Derivative Formula and Applications for Degenerate Diffusion Semigroups

By using the Malliavin calculus and solving a control problem, Bismut type derivative formulae are established for a class of degenerate diffusion semigroups with non-linear drifts. As applications, explicit gradient estimates and Harnack inequalities are derived.Comment: 18 page

Quantum Spin Liquid with Even Ising Gauge Field Structure on Kagome Lattice

Employing large-scale quantum Monte Carlo simulations, we study the extended $XXZ$ model on the kagome lattice. A $\mathbb Z_2$ quantum spin liquid phase with effective even Ising gauge field structure emerges from the delicate balance among three symmetry-breaking phases including stripe solid, staggered solid and ferromagnet. This $\mathbb{Z}_2$ spin liquid is stabilized by an extended interaction related to the Rokhsar-Kivelson potential in the quantum dimer model limit. The phase transitions from the staggered solid to a spin liquid or ferromagnet are found to be first order and so is the transition between the stripe solid and ferromagnet. However, the transition between a spin liquid and ferromagnet is found to be continuous and belongs to the 3D $XY^*$ universality class associated with the condensation of spinons. The transition between a spin liquid and stripe solid appears to be continuous and associated with the condensation of visons.Comment: 7 pages, 8 figure

High Current Matching over Full-Swing and Low-Glitch Charge Pump Circuit for PLLs

A high current matching over full-swing and low-glitch charge pump (CP) circuit is proposed. The current of the CP is split into two identical branches having one-half the original current. The two branches are connected in source-coupled structure, and a two-stage amplifier is used to regulate the common-source voltage for the minimum current mismatch. The proposed CP is designed in TSMC 0.18µm CMOS technology with a power supply of 1.8 V. SpectreRF based simulation results show the mismatch between the current source and the current sink is less than 0.1% while the current is 40 µA and output swing is 1.32 V ranging from 0.2 V to 1.52 V. Moreover, the transient output current presents nearly no glitches. The simulation results verify the usage of the CP in PLLs with the maximum tuning range from the voltage-controlled oscillator, as well as the low power supply applications

One-way cloak based on nonreciprocal photonic crystal

We propose a physical concept of non-reciprocal transformation optics, by which a one-way invisible cloak is designed. The one-way invisible cloak is made of a coordinate-transformed nonreciprocal photonic crystal, showing a perfect cloaking for wave incident from one direction but acting as a perfect reflector for wave from the counter direction. The proposed design shows a high promise of applications in military, as protecting the own information to be detected but efficiently grabbing the information from the “enemy” side