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