Detecting edge degeneracy in interacting topological insulators through entanglement entropy

The existence of degenerate or gapless edge states is a characteristic feature of topological insulators, but is difficult to detect in the presence of interactons. We propose a new method to obtain the degeneracy of the edge states from the perspective of entanglement entropy, which is very useful to identify interacting topological states. Employing the determinant quantum Monte Carlo technique, we investigate the interaction effect on two representative models of fermionic topological insulators in one and two dimensions, respectively. In the two topologically nontrivial phases, the edge degeneracies are reduced by interactions but remain to be nontrivial.Comment: 6 pages, 4 figure

Log-Harnack Inequality for Stochastic Burgers Equations and Applications

By proving an $L^2$-gradient estimate for the corresponding Galerkin approximations, the log-Harnack inequality is established for the semigroup associated to a class of stochastic Burgers equations. As applications, we derive the strong Feller property of the semigroup, the irreducibility of the solution, the entropy-cost inequality for the adjoint semigroup, and entropy upper bounds of the transition density

Singular stochastic equations on Hilbert spaces: Harnack inequalities for their transition semigroups

We consider stochastic equations in Hilbert spaces with singular drift in the framework of [Da Prato, R\"ockner, PTRF 2002]. We prove a Harnack inequality (in the sense of [Wang, PTRF 1997]) for its transition semigroup and exploit its consequences. In particular, we prove regularizing and ultraboundedness properties of the transition semigroup as well as that the corresponding Kolmogorov operator has at most one infinitesimally invariant measure $\mu$ (satisfying some mild integrability conditions). Finally, we prove existence of such a measure $\mu$ for non-continuous drifts

Strong Solutions of Stochastic Generalized Porous Media Equations: Existence, Uniqueness and Ergodicity

Explicit conditions are presented for the existence, uniqueness and ergodicity of the strong solution to a class of generalized stochastic porous media equations. Our estimate of the convergence rate is sharp according to the known optimal decay for the solution of the classical (deterministic) porous medium equation.Comment: 15 pages; BiBoS-Preprint No. 04-09-157; to appear in Commun. PD

Giant negative magnetoresistance induced by the chiral anomaly in individual Cd3As2 nanowires

Cd3As2 is a newly booming Dirac semimetal with linear dispersion along all three momentum directions and can be viewed as 3D analog of graphene. As breaking of either time reversal symmetry or spatial inversion symmetry, the Dirac semimetal is believed to transform into Weyl semimetal with exotic chiral anomaly effect, while the experimental evidence of the chiral anomaly is still missing in Cd3As2. Here we report the magneto-transport properties of individual Cd3As2 nanowires. Large negative magnetoresistance (MR) with magnitude of -63% at 60 K and -11% at 300 K are observed when the magnetic field is parallel with the electric field direction, giving the evidence of the chiral magnetic effect in Cd3As2 nanowires. In addition, the critical magnetic field BC, where there is an extremum of the negative MR, increases with increasing temperature. As the first observation of chiral anomaly induced negative MR in Cd3As2 nanowires, it may offer valuable insights for low dimensional physics in Dirac semimetals.Comment: 4 figure

The Design and Application of Automatic Control System for Inorganic Membrane Filter

AbstractFor the existing inorganic membrane filter, this paper set up an automatic control system using PLC and touching screen, unified regenerate counter blowing control, online discharging control, pneumatic conveying control, process monitoring display and alarm etc., to reach the remote and on-site control. Hardware composing and software function of control system has been built. Performance parameters, match with actual capacity, of dust removal system are set by application. The application indicates that: when the pressure drop set to 25000 pa, regeneration counter blowing program starts, counter blowing interval set to 15s, counter blowing time set to 0.15s, pulse cleaning pressure set to 6860000 pa, the whole system moves stably and reliably, and it has high efficiency of dust removal

Harnack Inequality and Strong Feller Property for Stochastic Fast-Diffusion Equations

This paper presents analogous results for stochastic fast-diffusion equations. Since the fast-diffusion equation possesses weaker dissipativity than the porous medium one does, some technical difficulties appear in the study. As a compensation to the weaker dissipativity condition, a Sobolev-Nash inequality is assumed for the underlying self-adjoint operator in applications. Some concrete examples are constructed to illustrate the main results.Comment: to appear in Journal of Mathematical Analysis and Application