2,710 research outputs found
Universal Leakage Elimination
``Leakage'' errors are particularly serious errors which couple states within
a code subspace to states outside of that subspace thus destroying the error
protection benefit afforded by an encoded state. We generalize an earlier
method for producing leakage elimination decoupling operations and examine the
effects of the leakage eliminating operations on decoherence-free or noiseless
subsystems which encode one logical, or protected qubit into three or four
qubits. We find that by eliminating the large class of leakage errors, under
some circumstances, we can create the conditions for a decoherence free
evolution. In other cases we identify a combination decoherence-free and
quantum error correcting code which could eliminate errors in solid-state
qubits with anisotropic exchange interaction Hamiltonians and enable universal
quantum computing with only these interactions.Comment: 14 pages, no figures, new version has references updated/fixe
Third-order superintegrable systems separable in parabolic coordinates
In this paper, we investigate superintegrable systems which separate in
parabolic coordinates and admit a third-order integral of motion. We give the
corresponding determining equations and show that all such systems are
multi-separable and so admit two second-order integrals. The third-order
integral is their Lie or Poisson commutator. We discuss how this situation is
different from the Cartesian and polar cases where new potentials were
discovered which are not multi-separable and which are expressed in terms of
Painlev\'e transcendents or elliptic functions
Characterizing Planetary Orbits and the Trajectories of Light
Exact analytic expressions for planetary orbits and light trajectories in the
Schwarzschild geometry are presented. A new parameter space is used to
characterize all possible planetary orbits. Different regions in this parameter
space can be associated with different characteristics of the orbits. The
boundaries for these regions are clearly defined. Observational data can be
directly associated with points in the regions. A possible extension of these
considerations with an additional parameter for the case of Kerr geometry is
briefly discussed.Comment: 49 pages total with 11 tables and 10 figure
Exact Solutions of a (2+1)-Dimensional Nonlinear Klein-Gordon Equation
The purpose of this paper is to present a class of particular solutions of a
C(2,1) conformally invariant nonlinear Klein-Gordon equation by symmetry
reduction. Using the subgroups of similitude group reduced ordinary
differential equations of second order and their solutions by a singularity
analysis are classified. In particular, it has been shown that whenever they
have the Painlev\'e property, they can be transformed to standard forms by
Moebius transformations of dependent variable and arbitrary smooth
transformations of independent variable whose solutions, depending on the
values of parameters, are expressible in terms of either elementary functions
or Jacobi elliptic functions.Comment: 16 pages, no figures, revised versio
Finite-level systems, Hermitian operators, isometries, and a novel parameterization of Stiefel and Grassmann manifolds
In this paper we obtain a description of the Hermitian operators acting on
the Hilbert space \C^n, description which gives a complete solution to the
over parameterization problem. More precisely we provide an explicit
parameterization of arbitrary -dimensional operators, operators that may be
considered either as Hamiltonians, or density matrices for finite-level quantum
systems. It is shown that the spectral multiplicities are encoded in a flag
unitary matrix obtained as an ordered product of special unitary matrices, each
one generated by a complex -dimensional unit vector, . As a
byproduct, an alternative and simple parameterization of Stiefel and Grassmann
manifolds is obtained.Comment: 21 page
Topological structures of adiabatic phase for multi-level quantum systems
The topological properties of adiabatic gauge fields for multi-level
(three-level in particular) quantum systems are studied in detail. Similar to
the result that the adiabatic gauge field for SU(2) systems (e.g. two-level
quantum system or angular momentum systems, etc) have a monopole structure, the
curvature two-forms of the adiabatic holonomies for SU(3) three-level and SU(3)
eight-level quantum systems are shown to have monopole-like (for all levels) or
instanton-like (for the degenerate levels) structures.Comment: 15 pages, no figures. Accepted by J.Phys.
A Simple Complete Search for Logic Programming
Here, we present a family of complete interleaving depth-first search strategies for embedded, domain-specific logic languages. We derive our search family from a stream-based implementation of incomplete depth-first search. The DSL\u27s programs\u27 texts induce particular strategies guaranteed to be complete
Driven Macroscopic Quantum Tunneling of Ultracold Atoms in Engineered Optical Lattices
Coherent macroscopic tunneling of a Bose-Einstein condensate between two
parts of an optical lattice separated by an energy barrier is theoretically
investigated. We show that by a pulsewise change of the barrier height, it is
possible to switch between tunneling regime and a self-trapped state of the
condensate. This property of the system is explained by effectively reducing
the dynamics to the nonlinear problem of a particle moving in a double square
well potential. The analysis is made for both attractive and repulsive
interatomic forces, and it highlights the experimental relevance of our
findings
Active Galactic Nuclei in Void Regions
We present a comprehensive study of accretion activity in the most underdense
environments in the universe, the voids, based on the SDSS DR2 data. Based on
investigations of multiple void regions, we show that AGN's occurrence rate and
properties differ from those in walls. AGN are more common in voids than in
walls, but only among moderately luminous and massive galaxies (M_r < -20, log
M_*/M_sun < 10.5), and this enhancement is more pronounced for the weakly
accreting systems (i.e., L_[O III] < 10^39 erg/s). Void AGN hosted by
moderately massive and luminous galaxies are accreting at equal or lower rates
than their wall counterparts, show less obscuration than in walls, and
similarly aged stellar populations. The very few void AGN in massive bright
hosts accrete more strongly, are more obscured, and are associated with younger
stellar emission than wall AGN. Thus, accretion strength is probably connected
to the availability of fuel supply, and accretion and star-formation co-evolve
and rely on the same source of fuel. Nearest neighbor statistics indicate that
the weak accretion activity (LINER-like) is not influenced by the local
environment. However, H IIs, Seyferts, and Transition objects prefer more
grouped small scale structures, indicating that the rate at which galaxies
interact with each other affects their activity. These trends support a
potential H II -> Seyfert/Transition Object -> LINER evolutionary sequence that
we show is apparent in many properties of actively line-emitting galaxies, in
both voids and walls. The subtle differences between void and wall AGN might be
explained by a longer, less disturbed duty cycle of these systems in voids.Comment: 19 pages, 7 figures (1 color); to appear in ApJ, submitted on May 11,
200
Conductivity of interacting massless Dirac particles in graphene: Collisionless regime
We provide detailed calculation of the a.c. conductivity in the case of
1/r-Coulomb interacting massless Dirac particles in graphene in the
collisionless limit when \omega >> T. The analysis of the electron self-energy,
current vertex function and polarization function, which enter into the
calculation of physical quantities including the a.c. conductivity, is carried
out by checking the Ward-Takahashi identities associated with the electrical
charge conservation and making sure that they are satisfied at each step. We
adopt a variant of the dimensional regularization of Veltman and t'Hooft by
taking the spatial dimension D=2-\epsilon, for \epsilon > 0. The procedure
adopted here yields a result for the conductivity correction which, while
explicitly preserving charge conservation laws, is nevertheless different from
the results reported previously in literature.Comment: 32 pages, no figures, published versio
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