5,296 research outputs found
A dynamical Mordell Lang property on the disk
We prove that two finite endomorphisms of the unit disk with degree at least
two have orbits with infinite intersections if and only if they have a common
iteration
Separability of Tripartite Quantum Systems
We investigate the separability of arbitrary dimensional tripartite sys-
tems. By introducing a new operator related to transformations on the
subsystems a necessary condition for the separability of tripartite systems is
presented.Comment: 8 page
Upper bound of the fully entangled fraction
We study the fully entangled fraction of quantum states. An upper bound is
obtained for arbitrary dimensional bipartite systems. This bound is shown to be
exact for the case of two-qubit systems. An inequality related the fully
entangled fraction of two qubits in a three-qubit mixed state has been also
presented.Comment: 8 pages, 2 figure
A semi-local holographic minimal model
We present a conjecture on the complete spectrum of single-trace operators in
the infinite N limit of W(N) minimal model and evidences for the conjecture. We
further propose that the holographic dual of W(N) minimal model in the 't Hooft
limit is an unusual "semi-local" higher spin gauge theory on AdS3 x S^1. At
each point on the S^1 lives a copy of three-dimensional Vasiliev theory, that
contains an infinite tower of higher spin gauge fields coupled to a single
massive complex scalar propagating in AdS3. The Vasiliev theories at different
points on the S^1 are correlated only through the AdS3 boundary conditions on
the massive scalars. All but one single tower of higher spin symmetries are
broken by the boundary conditions.Comment: 31 pages; typos corrected, references adde
Isogeny orbits in a family of abelian varieties
We prove that if a curve of a non-isotrivial family of abelian varieties over
a curve contains infinitely many isogeny orbits of a finitely generated
subgroup of a simple abelian variety then it is special
Families of Conformal Fixed Points of N=2 Chern-Simons-Matter Theories
We argue that a large class of N=2 Chern-Simons-matter theories in three
dimensions have a continuous family of exact IR fixed points described by
suitable quartic superpotentials, based on holomorphy. The entire family exists
in the perturbative regime. A nontrivial check is performed by computing the
4-loop beta function of the quartic couplings, in the 't Hooft limit, with a
large number of flavors. We find that the 4-loop beta function can only deform
the family of 2-loop fixed points, and does not change the dimension of this
family. We further present an explicit computation of a perturbative correction
to the Zamolodchikov metric on this space of three-dimensional superconformal
field theories.Comment: 27 pages, 108 figure
1/16 BPS States in N=4 SYM
We investigate the problem of counting 1/16 BPS operators in N=4
Super-Yang-Mills theory at weak coupling. We present the complete set of 1/16
BPS operators in the infinite N limit, which agrees with the counting of free
BPS multi-graviton states in the gravity dual AdS5xS5. Further, we conjecture
that all 1/16 BPS operators in N=4 SYM are of the multi-graviton form, and give
numerical evidences for this conjecture. We discuss the implication of our
conjecture and the seeming failure in reproducing the entropy of large 1/16 BPS
black holes in AdS5.Comment: 14 pages;a new section adde
Manipulating quantum information on the controllable systems or subspaces
In this paper, we explore how to constructively manipulate qubits by rotating
Bloch spheres. It is revealed that three-rotation and one-rotation Hamiltonian
controls can be constructed to steer qubits when two tunable Hamiltonian
controls are available. It is demonstrated in this research that local-wave
function controls such as Bang-Bang, triangle-function and quadratic function
controls can be utilized to manipulate quantum states on the Bloch sphere. A
new kind of time-energy performance index is proposed to trade-off time and
energy resource cost, in which control magnitudes are optimized in terms of
this kind of performance. It is further exemplified that this idea can be
generalized to manipulate encoded qubits on the controllable subspace
A scheme for realizing continuously tunable spectrum in the visible light region based on monatomic carbon chains
We propose a scheme for realizing the continuously tunable spectrum based on
monatomic carbon chains. By hybrid density functional calculations, we first
show that the direct band gap of monatomic carbon chains change continuously
from 1.58 to 3.8 eV as strain is applied from -5 to 10% to the chain, with
separated Van Hove singularity peaks enhanced. To realize this tunability, a
realistic stretching device is proposed by contacting the chain with graphene
sheets, which can apply up to 9% elongation to the chain, yielding tunable
light-emitting wavelengths from 345 to 561 nm
Message spreading in networks with stickiness and persistence: Large clustering does not always facilitate large-scale diffusion
Recent empirical studies have confirmed the key roles of complex contagion
mechanisms such as memory, social reinforcement, and decay effects in
information diffusion and behaviour spreading. Inspired by this fact, we here
propose a new agent--based model to capture the whole picture of the joint
action of the three mechanisms in information spreading, by quantifying the
complex contagion mechanisms as stickiness and persistence, and carry out
extensive simulations of the model on various networks. By numerical
simulations as well as theoretical analysis, we find that the stickiness of the
message determines the critical dynamics of message diffusion on tree-like
networks, whereas the persistence plays a decisive role on dense regular
lattices. In either network, the greater persistence can effectively make the
message more invasive. Of particular interest is that our research results
renew our previous knowledge that messages can spread broader in networks with
large clustering, which turns out to be only true when they can inform a
non-zero fraction of the population in the limit of large system size.Comment: 12pages, 7 figures, Supporting Information (20 pages), accepted by
Sci. Re
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