We consider the computation of out-of-time-ordered correlators (OTOCs) in the fishnet theories, with a mass term added. These fields theories are not unitary. We compute the growth exponent, in the planar limit, at any value of the coupling and show that the model exhibits chaos. At strong coupling the growth exponent violates the Maldacena-Shenker-Stanford bound. We also consider the mass deformed versions of the six dimensional honeycomb theories, which can also be solved in the planar limit. The honeycomb theory shows a very similar behavior to that exhibited by the fishnet theory. 1 robert@neo.phys.wits.ac.za
A representation of the SO(3) group is mapped into a maximally entangled two qubit state according to literatures. To show the evolution of the entangled state, a model is set up on an maximally entangled electron pair, two electrons of which pass independently through a rotating magnetic field. It is found that the evolution path of the entangled state in the SO(3) sphere breaks an odd or even number of times, corresponding to the double connectedness of the SO(3) group. An odd number of breaks leads to an additional π phase to the entangled state, but an even number of breaks does not. A scheme to trace the evolution of the entangled state is proposed by means of entangled photon pairs and Kerr medium, allowing observation of the additional π phase.
The spin density wave and its temperature dependence in oxypnictide are studied in a threeband model. The spin susceptibilities with various interactions are calculated in the random phase approximation(PPA). It is found that the spin susceptibility peaks around the M point show a spin density wave(SDW) with momentum (0, π) and a clear stripe-like spin configuration. The intraband Coulomb repulsion enhances remarkably the SDW but the Hund's coupling weakens it. It is shown that a new resonance appears at higher temperatures at the Γ point indicating the formation of a paramagnetic phase. There is a clear transition from the SDW phase to the paramagnetic phase.
Sustainable production for hybrid flow shop scheduling problem (HFSP) has attracted growing attention due to the environment and economy pressure in industry. As the major source of energyconsumption and cost, the selection of parallel machines for various jobs quite affect the sustainability in HFSP. However, the characteristic of parallel machines in job shops have not been addressed in current research, which hinder its practical application. Thus, in this work a novel sustainable HFSP model considering the characteristics of the machines is proposed through evaluation of the power, production efficiency and cost of the parallel machines. To solve this model, an improved genetic algorithm is developed, in which the matching distance between the parallel machines and the weights of the optimization objectives is introduced and integrated into iterations to accelerate the convergence. Finally, a case study is adopted to verify the proposed model and algorithm. Based on the optimization results, three kinds of typical scheduling modes, i.e., efficiency, energy-saving, and economic, are put forward to provide guidance for the sustainable production of hybrid flow-shop scheduling.
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