the system.Comment: 18 pages, 8 figure