Vector chiral states in low-dimensional quantum spin systems

A class of exact spin ground states with nonzero averages of vector spin chirality, $$, is presented. It is obtained by applying non-uniform O(2) rotations of spin operators in the XY plane on the SU(2)-invariant Affleck-Kennedy-Lieb-Tasaki (AKLT) states and their parent Hamiltonians. Excitation energies of the new ground states are studied with the use of single-mode approximation in one dimension for S=1. The excitation gap remains robust. Construction of chiral AKLT states is shown to be possible in higher dimensions. We also present a general idea to produce vector chirality-condensed ground states as non-uniform O(2) rotations of the non-chiral parent states. Dzyaloshinskii-Moriya interaction is shown to imply non-zero spin chirality.Comment: 4 pages, 1 figur

Extraction of information about periodic orbits from scattering functions

As a contribution to the inverse scattering problem for classical chaotic systems, we show that one can select sequences of intervals of continuity, each of which yields the information about period, eigenvalue and symmetry of one unstable periodic orbit.Comment: LaTeX, 13 pages (includes 5 eps-figures

Less-forgetful Learning for Domain Expansion in Deep Neural Networks

Expanding the domain that deep neural network has already learned without accessing old domain data is a challenging task because deep neural networks forget previously learned information when learning new data from a new domain. In this paper, we propose a less-forgetful learning method for the domain expansion scenario. While existing domain adaptation techniques solely focused on adapting to new domains, the proposed technique focuses on working well with both old and new domains without needing to know whether the input is from the old or new domain. First, we present two naive approaches which will be problematic, then we provide a new method using two proposed properties for less-forgetful learning. Finally, we prove the effectiveness of our method through experiments on image classification tasks. All datasets used in the paper, will be released on our website for someone's follow-up study.Comment: 8 pages, accepted to AAAI 201

Pointwise asymptotic behavior of modulated periodic reaction-diffusion waves

By working with the periodic resolvent kernel and Bloch-decomposition, we establish pointwise bounds for the Green function of the linearized equation associated with spatially periodic traveling waves of a system of reaction diffusion equations.With our linearized estimates together with a nonlinear iteration scheme developed by Johnson-Zumbrun, we obtain $L^p$- behavior($p \geq 1$) of a nonlinear solution to a perturbation equation of a reaction-diffusion equation with respect to initial data in $L^1 \cap H^1$ recovering and slightly sharpening results obtained by Schneider using weighted energy and renormalization techniques. We obtain also pointwise nonlinear estimates with respect to two different initial perturbations $|u_0|\leq E_0e^{-|x|^2/M}$ and $|u_0| \leq E_0(1+|x|)^{-3/2}$, respectively, $E_0>0$ sufficiently small and $M>1$ sufficiently large, showing that behavior is that of a heat kernel. These pointwise bounds have not been obtained elsewhere, and do not appear to be accessible by previous techniques

Coupling of phonons and spin waves in triangular antiferromagnet

We investigate the influence of the spin-phonon coupling in the triangular antiferromagnet where the coupling is of the exchange-striction type. The magnon dispersion is shown to be modified significantly at wave vector (2pi,0) and its symmetry-related points, exhibiting a roton-like minimum and an eventual instability in the dispersion. Various correlation functions such as equal-time phonon correlation, spin-spin correlation, and local magnetization are calculated in the presence of the coupling.Comment: 6 pages, 5 figures; references added, minor text revisions, submitted to PR