23,366 research outputs found
A generalization of Bohr's Equivalence Theorem
Based on a generalization of Bohr's equivalence relation for general
Dirichlet series, in this paper we study the sets of values taken by certain
classes of equivalent almost periodic functions in their strips of almost
periodicity. In fact, the main result of this paper consists of a result like
Bohr's equivalence theorem extended to the case of these functions.Comment: Because of a mistake detected in one of the references, the previous
version of this paper has been modified by the authors to restrict the scope
of its application to the case of existence of an integral basi
Bohr's equivalence relation in the space of Besicovitch almost periodic functions
Based on Bohr's equivalence relation which was established for general
Dirichlet series, in this paper we introduce a new equivalence relation on the
space of almost periodic functions in the sense of Besicovitch,
, defined in terms of polynomial approximations. From
this, we show that in an important subspace , where Parseval's equality and Riesz-Fischer theorem
holds, its equivalence classes are sequentially compact and the family of
translates of a function belonging to this subspace is dense in its own class.Comment: Because of a mistake detected in one of the references, the
equivalence relation which is inspired by that of Bohr is revised to adapt
correctly the situation in the general case. arXiv admin note: text overlap
with arXiv:1801.0803
Phase diagram of an extended quantum dimer model on the hexagonal lattice
We introduce a quantum dimer model on the hexagonal lattice that, in addition
to the standard three-dimer kinetic and potential terms, includes a competing
potential part counting dimer-free hexagons. The zero-temperature phase diagram
is studied by means of quantum Monte Carlo simulations, supplemented by
variational arguments. It reveals some new crystalline phases and a cascade of
transitions with rapidly changing flux (tilt in the height language). We
analyze perturbatively the vicinity of the Rokhsar-Kivelson point, showing that
this model has the microscopic ingredients needed for the "devil's staircase"
scenario [E. Fradkin et al., Phys. Rev. B 69, 224415 (2004)], and is therefore
expected to produce fractal variations of the ground-state flux.Comment: Published version. 5 pages + 8 (Supplemental Material), 31
references, 10 color figure
Mixed State Entanglement of Assistance and the Generalized Concurrence
We consider the maximum bipartite entanglement that can be distilled from a
single copy of a multipartite mixed entangled state, where we focus mostly on
-dimensional tripartite mixed states. We show that this {\em
assisted entanglement}, when measured in terms of the generalized concurrence
(named G-concurrence) is (tightly) bounded by an entanglement monotone, which
we call the G-concurrence of assistance. The G-concurrence is one of the
possible generalizations of the concurrence to higher dimensions, and for pure
bipartite states it measures the {\em geometric mean} of the Schmidt numbers.
For a large (non-trivial) class of -dimensional mixed states, we are
able to generalize Wootters formula for the concurrence into lower and upper
bounds on the G-concurrence. Moreover, we have found an explicit formula for
the G-concurrence of assistance that generalizes the expression for the
concurrence of assistance for a large class of dimensional
tripartite pure states.Comment: 7 page
Infinitesimal local operations and differential conditions for entanglement monotones
Much of the theory of entanglement concerns the transformations that are
possible to a state under local operations with classical communication (LOCC);
however, this set of operations is complicated and difficult to describe
mathematically. An idea which has proven very useful is that of the {\it
entanglement monotone}: a function of the state which is invariant under local
unitary transformations and always decreases (or increases) on average after
any local operation. In this paper we look on LOCC as the set of operations
generated by {\it infinitesimal local operations}, operations which can be
performed locally and which leave the state little changed. We show that a
necessary and sufficient condition for a function of the state to be an
entanglement monotone under local operations that do not involve information
loss is that the function be a monotone under infinitesimal local operations.
We then derive necessary and sufficient differential conditions for a function
of the state to be an entanglement monotone. We first derive two conditions for
local operations without information loss, and then show that they can be
extended to more general operations by adding the requirement of {\it
convexity}. We then demonstrate that a number of known entanglement monotones
satisfy these differential criteria. Finally, as an application, we use the
differential conditions to construct a new polynomial entanglement monotone for
three-qubit pure states. It is our hope that this approach will avoid some of
the difficulties in the theory of multipartite and mixed-state entanglement.Comment: 21 pages, RevTeX format, no figures, three minor corrections,
including a factor of two in the differential conditions, the tracelessness
of the matrix in the convexity condition, and the proof that the local purity
is a monotone under local measurements. The conclusions of the paper are
unaffecte
UVMULTIFIT: A versatile tool for fitting astronomical radio interferometric data
The analysis of astronomical interferometric data is often performed on the
images obtained after deconvolution of the interferometer's point spread
function (PSF). This strategy can be understood (especially for cases of sparse
arrays) as fitting models to models, since the deconvolved images are already
non-unique model representations of the actual data (i.e., the visibilities).
