44,091 research outputs found
Resources Required for Topological Quantum Factoring
We consider a hypothetical topological quantum computer where the qubits are
comprised of either Ising or Fibonacci anyons. For each case, we calculate the
time and number of qubits (space) necessary to execute the most computationally
expensive step of Shor's algorithm, modular exponentiation. For Ising anyons,
we apply Bravyi's distillation method [S. Bravyi, Phys. Rev. A 73, 042313
(2006)] which combines topological and non-topological operations to allow for
universal quantum computation. With reasonable restrictions on the physical
parameters we find that factoring a 128 bit number requires approximately 10^3
Fibonacci anyons versus at least 3 x 10^9 Ising anyons. Other distillation
algorithms could reduce the resources for Ising anyons substantially.Comment: 4+epsilon pages, 4 figure
Rigorous conditions for the existence of bound states at the threshold in the two-particle case
In the framework of non-relativistic quantum mechanics and with the help of
the Greens functions formalism we study the behavior of weakly bound states as
they approach the continuum threshold. Through estimating the Green's function
for positive potentials we derive rigorously the upper bound on the wave
function, which helps to control its falloff. In particular, we prove that for
potentials whose repulsive part decays slower than the bound states
approaching the threshold do not spread and eventually become bound states at
the threshold. This means that such systems never reach supersizes, which would
extend far beyond the effective range of attraction. The method presented here
is applicable in the many--body case
The first-mover advantage in scientific publication
Mathematical models of the scientific citation process predict a strong
"first-mover" effect under which the first papers in a field will, essentially
regardless of content, receive citations at a rate enormously higher than
papers published later. Moreover papers are expected to retain this advantage
in perpetuity -- they should receive more citations indefinitely, no matter how
many other papers are published after them. We test this conjecture against
data from a selection of fields and in several cases find a first-mover effect
of a magnitude similar to that predicted by the theory. Were we wearing our
cynical hat today, we might say that the scientist who wants to become famous
is better off -- by a wide margin -- writing a modest paper in next year's
hottest field than an outstanding paper in this year's. On the other hand,
there are some papers, albeit only a small fraction, that buck the trend and
attract significantly more citations than theory predicts despite having
relatively late publication dates. We suggest that papers of this kind, though
they often receive comparatively few citations overall, are probably worthy of
our attention.Comment: 7 pages, 3 figure
Simple Non Linear Klein-Gordon Equations in 2 space dimensions, with long range scattering
We establish that solutions, to the most simple NLKG equations in 2 space
dimensions with mass resonance, exhibits long range scattering phenomena.
Modified wave operators and solutions are constructed for these equations. We
also show that the modified wave operators can be chosen such that they
linearize the non-linear representation of the Poincar\'e group defined by the
NLKG.Comment: 19 pages, LaTeX, To appear in Lett. Math. Phy
Proof of Bose-Einstein Condensation for Dilute Trapped Gases
The ground state of bosonic atoms in a trap has been shown experimentally to
display Bose-Einstein condensation (BEC). We prove this fact theoretically for
bosons with two-body repulsive interaction potentials in the dilute limit,
starting from the basic Schroedinger equation; the condensation is 100% into
the state that minimizes the Gross-Pitaevskii energy functional. This is the
first rigorous proof of BEC in a physically realistic, continuum model.Comment: Revised version with some simplifications and clarifications. To
appear in Phys. Rev. Let
Spinful Composite Fermions in a Negative Effective Field
In this paper we study fractional quantum Hall composite fermion
wavefunctions at filling fractions \nu = 2/3, 3/5, and 4/7. At each of these
filling fractions, there are several possible wavefunctions with different spin
polarizations, depending on how many spin-up or spin-down composite fermion
Landau levels are occupied. We calculate the energy of the possible composite
fermion wavefunctions and we predict transitions between ground states of
different spin polarizations as the ratio of Zeeman energy to Coulomb energy is
varied. Previously, several experiments have observed such transitions between
states of differing spin polarization and we make direct comparison of our
predictions to these experiments. For more detailed comparison between theory
and experiment, we also include finite-thickness effects in our calculations.
We find reasonable qualitative agreement between the experiments and composite
fermion theory. Finally, we consider composite fermion states at filling
factors \nu = 2+2/3, 2+3/5, and 2+4/7. The latter two cases we predict to be
spin polarized even at zero Zeeman energy.Comment: 17 pages, 5 figures, 4 tables. (revision: incorporated referee
suggestions, note added, updated references
Nuclear skin emergence in Skyrme deformed Hartree-Fock calculations
A study of the charge and matter densities and the corresponding rms radii
for even-even isotopes of Ni, Kr, and Sn has been performed in the framework of
deformed self-consistent mean field Skyrme HF+BCS method. The resulting charge
radii and neutron skin thicknesses of these nuclei are compared with available
experimental data, as well as with other theoretical predictions. The formation
of a neutron skin, which manifests itself in an excess of neutrons at distances
greater than the radius of the proton distribution, is analyzed in terms of
various definitions. Formation of a proton skin is shown to be unlikely. The
effects of deformation on the neutron skins in even-even deformed nuclei far
from the stability line are discussed.Comment: 16 pages, 17 figures, to be published in Physical Review
Nuclear effects in atomic transitions
Atomic electrons are sensitive to the properties of the nucleus they are
bound to, such as nuclear mass, charge distribution, spin, magnetization
distribution, or even excited level scheme. These nuclear parameters are
reflected in the atomic transition energies. A very precise determination of
atomic spectra may thus reveal information about the nucleus, otherwise hardly
accessible via nuclear physics experiments. This work reviews theoretical and
experimental aspects of the nuclear effects that can be identified in atomic
structure data. An introduction to the theory of isotope shifts and hyperfine
splitting of atomic spectra is given, together with an overview of the typical
experimental techniques used in high-precision atomic spectroscopy. More exotic
effects at the borderline between atomic and nuclear physics, such as parity
violation in atomic transitions due to the weak interaction, or nuclear
polarization and nuclear excitation by electron capture, are also addressed.Comment: review article, 53 pages, 14 figure
Hamilton's Turns for the Lorentz Group
Hamilton in the course of his studies on quaternions came up with an elegant
geometric picture for the group SU(2). In this picture the group elements are
represented by ``turns'', which are equivalence classes of directed great
circle arcs on the unit sphere , in such a manner that the rule for
composition of group elements takes the form of the familiar parallelogram law
for the Euclidean translation group. It is only recently that this construction
has been generalized to the simplest noncompact group , the double cover of SO(2,1). The present work develops a theory of
turns for , the double and universal cover of SO(3,1) and ,
rendering a geometric representation in the spirit of Hamilton available for
all low dimensional semisimple Lie groups of interest in physics. The geometric
construction is illustrated through application to polar decomposition, and to
the composition of Lorentz boosts and the resulting Wigner or Thomas rotation.Comment: 13 pages, Late
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