1,457 research outputs found
Low rank positive partial transpose states and their relation to product vectors
It is known that entangled mixed states that are positive under partial
transposition (PPT states) must have rank at least four. In a previous paper we
presented a classification of rank four entangled PPT states which we believe
to be complete. In the present paper we continue our investigations of the low
rank entangled PPT states. We use perturbation theory in order to construct
rank five entangled PPT states close to the known rank four states, and in
order to compute dimensions and study the geometry of surfaces of low rank PPT
states. We exploit the close connection between low rank PPT states and product
vectors. In particular, we show how to reconstruct a PPT state from a
sufficient number of product vectors in its kernel. It may seem surprising that
the number of product vectors needed may be smaller than the dimension of the
kernel.Comment: 29 pages, 4 figure
A Comparison of the Achievement Records of a United States History Class Taught by Socialized Methods and a United States History Class Taught by the Lecture-question Method
The basic problem confronting all teachers is how to help each student develop himself to full capacity, mentally and socially. Lack of student interest is often an important factor in the consideration of poor school records. This lack of interest is especially apparent in such courses as government and history. Various educators have suggested improved methods of instruction as one answer to this problem. Proponents of socialized recitation claim that the emphasis must be taken from the teacher and placed on the pupils. They believe that attitudes developed through study and classroom procedures are more important than the acquisition of knowledge. The aim of this study is to compare the achievement records of two United States History classes, in which different teaching procedures were used, and to find out which group made the most progress
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 , then the thermal conductivity can be expressed in terms of the system size
as with . This result predicts that
a normal diffusion () implies a normal heat conduction obeying the
Fourier law (), a superdiffusion () implies an anomalous
heat conduction with a divergent thermal conductivity (), and more
interestingly, a subdiffusion () implies an anomalous heat
conduction with a convergent thermal conductivity (), 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
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
Wetting of Curved Surfaces
As a first step towards a microscopic understanding of the effective
interaction between colloidal particles suspended in a solvent we study the
wetting behavior of one-component fluids at spheres and fibers. We describe
these phenomena within density functional theory which keeps track of the
microscopic interaction potentials governing these systems. In particular we
properly take into account the power-law decay of both the fluid-fluid
interaction potentials and the substrate potentials. The thicknesses of the
wetting films as a function of temperature and chemical potential as well as
the wetting phase diagrams are determined by minimizing an effective interface
potential which we obtain by applying a sharp-kink approximation to the density
functional. We compare our results with previous approaches to this problem.Comment: 54 pages, 17 figures, accepted for publication in Physica
Thermodynamic formalism for the Lorentz gas with open boundaries in 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 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
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
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