The surface states of topological insulators - Dirac fermion in curved two dimensional spaces

The surface of a topological insulator is a closed two dimensional manifold. The surface states are described by the Dirac Hamiltonian in curved two dimensional spaces. For a slab-like sample with a magnetic field perpendicular to its top and bottom surfaces, there are chiral states delocalized on the four side faces. These "chiral sheets" carry both charge and spin currents. In strong magnetic fields the quantized charge Hall effect (\s_{xy}=(2n+1)e^2/h) will coexist with spin Hall effect.Comment: PRL accepted version, new information on thickness dependence adde

On subgroups in division rings of type 22

Let $D$ be a division ring with center $F$. We say that $D$ is a {\em division ring of type $2$} if for every two elements $x, y\in D,$ the division subring $F(x, y)$ is a finite dimensional vector space over $F$. In this paper we investigate multiplicative subgroups in such a ring.Comment: 10 pages, 0 figure

Model and Reinforcement Learning for Markov Games with Risk Preferences

We motivate and propose a new model for non-cooperative Markov game which considers the interactions of risk-aware players. This model characterizes the time-consistent dynamic "risk" from both stochastic state transitions (inherent to the game) and randomized mixed strategies (due to all other players). An appropriate risk-aware equilibrium concept is proposed and the existence of such equilibria is demonstrated in stationary strategies by an application of Kakutani's fixed point theorem. We further propose a simulation-based Q-learning type algorithm for risk-aware equilibrium computation. This algorithm works with a special form of minimax risk measures which can naturally be written as saddle-point stochastic optimization problems, and covers many widely investigated risk measures. Finally, the almost sure convergence of this simulation-based algorithm to an equilibrium is demonstrated under some mild conditions. Our numerical experiments on a two player queuing game validate the properties of our model and algorithm, and demonstrate their worth and applicability in real life competitive decision-making.Comment: 38 pages, 6 tables, 5 figure

Law and Development

This is a draft of a book to accompany a course on the sociology of law and law and development at Boston University

Control of the persistent currents in two interacting quantum rings through the Coulomb interaction and inter-ring tunneling

The persistent current in two vertically coupled quantum rings containing few electrons is studied. We find that the Coulomb interaction between the rings in the absence of tunneling affects the persistent current in each ring and the ground state configurations. Quantum tunneling between the rings alters significantly the ground state and the persistent current in the system.Comment: accepted for publication in Phys. Rev.

A Common Origin for Quasar Extended Emission-Line Regions and Their Broad-Line Regions

We present a correlation between the presence of luminous extended emission-line regions (EELRs) and the metallicity of the broad-line regions (BLRs) of low-redshift quasars. The result is based on ground-based [O III] 5007 narrow-band imaging and Hubble Space Telescope UV spectra of 12 quasars at 0.20 < z < 0.45. Quasars showing luminous EELRs have low-metallicity BLRs (Z < 0.6 Z_Solar), while the remaining quasars show typical metal-rich gas (Z > Z_Solar). Previous studies have shown that EELRs themselves also have low metallicities (Z < 0.5 Z_Solar). The correlation between the occurrence of EELRs and the metallicity of the BLRs, strengthened by the sub-Solar metallicity in both regions, indicates a common external origin for the gas, almost certainly from the merger of a gas-rich galaxy. Our results provide the first direct observational evidence that the gas from a merger can indeed be driven down to the immediate vicinity (< 1 pc) of the central black hole.Comment: Accepted for publication in ApJ Letters. 4 pages, 1 figure, 1 tabl

Two-body hadronic charmed meson decays

We study in this work the two-body hadronic charmed meson decays, including both the PP and VP modes. The latest experimental data are first analyzed in the diagrammatic approach. The magnitudes and strong phases of the flavor amplitudes are extracted from the Cabibbo-favored (CF) decay modes using $\chi^2$ minimization. The best-fitted values are then used to predict the branching fractions of the singly-Cabibbo-suppressed (SCS) and doubly-Cabibbo-suppressed decay modes in the flavor SU(3) symmetry limit. We observe significant SU(3) breaking effects in some of SCS channels. In the case of VP modes, we point out that the $A_P$ and $A_V$ amplitudes cannot be completely determined based on currently available data. We conjecture that the quoted experimental results for both $D_s^+\to\bar K^0K^{*+}$ and $D_s^+\to \rho^+\eta'$ are overestimated. We compare the sizes of color-allowed and color-suppressed tree amplitudes extracted from the diagrammatical approach with the effective parameters $a_1$ and $a_2$ defined in the factorization approach. The ratio $|a_2/a_1|$ is more or less universal among the $D \to {\bar K} \pi$, ${\bar K}^* \pi$ and ${\bar K} \rho$ modes. This feature allows us to discriminate between different solutions of topological amplitudes. For the long-standing puzzle about the ratio $\Gamma(D^0\to K^+K^-)/\Gamma(D^0\to\pi^+\pi^-)$, we argue that, in addition to the SU(3) breaking effect in the spectator amplitudes, the long-distance resonant contribution through the nearby resonance $f_0(1710)$ can naturally explain why $D^0$ decays more copiously to $K^+ K^-$ than $\pi^+ \pi^-$ through the $W$-exchange topology.Comment: 32 pages, 5 figures. An alternative method for error bar extraction is used; last columns of Tables~I to VI, and all entries in Tables~VII, VIII and X are modified. To appear in PRD