Nonlinear Young integrals via fractional calculus

For H\"older continuous functions $W(t,x)$ and $\varphi_t$, we define nonlinear integral $\int_a^b W(dt, \varphi_t)$ via fractional calculus. This nonlinear integral arises naturally in the Feynman-Kac formula for stochastic heat equations with random coefficients. We also define iterated nonlinear integrals.Comment: arXiv admin note: substantial text overlap with arXiv:1404.758

Relationship between ferroelectricity and Dzyaloshinskii-Moriya interaction in multiferroics and the effect of bond-bending

We studied the microscopic mechanism of multiferroics, in particular with the "spin current" model (Hosho Katsura, Naoto Nagaosa and Aleander V. Balatsky, Phys. Rev. Lett. 95, 057205 (2005)). Starting from a system with helical spin configuration, we solved for the forms of the electron wave functions and analyzed their characteristics. The relation between ferroelectricity and Dzyaloshinskii-Moriya interaction (I. Dzyaloshinskii, J. Phys. Chem. Solids 4, 241 (1958) and T. Moriya, Phys. Rev. 120, 91 (1960)) is clearly established. There is also a simple relation between the electric polarization and the wave vector of magnetic orders. Finally, we show that the bond-bending exists in transition metal oxides can enhance ferroelectricity.Comment: 14 pages, 3 figures. acceptby Physical Review

Photometric Redshift Requirements for Self-Calibration of Cluster Dark Energy Studies

The ability to constrain dark energy from the evolution of galaxy cluster counts is limited by the imperfect knowledge of cluster redshifts. Ongoing and upcoming surveys will mostly rely on redshifts estimated from broad-band photometry (photo-z's). For a Gaussian distribution for the cluster photo-z errors and a high cluster yield cosmology defined by the WMAP 1 year results, the photo-z bias and scatter needs to be known better than 0.003 and 0.03, respectively, in order not to degrade dark energy constrains by more than 10% for a survey with specifications similar to the South Pole Telescope. Smaller surveys and cosmologies with lower cluster yields produce weaker photo-z requirements, though relative to worse baseline constraints. Comparable photo-z requirements are necessary in order to employ self-calibration techniques when solving for dark energy and observable-mass parameters simultaneously. On the other hand, self-calibration in combination with external mass inferences helps reduce photo-z requirements and provides important consistency checks for future cluster surveys. In our fiducial model, training sets with spectroscopic redshifts for ~5%-15% of the detected clusters are required in order to keep degradations in the dark energy equation of state lower than 20%.Comment: 18 pages, 8 figures, submitted to PR

Effects of disorder on quantum fluctuations and superfluid density of a Bose-Einstein condensate in a two-dimensional optical lattice

We investigate a Bose-Einstein condensate trapped in a 2D optical lattice in the presence of weak disorder within the framework of the Bogoliubov theory. In particular, we analyze the combined effects of disorder and an optical lattice on quantum fluctuations and superfluid density of the BEC system. Accordingly, the analytical expressions of the ground state energy and quantum depletion of the system are obtained. Our results show that the lattice still induces a characteristic 3D to 1D crossover in the behavior of quantum fluctuations, despite the presence of weak disorder. Furthermore, we use the linear response theory to calculate the normal fluid density of the condensate induced by disorder. Our results in the 3D regime show that the combined presence of disorder and lattice induce a normal fluid density that asymptotically approaches 4/3 of the corresponding condensate depletion. Conditions for possible experimental realization of our scenario are also proposed.Comment: 8 pages, 0 figure. To appear in Physical Review