1,134 research outputs found
SoftNet: A Package for the Analysis of Complex Networks
Identifying the most important nodes according to specific centrality indices is an important issue in network analysis. Node metrics based on the computation of functions of the adjacency matrix of a network were defined by Estrada and his collaborators in various papers. This paper describes a MATLAB toolbox for computing such centrality indices using efficient numerical algorithms based on the connection between the Lanczos method and Gauss-type quadrature rules
Trapping cold atoms near carbon nanotubes: thermal spin flips and Casimir-Polder potential
We investigate the possibility to trap ultracold atoms near the outside of a
metallic carbon nanotube (CN) which we imagine to use as a miniaturized
current-carrying wire. We calculate atomic spin flip lifetimes and compare the
strength of the Casimir-Polder potential with the magnetic trapping potential.
Our analysis indicates that the Casimir-Polder force is the dominant loss
mechanism and we compute the minimum distance to the carbon nanotube at which
an atom can be trapped.Comment: 8 pages, 3 figure
Dynamically controlled toroidal and ring-shaped magnetic traps
We present traps with toroidal and ring-shaped topologies, based on
adiabatic potentials for radio-frequency dressed Zeeman states in a ring-shaped
magnetic quadrupole field. Simple adjustment of the radio-frequency fields
provides versatile possibilities for dynamical parameter tuning, topology
change, and controlled potential perturbation. We show how to induce toroidal
and poloidal rotations, and demonstrate the feasibility of preparing degenerate
quantum gases with reduced dimensionality and periodic boundary conditions. The
great level of dynamical and even state dependent control is useful for atom
interferometry.Comment: 6 pages, 4 figures. Paragraphs on gravity compensation and expected
trap lifetimes adde
Quantitative study of quasi-one-dimensional Bose gas experiments via the stochastic Gross-Pitaevskii equation
The stochastic Gross-Pitaevskii equation is shown to be an excellent model
for quasi-one-dimensional Bose gas experiments, accurately reproducing the in
situ density profiles recently obtained in the experiments of Trebbia et al.
[Phys. Rev. Lett. 97, 250403 (2006)] and van Amerongen et al. [Phys. Rev. Lett.
100, 090402 (2008)], and the density fluctuation data reported by Armijo et al.
[Phys. Rev. Lett. 105, 230402 (2010)]. To facilitate such agreement, we propose
and implement a quasi-one-dimensional stochastic equation for the low-energy,
axial modes, while atoms in excited transverse modes are treated as independent
ideal Bose gases.Comment: 10 pages, 5 figures; updated figures with experimental dat
Eigenvector sensitivity under general and structured perturbations of tridiagonal Toeplitz-type matrices
The sensitivity of eigenvalues of structured matrices under general or
structured perturbations of the matrix entries has been thoroughly studied in
the literature. Error bounds are available and the pseudospectrum can be
computed to gain insight. Few investigations have focused on analyzing the
sensitivity of eigenvectors under general or structured perturbations. The
present paper discusses this sensitivity for tridiagonal Toeplitz and
Toeplitz-type matrices.Comment: 21 pages, 4 figure
Theoretical analysis of the implementation of a quantum phase gate with neutral atoms on atom chips
We present a detailed, realistic analysis of the implementation of a proposal
for a quantum phase gate based on atomic vibrational states, specializing it to
neutral rubidium atoms on atom chips. We show how to create a double--well
potential with static currents on the atom chips, using for all relevant
parameters values that are achieved with present technology. The potential
barrier between the two wells can be modified by varying the currents in order
to realize a quantum phase gate for qubit states encoded in the atomic external
degree of freedom. The gate performance is analyzed through numerical
simulations; the operation time is ~10 ms with a performance fidelity above
99.9%. For storage of the state between the operations the qubit state can be
transferred efficiently via Raman transitions to two hyperfine states, where
its decoherence is strongly inhibited. In addition we discuss the limits
imposed by the proximity of the surface to the gate fidelity.Comment: 9 pages, 5 color figure
Extracting Atoms on Demand with Lasers
We propose a scheme that allows to coherently extract cold atoms from a
reservoir in a deterministic way. The transfer is achieved by means of
radiation pulses coupling two atomic states which are object to different
trapping conditions. A particular realization is proposed, where one state has
zero magnetic moment and is confined by a dipole trap, whereas the other state
with non-vanishing magnetic moment is confined by a steep microtrap potential.
We show that in this setup a predetermined number of atoms can be transferred
from a reservoir, a Bose-Einstein condensate, into the collective quantum state
of the steep trap with high efficiency in the parameter regime of present
experiments.Comment: 11 pages, 8 figure
The structure of iterative methods for symmetric linear discrete ill-posed problems
The iterative solution of large linear discrete ill-posed problems with an error contaminated data vector requires the use of specially designed methods in order to avoid severe error propagation. Range restricted minimal residual methods have been found to be well suited for the solution of many such problems. This paper discusses the structure of matrices that arise in a range restricted minimal residual method for the solution of large linear discrete ill-posed problems with a symmetric matrix. The exploitation of the structure results in a method that is competitive with respect to computer storage, number of iterations, and accuracy.Acknowledgments We would like to thank the referees for comments. The work of F. M. was supported
by Dirección General de Investigación Científica y Técnica, Ministerio de Economía y Competitividad of
Spain under grant MTM2012-36732-C03-01. Work of L. R. was supported by Universidad Carlos III de
Madrid in the Department of Mathematics during the academic year 2010-2011 within the framework of
the Chair of Excellence Program and by NSF grant DMS-1115385
Impact of localization on Dyson's circular ensemble
A wide variety of complex physical systems described by unitary matrices have
been shown numerically to satisfy level statistics predicted by Dyson's
circular ensemble. We argue that the impact of localization in such systems is
to provide certain restrictions on the eigenvalues. We consider a solvable
model which takes into account such restrictions qualitatively and find that
within the model a gap is created in the spectrum, and there is a transition
from the universal Wigner distribution towards a Poisson distribution with
increasing localization.Comment: To be published in J. Phys.
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