130,268 research outputs found
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 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 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 (), but not for ratio of
radio core to extended flux () and Eddington ratio. Compared with
NFBs, FBs have larger mean jet power, and 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
() 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
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
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 , 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 shoulder prior to the first 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 versus synchrotron peak luminosity )
is revisited. It is found that there is significant anti-correlation between
and for blazars. However, after being Doppler
corrected, the anti-correlation disappears. The jet cavity power () is estimated from extended radio luminosity. So it is free of beaming
effect. We find that there are significant anti-correlations between and beam-corrected 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 -ray photon index).Comment: 7 pages, 2 table, 5 figures, accepted for publication in MNRA
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 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 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
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