2,800 research outputs found
Trees and the dynamics of polynomials
The basin of infinity of a polynomial map f : {\bf C} \arrow {\bf C}
carries a natural foliation and a flat metric with singularities, making it
into a metrized Riemann surface . As diverges in the moduli space of
polynomials, the surface collapses along its foliation to yield a
metrized simplicial tree , with limiting dynamics F : T \arrow T.
In this paper we characterize the trees that arise as limits, and show they
provide a natural boundary \PT_d compactifying the moduli space of
polynomials of degree . We show that records the limiting
behavior of multipliers at periodic points, and that any divergent meromorphic
family of polynomials \{f_t(z) : t \mem \Delta^* \} can be completed by a
unique tree at its central fiber. Finally we show that in the cubic case, the
boundary of moduli space \PT_3 is itself a tree.
The metrized trees provide a counterpart, in the setting of
iterated rational maps, to the -trees that arise as limits of
hyperbolic manifolds.Comment: 60 page
Percutaneous Nephrolithotomy in Children
The surgical management of pediatric stone disease has evolved significantly over the last three decades. Prior to the introduction of shockwave lithotripsy (SWL) in the 1980s, open lithotomy was the lone therapy for children with upper tract calculi. Since then, SWL has been the procedure of choice in most pediatric centers for children with large renal calculi. While other therapies such as percutaneous nephrolithotomy (PNL) were also being advanced around the same time, PNL was generally seen as a suitable therapy in adults because of the concerns for damage in the developing kidney. However, recent advances in endoscopic instrumentation and renal access techniques have led to an increase in its use in the pediatric population, particularly in those children with large upper tract stones. This paper is a review of the literature focusing on the indications, techniques, results, and complications of PNL in children with renal calculi
Rapidly Rotating Fermi Gases
We show that the density profile of a Fermi gas in rapidly rotating potential
will develop prominent features reflecting the underlying Landau level like
energy spectrum. Depending on the aspect ratio of the trap, these features can
be a sequence of ellipsoidal volumes or a sequence of quantized steps.Comment: 4 pages, 1 postscript fil
Random-phase approximation study of collective excitations in the Bose-Fermi mixed condensate of alkali-metal gases
We perform Random Phase Approximation (RPA) study of collective excitations
in the bose-fermi mixed degenerate gas of Alkali-metal atoms at T=0. The
calculation is done by diagonalization in a model space composed of
particle-hole type excitations from the ground state, the latter being obtained
from the coupled Gross-Pitaevskii and Thomas-Fermi equations. We investigate
strength distributions for different combinations of bose and fermi multipole
() operators with . Transition densities and dynamical structure
factors are calculated for collective excitations. Comparison with the sum rule
prediction for the collective frequency is given. Time dependent behavior of
the system after an external impulse is studied.Comment: 28 pages, 13 figures, submitted to Phys. Rev.
Quantum information processing with trapped ions
Experiments directed towards the development of a quantum computer based on
trapped atomic ions are described briefly. We discuss the implementation of
single qubit operations and gates between qubits. A geometric phase gate
between two ion qubits is described. Limitations of the trapped-ion method such
as those caused by Stark shifts and spontaneous emission are addressed.
Finally, we describe a strategy to realize a large-scale device.Comment: Article submitted by D. J. Wineland ([email protected])
for proceeding of the Discussion Meeting on Practical Realisations of Quantum
Information Processing, held at the Royal Society, Nov. 13,14, 200
Panchromatic Studies of Distant Clusters of Galaxies
High redshift (z >~ 1) clusters are ideal probes to study the formation and
evolution of large scale structures and galaxies in the universe. A 10-m class
ground based telescope, X-ray observatories (Chandra, XMM-Newton) and HST/ACS
are allowing us to perform an unprecedented study of distant massive clusters
of galaxies in the redshift range 0.84<z<1.3, selected from X-rays surveys. In
this paper we summarize our results on the structure and dynamics of two of
these clusters derived from imaging and spectroscopic data as well as our
results on the evolution of early-type galaxies.Comment: 14 pages, 2 figures. Accepted for publication in Modern Physics
Letters A (invited brief review). v2: Order of authors in the .tex version
corrected to match that in journa
Pauli Blocking of Collisions in a Quantum Degenerate Atomic Fermi Gas
We have produced an interacting quantum degenerate Fermi gas of atoms
composed of two spin-states of magnetically trapped K. The relative
Fermi energies are adjusted by controlling the population in each spin-state.
Measurements of the thermodynamics reveal the resulting imbalance in the mean
energy per particle between the two species, which is as large as a factor of
1.4 at our lowest temperature. This imbalance of energy comes from a
suppression of collisions between atoms in the gas due to the Pauli exclusion
principle. Through measurements of the thermal relaxation rate we have directly
observed this Pauli blocking as a factor of two reduction in the effective
collision cross-section in the quantum degenerate regime.Comment: 11 pages, 4 figure
Collective excitations in a fermion-fermion mixture with different Fermi surfaces
In this paper, collective excitations in a homogeneous fermion-fermion
mixture with different Fermi surfaces are studied. In the Fermi liquid phase,
the zero-sound velocity is found to be larger than the largest Fermi velocity.
With attractive interactions, the superfluid phase appears below a critical
temperature, and the phase mode is the low-energy collective excitation. The
velocity of the phase mode is proportional to the geometric mean of the two
Fermi velocities. The difference between the two velocities may serve as a tool
to detect the superfluid phase.Comment: 4 pages. To be published in Phys. Rev.
Resonant control of elastic collisions in an optically trapped Fermi gas of atoms
We have loaded an ultracold gas of fermionic atoms into a far off resonance
optical dipole trap and precisely controlled the spin composition of the
trapped gas. We have measured a magnetic-field Feshbach resonance between atoms
in the two lowest energy spin-states, |9/2, -9/2> and |9/2, -7/2>. The
resonance peaks at a magnetic field of 201.5 plus or minus 1.4 G and has a
width of 8.0 plus or minus 1.1 G. Using this resonance we have changed the
elastic collision cross section in the gas by nearly 3 orders of magnitude.Comment: 4 pages, 3 figure
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