Orbital-transverse density-wave instabilities in iron-based superconductors

Besides the conventional spin-density-wave (SDW) state, a new kind of orbital-transverse density-wave (OTDW) state is shown to exist generally in multi-orbital systems. We demonstrate that the orbital character of Fermi surface nesting plays an important role in density responses. The relationship between antiferromagnetism and structural phase transition in LaFeAsO (1111) and BaFe$_2$As$_2$ (122) compounds of iron-based superconductors may be understood in terms of the interplay between the SDW and OTDW with a five-orbital Hamiltonian. We propose that the essential difference between 1111 and 122 compounds is crucially determined by the presence of the two-dimensional $d_{xy}$-like Fermi surface around (0,0) being only in 1111 parent compounds.Comment: several parts were rewritten for clarity. 6 pages, 3 figures, 1 tabl

Maximum Principle for General Controlled Systems Driven by Fractional Brownian Motions

We obtain a maximum principle for stochastic control problem of general controlled stochastic differential systems driven by fractional Brownian motions (of Hurst parameter $H>1/2$). This maximum principle specifies a system of equations that the optimal control must satisfy (necessary condition for the optimal control). This system of equations consists of a backward stochastic differential equation driven by both fractional Brownian motion and the corresponding underlying standard Brownian motion. In addition to this backward equation, the maximum principle also involves the Malliavin derivatives. Our approach is to use conditioning and Malliavin calculus. To arrive at our maximum principle we need to develop some new results of stochastic analysis of the controlled systems driven by fractional Brownian motions via fractional calculus. Our approach of conditioning and Malliavin calculus is also applied to classical system driven by standard Brownian motion while the controller has only partial information. As a straightforward consequence, the classical maximum principle is also deduced in this more natural and simpler way.Comment: 44 page

Small-World Network Effect in Competing Glauber- and Kawasaki-type Dynamics

In this article, we investigate the competing Glauber-type and Kawasaki-type dynamics with small-world network (SWN) effect, in the framework of the Gaussian model. The Glauber-type single-spin transition mechanism with probability p simulates the contact of the system with a heat bath and the Kawasaki-type dynamics with probability 1-p simulates an external energy flux. Two different types of SWN effect are studied, one with the total number of links increased and the other with it conserved. The competition of the dynamics leads to an interesting self-organization process that can be characterized by a phase diagram with two identifiable temperatures. By studying the modification of the phase diagrams, the SWN effect on the two dynamics is analyzed. For the Glauber-type dynamics, more important is the altered average coordination number while the Kawasaki-type dynamics is enhanced by the long range spin interaction and redistribution.Comment: 18 pages, 1 figure. Accepted for publication in "The European Physical Journal B (EPJB)