Berry-Phase Induced Dynamical Instability and Minimum Conductivity in Graphene

Single-layer carbon, or graphene, demonstrates amazing transport properties, such as the minimum conductivity near $\frac{4e^2}{h}$ independent of shapes and mobility of samples. This indicates there exist some unusual effects due to specific Dirac dispersion relation of fermion in two dimensions. By deriving fermion-lattice interaction Hamiltonian we show that Berry phases can be produced in fermion states around two Dirac points by relative rotations of two sublattices. The Berry phases in turn remove the degeneracies of energies for states near the Fermi surface, leading to a dynamical instability of the lattice with respect to the rotations. By considering the Berry phases emerging in an uncertain way on fermion wavefunctions in vicinities of the Fermi surface, the conductivity is calculated by using the Landauer-B\"{u}tticker formula together with the transfer-matrix technique, verifying $\sim \frac{4e^2}{h}$ quantized minimum conductivity as observed in experiments independent of shapes and sizes. The relationship between the chaotic structure of fermions due to the Berry phases and the classical transport properties are discussed. The physical meaning is profound as this relationship provides an excellent example to elucidate the mechanism of quantum-classical transition.Comment: 8 pages, 3 figure

Basic properties of Fermi blazars and the "blazar sequence"

By statistically analyzing a large sample which includes blazars of Fermi detection (FBs) and non-Fermi detection (NFBs), we find that there are significant differences between FBs and NFBs for redshift, black hole mass, jet kinetic power from "cavity" power, broad-line luminosity, and ratio of core luminosity to absolute V-band magnitude ($R_{\rm v}$), but not for ratio of radio core to extended flux ($R_{\rm c}$) and Eddington ratio. Compared with NFBs, FBs have larger mean jet power, $R_{\rm c}$ and $R_{\rm v}$ while smaller mean redshift, black hole mass, broad-line luminosity. These results support that the beaming effect is main reason for differences between FBs and NFBs, and that FBs are likely to have a more powerful jet. For both Fermi and non-Fermi blazars, there are significant correlations between jet power and the accretion rate (traced by the broad-emission-lines luminosity), between jet power and black hole mass; for Fermi blazars, the black hole mass does not have significant influence on jet power while for non-Fermi blazars, both accretion rate and black hole mass have contributions to the jet power. Our results support the "blazar sequence" and show that synchrotron peak frequency ($\nu_{\rm peak}$) is associated with accretion rate but not with black hole mass.Comment: 13 pages, 1 table, 13 figures, accepted for publication in MNRAS. arXiv admin note: text overlap with arXiv:1001.0731 by other author

Anti-Resonance and the 0.7 Anomaly in Conductance through a Quantum Point Contact

We investigate the transmission of electrons through a quantum point contact by using a quasi-one-dimensional model with a local bound state below the band bottom. While the complete transmission in lower channels gives rise to plateaus of conductance at multiples of $2e^{2}/h$, the electrons in the lowest channel are scattered by the local bound state when it is singly occupied. This scattering produces a wide zero-transmittance (anti-resonance) for a singlet formed by tunneling and local electrons, and has no effect on triplets, leading to an exact $0.75(2e^{2}/h)$ shoulder prior to the first $2e^{2}/h$ plateau. Formation of a Kondo singlet from electrons in the Fermi sea screens the local moment and reduces the effects of anti-resonance, complementing the shoulder from 0.75 to 1 at low temperatures.Comment: 4 pages, 3 figure

From the "blazar sequence" to unification of blazars and radio galaxies

Based on a large Fermi blazar sample, the blazar sequence (synchrotron peak frequency $\nu_{\rm peak}$ versus synchrotron peak luminosity $L_{\rm peak}$) is revisited. It is found that there is significant anti-correlation between $\nu_{\rm peak}$ and $L_{\rm peak}$ for blazars. However, after being Doppler corrected, the anti-correlation disappears. The jet cavity power ($P_{\rm jet}$) is estimated from extended radio luminosity. So it is free of beaming effect. We find that there are significant anti-correlations between $P_{\rm jet}$ and beam-corrected $\nu_{\rm peak}^{'}$ for both blazars and radio galaxies, which supports the blazar sequence and unification of blazars and radio galaxies (an alternative relationship is the correlation between jet power and $\gamma$-ray photon index).Comment: 7 pages, 2 table, 5 figures, accepted for publication in MNRA

