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

The North American Freshwater Turtle Research Group (NAFTRG): An undergraduate research experience (URE) and citizen scientist project

Researchers today understand the importance of incorporating undergraduate research experiences (URE) and citizen-science methods into data collection and long-term research projects. The North American Freshwater Turtle Research Group (NAFTRG) is an example of a project in which both methods are implemented. The NAFTRG conducts long-term studies on turtle populations in seven state park springs in Florida and the largest freshwater spring in Texas. Although the study began as an undergraduate biology class, it has expanded throughout the years into a study that many parks and researchers rely upon for important data on turtle populations and for information that helps manage the stability of ecosystems. Through the use of UREs, the research investigators are enabling undergraduates to gain valuable research experiences while maintaining a volunteer base that has a vested interest in the study itself. Students from Pennsylvania State University, University of North Florida, Peninsula College, Freed-Hardeman University, and Western Washington University have chosen to participate in the study. Many of these students have volunteered additional time and efforts during subsequent research trips. A project of this nature enables students to see the importance of ecosystem awareness. Through the use of citizen science, investigators can form a large volunteer base while incorporating sophisticated ecological methodologies and furthering coonservation efforts. Many participating citizen scientists have jobs unrelated to the sciences; they volunteer their time because they understand the importance of the group’s objectives and are willing to support them with their time and energy. Our current volunteer base receives further support from local zoos, aquariums, amusement parks, and the public. Based on standardized values for volunteer work, citizen scientists and donations from governmental and non-governmental organizations have contributed approximately one million dollars to this project. Citizen science is helping to bridge the gap between the general public and the scientific community by allowing the two to work together in monitoring, managing, maintaining, and understanding the ecological issues around us. &nbsp

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

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

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

Plasma Analogy and Non-Abelian Statistics for Ising-type Quantum Hall States

We study the non-Abelian statistics of quasiparticles in the Ising-type quantum Hall states which are likely candidates to explain the observed Hall conductivity plateaus in the second Landau level, most notably the one at filling fraction nu=5/2. We complete the program started in Nucl. Phys. B 506, 685 (1997) and show that the degenerate four-quasihole and six-quasihole wavefunctions of the Moore-Read Pfaffian state are orthogonal with equal constant norms in the basis given by conformal blocks in a c=1+1/2 conformal field theory. As a consequence, this proves that the non-Abelian statistics of the excitations in this state are given by the explicit analytic continuation of these wavefunctions. Our proof is based on a plasma analogy derived from the Coulomb gas construction of Ising model correlation functions involving both order and (at most two) disorder operators. We show how this computation also determines the non-Abelian statistics of collections of more than six quasiholes and give an explicit expression for the corresponding conformal block-derived wavefunctions for an arbitrary number of quasiholes. Our method also applies to the anti-Pfaffian wavefunction and to Bonderson-Slingerland hierarchy states constructed over the Moore-Read and anti-Pfaffian states.Comment: 68 pages, 3 figures; v2: substantial revisions and additions for clarity, minor correction

A new model for simulating colloidal dynamics

We present a new hybrid lattice-Boltzmann and Langevin molecular dynamics scheme for simulating the dynamics of suspensions of spherical colloidal particles. The solvent is modeled on the level of the lattice-Boltzmann method while the molecular dynamics is done for the solute. The coupling between the two is implemented through a frictional force acting both on the solvent and on the solute, which depends on the relative velocity. A spherical colloidal particle is represented by interaction sites at its surface. We demonstrate that this scheme quantitatively reproduces the translational and rotational diffusion of a neutral spherical particle in a liquid and show preliminary results for a charged spherical particle. We argue that this method is especially advantageous in the case of charged colloids.Comment: For a movie click on the link below Fig

Anomalous fluctuations of the condensate in interacting Bose gases

We find that the fluctuations of the condensate in a weakly interacting Bose gas confined in a box of volume $V$ follow the law $\sim V^{4/3}$. This anomalous behaviour arises from the occurrence of infrared divergencies due to phonon excitations and holds also for strongly correlated Bose superfluids. The analysis is extended to an interacting Bose gas confined in a harmonic trap where the fluctuations are found to exhibit a similar anomaly.Comment: 4 pages, RevTe

Interfacial fluctuations near the critical filling transition

We propose a method to describe the short-distance behavior of an interface fluctuating in the presence of the wedge-shaped substrate near the critical filling transition. Two different length scales determined by the average height of the interface at the wedge center can be identified. On one length scale the one-dimensional approximation of Parry et al. \cite{Parry} which allows to find the interfacial critical exponents is extracted from the full description. On the other scale the short-distance fluctuations are analyzed by the mean-field theory.Comment: 13 pages, 3 figure

Density expansion for transport coefficients: Long-wavelength versus Fermi surface nonanalyticities

The expansion of the conductivity in 2-d quantum Lorentz models in terms of the scatterer density n is considered. We show that nonanalyticities in the density expansion due to scattering processes with small and large momentum transfers, respectively, have different functional forms. Some of the latter are not logarithmic, but rather of power-law nature, in sharp contrast to the 3-d case. In a 2-d model with point-like scatterers we find that the leading nonanalytic correction to the Boltzmann conductivity, apart from the frequency dependent weak-localization term, is of order n^{3/2}.Comment: 4 pp., REVTeX, epsf, 3 eps figs, final version as publishe