Gauge choices and Entanglement Entropy of two dimensional lattice gauge fields

In this paper, we explore the question of how different gauge choices in a gauge theory affect the tensor product structure of the Hilbert space in configuration space. In particular, we study the Coulomb gauge and observe that the naive gauge potential degrees of freedom cease to be local operators as soon as we impose the Dirac brackets. We construct new local set of operators and compute the entanglement entropy according to this algebra in $2+1$ dimensions. We find that our proposal would lead to an entanglement entropy that behave very similar to a single scalar degree of freedom if we do not include further centers, but approaches that of a gauge field if we include non-trivial centers. We explore also the situation where the gauge field is Higgsed, and construct a local operator algebra that again requires some deformation. This should give us some insight into interpreting the entanglement entropy in generic gauge theories and perhaps also in gravitational theories.Comment: 38 pages,25 figure

Tensor network and (pp-adic) AdS/CFT

We use the tensor network living on the Bruhat-Tits tree to give a concrete realization of the recently proposed $p$-adic AdS/CFT correspondence (a holographic duality based on the $p$-adic number field $\mathbb{Q}_p$). Instead of assuming the $p$-adic AdS/CFT correspondence, we show how important features of AdS/CFT such as the bulk operator reconstruction and the holographic computation of boundary correlators are automatically implemented in this tensor network.Comment: 59 pages, 18 figures; v3: improved presentation, added figures and reference

Vertical or horizontal: optimal integration strategy under separation of ownership and control

This study proposes a framework to analyze the strategic value of integration, when separation of ownership and control is considered. According to this framework, we investigate the optimal integration strategy in different control distribution and discuss how external market influences the best strategic choice. Beside theoretical analysis, we also provide evidence from Chinese listed firms to validate our research. The key results of our study show that first, unintegrated strategy works best, if the level of controlownership disparity is extremely high. Second, in general, vertical strategy is more appropriate for substitute markets, while horizontal strategy may bring more benefits in a highly complementary market. Third, the impact of integration strategy on a firm’s performance is negatively moderated by control-ownership disparity. However, this moderate effect may be weakened by market structure. Our results provide a new and comprehensive perspective for understanding the inconsistent results from previous studies. Moreover, the analysis in this study also highlights a firm’s strategic decision and market regulation policy

Crystal structure of hexaaqua-{(E)-N′-(1-(pyrazin-2-yl)ethylidene)isonicotinohydrazide-κ3N,N′,O}praseodym(III) trichloride monohydrate, C12H25Cl3N5O8Pr

Abstract C12H25Cl3N5O8Pr, triclinic, P1̄ (no. 2), a = 9.4800(10) Å, b = 9.9591(12) Å, c = 12.4897(143) Å, α = 88.855(2)°, β = 76.897(2)°, γ = 89.182(2)°, V = 1148.2(2) Å3, Z = 2, R gt(F) = 0.0372, wR ref(F 2) = 0.0918, T = 296(2) K

Dynamics in a delayed diffusive cell cycle model

In this paper, we construct a delayed diffusive model to explore the spatial dynamics of cell cycle in G2/M transition. We first obtain the local stability of the unique positive equilibrium for this model, which is irrelevant to the diffusion. Then, through investigating the delay-induced Hopf bifurcation in this model, we establish the existence of spatially homogeneous and inhomogeneous bifurcating periodic solutions. Applying the normal form and center manifold theorem of functional partial differential equations, we also determine the stability and direction of these bifurcating periodic solutions. Finally, numerical simulations are presented to validate our theoretical results

Quantum logical gates with four-level SQUIDs coupled to a superconducting resonator

We propose a way for realizing a two-qubit controlled phase gate with superconducting quantum interference devices (SQUIDs) coupled to a superconducting resonator. In this proposal, the two lowest levels of each SQUID serve as the logical states and two intermediate levels of each SQUID are used for the gate realization. We show that neither adjustment of SQUID level spacings during the gate operation nor uniformity in SQUID parameters is required by this proposal. In addition, this proposal does not require the adiabatic passage or a second-order detuning and thus the gate is much faster.Comment: 6 pages, 3 figure