140,648 research outputs found
Drawing Arrangement Graphs In Small Grids, Or How To Play Planarity
We describe a linear-time algorithm that finds a planar drawing of every
graph of a simple line or pseudoline arrangement within a grid of area
O(n^{7/6}). No known input causes our algorithm to use area
\Omega(n^{1+\epsilon}) for any \epsilon>0; finding such an input would
represent significant progress on the famous k-set problem from discrete
geometry. Drawing line arrangement graphs is the main task in the Planarity
puzzle.Comment: 12 pages, 8 figures. To appear at 21st Int. Symp. Graph Drawing,
Bordeaux, 201
Complex WKB Analysis of a PT Symmetric Eigenvalue Problem
The spectra of a particular class of PT symmetric eigenvalue problems has
previously been studied, and found to have an extremely rich structure. In this
paper we present an explanation for these spectral properties in terms of
quantisation conditions obtained from the complex WKB method. In particular, we
consider the relation of the quantisation conditions to the reality and
positivity properties of the eigenvalues. The methods are also used to examine
further the pattern of eigenvalue degeneracies observed by Dorey et al. in
[1,2].Comment: 22 pages, 13 figures. Added references, minor revision
Symmetry breaking and Wigner molecules in few-electron quantum dots
We discuss symmetry breaking in two-dimensional quantum dots resulting from
strong interelectron repulsion relative to the zero-point kinetic energy
associated with the confining potential. Such symmetry breaking leads to the
emergence of crystalline arrangements of electrons in the dot. The so-called
Wigner molecules form already at field-free conditions. The appearance of
rotating Wigner molecules in circular dots under high magnetic field, and their
relation to magic angular momenta and quantum-Hall-effect fractional fillings,
is also discussed. Recent calculations for two electrons in an elliptic quantum
dot, using exact diagonalization and an approximate generalized-Heitler-London
treatment, show that the electrons can localize and form a molecular dimer for
screened interelectron repulsion. The calculated singlet-triplet splitting (J)
as a function of the magnetic field (B) agrees with cotunneling measurements;
its behavior reflects the effective dissociation of the dimer for large B.
Knowledge of the dot shape and of J(B) allows determination of two measures of
entanglement (concurrence and von Neumann entropy for indistinguishable
fermions), whose behavior correlates also with the dissociation of the dimer.
The theoretical value for the concurrence at B=0 agrees with the experimental
estimates.Comment: LATEX, 12 pages with 6 figures. Invited talk at TNT2005 (Trends in
Nanotechnology). To download a file with figures of higher quality, click
http://www.prism.gatech.edu/~ph274cy/ (go to publication #74
Practical Guide to Monte Carlo
I show how to construct Monte Carlo algorithms (programs), prove that they
are correct and document them. Complicated algorithms are build using a handful
of elementary methods. This construction process is transparently illustrated
using graphical representation in which complicated graphs consist of only
several elementary building blocks. In particular I discuss the equivalent
algorithms, that is different MC algorithms, with different arrangements of the
elementary building blocks, which generate the same final probability
distribution. I also show how to transform a given MC algorithm into another
equivalent one and discuss advantages of the various ``architectures''
From a few to many electrons in quantum dots under strong magnetic fields: Properties of rotating electron molecules with multiple rings
Using the method of breaking of circular symmetry and of subsequent symmetry
restoration via projection techiques, we present calculations for the
ground-state energies and excitation spectra of N-electron parabolic quantum
dots in strong magnetic fields in the medium-size range 10 <= N <= 30. The
physical picture suggested by our calculations is that of finite rotating
electron molecules (REMs) comprising multiple rings, with the rings rotating
independently of each other. An analytic expression for the energetics of such
non-rigid multi-ring REMs is derived; it is applicable to arbitrary sizes given
the corresponding equilibrium configuration of classical point charges. We show
that the rotating electron molecules have a non-rigid (non-classical)
rotational inertia exhibiting simultaneous crystalline correlations and
liquid-like (non-rigidity) characteristics. This mixed phase appears in high
magnetic fields and contrasts with the picture of a classical rigid Wigner
crystal in the lowest Landau level.Comment: REVTEX4, 15 pages with 12 figures. Accepted for publication in
Physical Review B. To download a file with figures of higher quality, click
http://www.prism.gatech.edu/~ph274cy/ (go to publication #72
The speed of range shifts in fragmented landscapes
Peer reviewedPublisher PD
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