78,465 research outputs found
Multiple boundary peak solutions for some singularly perturbed Neumann problems
We consider the problem \left \{
\begin{array}{rcl} \varepsilon^2 \Delta u - u + f(u) = 0 & \mbox{ in }& \ \Omega\\ u > 0 \ \mbox{ in} \ \Omega, \ \frac{\partial u}{\partial \nu} = 0 & \mbox{ on }& \ \partial\Omega,
\end{array} \right. where \Omega is a bounded smooth domain in R^N, \varepsilon>KK-peakH(P)K-peak$ solutions.
We first use the Liapunov-Schmidt method to reduce the problem to finite dimensions.
Then we use a maximizing procedure to obtain multiple boundary spikes
Effective Dynamics, Big Bounces and Scaling Symmetry in Bianchi Type I Loop Quantum Cosmology
The detailed formulation for loop quantum cosmology (LQC) in the Bianchi I
model with a scalar massless field has been constructed. In this paper, its
effective dynamics is studied in two improved strategies for implementing the
LQC discreteness corrections. Both schemes show that the big bang is replaced
by the big bounces, which take place up to three times, once in each diagonal
direction, when the area or volume scale factor approaches the critical values
in the Planck regime measured by the reference of the scalar field momentum.
These two strategies give different evolutions: In one scheme, the effective
dynamics is independent of the choice of the finite sized cell prescribed to
make Hamiltonian finite; in the other, the effective dynamics reacts to the
macroscopic scales introduced by the boundary conditions. Both schemes reveal
interesting symmetries of scaling, which are reminiscent of the relational
interpretation of quantum mechanics and also suggest that the fundamental
spatial scale (area gap) may give rise to a temporal scale.Comment: 19 pages, 6 figures, 1 table; one reference added; version to appear
in PR
The ordered K-theory of a full extension
Let A be a C*-algebra with real rank zero which has the stable weak
cancellation property. Let I be an ideal of A such that I is stable and
satisfies the corona factorization property. We prove that 0->I->A->A/I->0 is a
full extension if and only if the extension is stenotic and K-lexicographic. As
an immediate application, we extend the classification result for graph
C*-algebras obtained by Tomforde and the first named author to the general
non-unital case. In combination with recent results by Katsura, Tomforde, West
and the first author, our result may also be used to give a purely
K-theoretical description of when an essential extension of two simple and
stable graph C*-algebras is again a graph C*-algebra.Comment: Version IV: No changes to the text. We only report that Theorem 4.9
is not correct as stated. See arXiv:1505.05951 for more details. Since
Theorem 4.9 is an application to the main results of the paper, the main
results of this paper are not affected by the error. Version III comments:
Some typos and errors corrected. Some references adde
Measures of entanglement in multipartite bound entangled states
Bound entangled states are states that are entangled but from which no
entanglement can be distilled if all parties are allowed only local operations
and classical communication. However, in creating these states one needs
nonzero entanglement resources to start with. Here, the entanglement of two
distinct multipartite bound entangled states is determined analytically in
terms of a geometric measure of entanglement and a related quantity. The
results are compared with those for the negativity and the relative entropy of
entanglement.Comment: 5 pages, no figure; title change
Closed formula for the relative entropy of entanglement
The long-standing problem of finding a closed formula for the relative
entropy of entanglement (REE) for two qubits is addressed. A compact-form
solution to the inverse problem, which characterizes an entangled state for a
given closest separable state, is obtained. Analysis of the formula for a large
class of entangled states strongly suggests that a compact analytical solution
of the original problem, which corresponds to finding the closest separable
state for a given entangled state, can be given only in some special cases. A
few applications of the compact-form formula are given to show additivity of
the REE, to relate the REE with the Rains upper bound for distillable
entanglement, and to show that a Bell state does not have a unique closest
separable state.Comment: 7 pages, the title was modified as suggested by the PRA editor
Relative entropy of entanglement for certain multipartite mixed states
We prove conjectures on the relative entropy of entanglement (REE) for two
families of multipartite qubit states. Thus, analytic expressions of REE for
these families of states can be given. The first family of states are composed
of mixture of some permutation-invariant multi-qubit states. The results
generalized to multi-qudit states are also shown to hold. The second family of
states contain D\"ur's bound entangled states. Along the way, we have discussed
the relation of REE to two other measures: robustness of entanglement and
geometric measure of entanglement, slightly extending previous results.Comment: Single column, 22 pages, 9 figures, comments welcom
Connections of geometric measure of entanglement of pure symmetric states to quantum state estimation
We study the geometric measure of entanglement (GM) of pure symmetric states
related to rank-one positive-operator-valued measures (POVMs) and establish a
general connection with quantum state estimation theory, especially the maximum
likelihood principle. Based on this connection, we provide a method for
computing the GM of these states and demonstrate its additivity property under
certain conditions. In particular, we prove the additivity of the GM of pure
symmetric multiqubit states whose Majorana points under Majorana representation
are distributed within a half sphere, including all pure symmetric three-qubit
states. We then introduce a family of symmetric states that are generated from
mutually unbiased bases (MUBs), and derive an analytical formula for their GM.
These states include Dicke states as special cases, which have already been
realized in experiments. We also derive the GM of symmetric states generated
from symmetric informationally complete POVMs (SIC~POVMs) and use it to
characterize all inequivalent SIC~POVMs in three-dimensional Hilbert space that
are covariant with respect to the Heisenberg--Weyl group. Finally, we describe
an experimental scheme for creating the symmetric multiqubit states studied in
this article and a possible scheme for measuring the permanent of the related
Gram matrix.Comment: 11 pages, 1 figure, published versio
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