2,422,469 research outputs found
Grover Algorithm with zero theoretical failure rate
In standard Grover's algorithm for quantum searching, the probability of
finding the marked item is not exactly 1. In this Letter we present a modified
version of Grover's algorithm that searches a marked state with full successful
rate. The modification is done by replacing the phase inversion by two phase
rotation through angle . The rotation angle is given analytically to be
, where
, the number of items in the database, and
an integer equal to or greater than the integer part of . Upon measurement at -th iteration, the marked state
is obtained with certainty.Comment: 5 pages. Accepted for publication in Physical Review
Regularization of gravity theories and local Lorentz transformation
We regularized the field equations of gravity theories such that the
effect of Local Lorentz Transformation (LLT), in the case of spherical
symmetry, is removed. A "general tetrad field", with an arbitrary function of
radial coordinate preserving spherical symmetry is provided. We split that
tetrad field into two matrices; the first represents a LLT, which contains an
arbitrary function, the second matrix represents a proper tetrad field which is
a solution to the field equations of gravitational theory, (which are
not invariant under LLT). This "general tetrad field" is then applied to the
regularized field equations of . We show that the effect of the arbitrary
function which is involved in the LLT invariably disappears.Comment: 12 page
Pair condensation of polarized fermions in the BCS-BEC crossover
We investigate a two-component Fermi gas with unequal spin populations along
the BCS-BEC crossover. By using the extended BCS equations and the concept of
off-diagonal-long-range-order we derive a formula for the condensate number of
Cooper pairs as a function of energy gap, average chemical potential, imbalance
chemical potential and temperature. Then we study the zero-temperature
condensate fraction of Cooper pairs by varying interaction strength and
polarization, finding a depletion of the condensate fraction by increasing the
population imbalance. We also consider explicitly the presence of an external
harmonic confinement and we study, within the local-density approximation, the
phase separation between superfluid and normal phase regions of the polarized
fermionic cloud. In particular, we calculate both condensate density profiles
and total density profiles from the inner superfluid core to the normal region
passing for the interface, where a finite jump in the density is a clear
manifestation of this phase-separated regime. Finally, we compare our
theoretical results with the available experimental data on the condensate
fraction of polarized 6Li atoms [Science 311, 492 (2006)]. These experimental
data are in reasonable agreement with our predictions in a suitable range of
polarizations, but only in the BCS side of the crossover up to unitarity.Comment: 13 pages, 3 figures, improved version, added a section on the
interpretation of the results, to be published in J. Phys.
On the Regularization of Kerr-NUT spacetime: I
Within the framework of teleparallel equivalent of general relativity (TEGR)
theory, calculation of the total energy and momentum of Kerr-NUT spacetimes
have been employed using two methods of the gravitational energy-momentum,
which is coordinate independent, and the Riemannian connection 1-form,
. It has been shown that the two methods
give the same an unacceptable result, i.e., divergent value. Therefore, a local
Lorentz transformation that plays a role of a regularizing tool, which
subtracts the inertial effects without distorting the true gravitational
contribution, has been suggested. This transformation keeps the resulting
spacetime to be a solution of the equations of motion of TEGR.Comment: 10 pages, Latex (Will appear in Prog. Theor. Phys.
Do phase transitions survive binomial reducibility and thermal scaling?
First order phase transitions are described in terms of the microcanonical
and canonical ensemble, with special attention to finite size effects.
Difficulties in interpreting a "caloric curve" are discussed. A robust
parameter indicating phase coexistence (univariance) or single phase
(bivariance) is extracted for charge distributions.Comment: 10 pages, TeX type, psfig, also available at
http://csa5.lbl.gov/moretto/ps/lgm.ps, to appear in the Proceedings of the
1st Catania Relativistic Ion Studies: Critical Phenomena and Collective
Observables, Acicastello, May 27-31, 199
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