40,281 research outputs found
The Grad-Shafranov Reconstruction of Toroidal Magnetic Flux Ropes: Method Development and Benchmark Studies
We develop an approach of Grad-Shafranov (GS) reconstruction for toroidal
structures in space plasmas, based on in-situ spacecraft measurements. The
underlying theory is the GS equation that describes two-dimensional
magnetohydrostatic equilibrium as widely applied in fusion plasmas. The
geometry is such that the arbitrary cross section of the torus has rotational
symmetry about the rotation axis , with a major radius . The magnetic
field configuration is thus determined by a scalar flux function and a
functional that is a single-variable function of . The algorithm is
implemented through a two-step approach: i) a trial-and-error process by
minimizing the residue of the functional to determine an optimal
axis orientation, and ii) for the chosen , a minimization process
resulting in the range of . Benchmark studies of known analytic solutions
to the toroidal GS equation with noise additions are presented to illustrate
the two-step procedures and to demonstrate the performance of the numerical GS
solver, separately. For the cases presented, the errors in and are
9 and 22\%, respectively, and the relative percent error in the
numerical GS solutions is less than 10\%. We also make public the computer
codes for these implementations and benchmark studies.Comment: submitted to Sol. Phys. late Dec 2016; under review; code will be
made public once review is ove
Low-decoherence flux qubit
A flux qubit can have a relatively long decoherence time at the degeneracy
point, but away from this point the decoherence time is greatly reduced by
dephasing. This limits the practical applications of flux qubits. Here we
propose a new qubit design modified from the commonly used flux qubit by
introducing an additional capacitor shunted in parallel to the smaller
Josephson junction (JJ) in the loop. Our results show that the effects of noise
can be considerably suppressed, particularly away from the degeneracy point, by
both reducing the coupling energy of the JJ and increasing the shunt
capacitance. This shunt capacitance provides a novel way to improve the qubit.Comment: 4 pages, 4 figure
Power Set of Some Quasinilpotent Weighted shifts on
For a quasinilpotent operator on a Banach space , Douglas and Yang
defined for each nonzero vector , and call the power set of .
have a close link with 's lattice of hyperinvariant
subspaces.
This paper computes the power set of quasinilpotent weighted shifts on
for .
We obtain the following results:
(1) If is an injective quasinilpotent forward unilateral weighted shift
on , then
when , where be the
canonical basis for ;
(2) There is a class of backward unilateral weighted shifts on
whose power set is
;
(3) There exists a bilateral weighted shift on with power
set
for .Comment: 22 page
Geometric entanglement from matrix product state representations
An efficient scheme to compute the geometric entanglement per lattice site
for quantum many-body systems on a periodic finite-size chain is proposed in
the context of a tensor network algorithm based on the matrix product state
representations. It is systematically tested for three prototypical critical
quantum spin chains, which belong to the same Ising universality class. The
simulation results lend strong support to the previous claim [Q.-Q. Shi, R.
Or\'{u}s, J. O. Fj{\ae}restad, and H.-Q. Zhou, New J. Phys \textbf{12}, 025008
(2010); J.-M. St\'{e}phan, G. Misguich, and F. Alet, Phys. Rev. B \textbf{82},
180406R (2010)] that the leading finite-size correction to the geometric
entanglement per lattice site is universal, with its remarkable connection to
the celebrated Affleck-Ludwig boundary entropy corresponding to a conformally
invariant boundary condition.Comment: 4+ pages, 3 figure
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