Discussion on Mechanical Learning and Learning Machine

Mechanical learning is a computing system that is based on a set of simple and fixed rules, and can learn from incoming data. A learning machine is a system that realizes mechanical learning. Importantly, we emphasis that it is based on a set of simple and fixed rules, contrasting to often called machine learning that is sophisticated software based on very complicated mathematical theory, and often needs human intervene for software fine tune and manual adjustments. Here, we discuss some basic facts and principles of such system, and try to lay down a framework for further study. We propose 2 directions to approach mechanical learning, just like Church-Turing pair: one is trying to realize a learning machine, another is trying to well describe the mechanical learning.Comment: 11 pages, 2 figure

Why does bulk boundary correspondence fail in some non-hermitian topological models

Bulk boundary correspondence is crucial to topological insulator as it associates the boundary states (with zero energy, chiral or helical) to topological numbers defined in bulk. The application of this correspondence needs a prerequisite condition which is usually not mentioned explicitly: the boundaries themselves cannot alter the bulk states, so as to the topological numbers defined on them. In non-hermitian models with fractional winding number, we prove that such precondition fails and the bulk boundary correspondence is cut out. We show that, as eliminating the hopping between the boundaries to simulate the evolution of a system from the periodic boundary condition to the open boundary condition, exceptional points must be passed through and the topological structure of the spectrum has been changed. This makes the topological structures of a chain with open boundary totally different from that without the boundary. We also argue that such exotic behavior does not emerge when the open boundary is replaced by a domain-wall. So the index theorem can be applied to the systems with domain-walls but cannot be further used to those with open boundary.Comment: 6 pages, 4 figure

An explicit multistep method for the Wigner problem

An explicit multistep scheme is proposed for solving the initial-value Wigner problem. In this scheme, the integrated form of the Wigner equation is approximated by extrapolation or interpolation polynomials on backwards characteristics, and the pseudo-differential operator is tackled by the spectral collocation method. Since it exploits the exact Lagrangian advection, the time stepping of the multistep scheme is not restricted by the CFL-type condition. It is also demonstrated that the calculations of the Wigner potential can be carried out by two successive FFTs, thereby reducing the computational complexity dramatically. Numerical examples illustrating its accuracy are presented

Local optimization-based statistical inference

This paper introduces a local optimization-based approach to test statistical hypotheses and to construct confidence intervals. This approach can be viewed as an extension of bootstrap, and yields asymptotically valid tests and confidence intervals as long as there exist consistent estimators of unknown parameters. We present simple algorithms including a neighborhood bootstrap method to implement the approach. Several examples in which theoretical analysis is not easy are presented to show the effectiveness of the proposed approach

Fano resonances can provide two criteria to distinguish Majorana bound states from other candidates in experiments

There are still debates on whether the observed zero energy peak in the experiment by Stevan {\it et al.} [Science 346, 602(2014)] reveals the existence of the long pursuing Majorana bound states (MBS). we propose that, by mounting two scanning tunneling microscopic tips on top of the topological superconducting chain and measure the transmission spectrum between these two metallic tips, there are two kinds of characteristics on the spectrum that are caused by MBS uniquely. One is symmetric peaks with respect to zero energy and the other is $4\pi$ period caused by a nearby Josephson junction. The former refers to the fact that MBS are composited by Majorana fermions which distributed in the particle and hole subspaces equally. The latter is based on the well known $4\pi$ period of Josephson effect in topological superconductor. We think such two characteristics can be used as criteria to distinguish MBS from other candidates, such as impurities, Kondo effect and traditional Andreev bound states.Comment: 5 pages, 4 figure

Two congruences involving Andrews-Paule's broken 3-diamond partitions and 5-diamond partitions

In this note, we will give proofs of two congruences involving broken 3-diamond partitions and broken 5-diamond partitions which were conjectured by Peter Paule and Silviu Radu.Comment: 6 page