Indeed, the interferometric images may be affected by visibility gridding,
weighting schemes (e.g., natural vs. uniform), and the particulars of the
(non-linear) deconvolution algorithms. Fitting models to the direct
interferometric observables (i.e., the visibilities) is preferable in the cases
of simple (analytical) sky intensity distributions. In this paper, we present
UVMULTIFIT, a versatile library for fitting visibility data, implemented in a
Python-based framework. Our software is currently based on the CASA package,
but can be easily adapted to other analysis packages, provided they have a
Python API. We have tested the software with synthetic data, as well as with
real observations. In some cases (e.g., sources with sizes smaller than the
diffraction limit of the interferometer), the results from the fit to the
visibilities (e.g., spectra of close by sources) are far superior to the output
obtained from the mere analysis of the deconvolved images. UVMULTIFIT is a
powerful improvement of existing tasks to extract the maximum amount of
information from visibility data, especially in cases close to the
sensitivity/resolution limits of interferometric observations.Comment: 10 pages, 4 figures. Accepted in A&A. Code available at
http://nordic-alma.se/support/software-tool
Finite-Size Scaling Exponents in the Dicke Model
We consider the finite-size corrections in the Dicke model and determine the
scaling exponents at the critical point for several quantities such as the
ground state energy or the gap. Therefore, we use the Holstein-Primakoff
representation of the angular momentum and introduce a nonlinear transformation
to diagonalize the Hamiltonian in the normal phase. As already observed in
several systems, these corrections turn out to be singular at the transition
point and thus lead to nontrivial exponents. We show that for the atomic
observables, these exponents are the same as in the Lipkin-Meshkov-Glick model,
in agreement with numerical results. We also investigate the behavior of the
order parameter related to the radiation mode and show that it is driven by the
same scaling variable as the atomic one.Comment: 4 pages, published versio
Entanglement of Assistance is not a bipartite measure nor a tripartite monotone
The entanglement of assistance quantifies the entanglement that can be
generated between two parties, Alice and Bob, given assistance from a third
party, Charlie, when the three share a tripartite state and where the
assistance consists of Charlie initially performing a measurement on his share
and communicating the result to Alice and Bob through a one-way classical
channel. We argue that if this quantity is to be considered an operational
measure of entanglement, then it must be understood to be a tripartite rather
than a bipartite measure. We compare it with a distinct tripartite measure that
quantifies the entanglement that can be generated between Alice and Bob when
they are allowed to make use of a two-way classical channel with Charlie. We
show that the latter quantity, which we call the entanglement of collaboration,
can be greater than the entanglement of assistance. This demonstrates that the
entanglement of assistance (considered as a tripartite measure of
entanglement), and its multipartite generalizations such as the localizable
entanglement, are not entanglement monotones, thereby undermining their
operational significance.Comment: 5 pages, revised, title changed, added a discussion explaining why
entanglement of assistance can not be considered as a bipartite measure, to
appear in Phys. Rev.
Ground state entanglement and geometric entropy in the Kitaev's model
We study the entanglement properties of the ground state in Kitaev's model.
This is a two-dimensional spin system with a torus topology and nontrivial
four-body interactions between its spins. For a generic partition of
the lattice we calculate analytically the von Neumann entropy of the reduced
density matrix in the ground state. We prove that the geometric
entropy associated with a region is linear in the length of its boundary.
Moreover, we argue that entanglement can probe the topology of the system and
reveal topological order. Finally, no partition has zero entanglement and we
find the partition that maximizes the entanglement in the given ground state.Comment: 4 pages, one fig, ReVTeX 4; updated to the published versio
Interactions in Quasicrystals
Although the effects of interactions in solid state systems still remains a
widely open subject, some limiting cases such as the three dimensional Fermi
liquid or the one-dimensional Luttinger liquid are by now well understood when
one is dealing with interacting electrons in {\it periodic} crystalline
structures. This problem is much more fascinating when periodicity is lacking
as it is the case in {\it quasicrystalline} structures. Here, we discuss the
influence of the interactions in quasicrystals and show, on a controlled
one-dimensional model, that they lead to anomalous transport properties,
intermediate between those of an interacting electron gas in a periodic and in
a disordered potential.Comment: Proceedings of the Many Body X conference (Seattle, Sept. 99); 9
pages; uses epsfi
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