16,224 research outputs found
Topological invariants for phase transition points of one-dimensional topological systems
We study topological properties of phase transition points of two
topologically non-trivial classes (D and DIII) in one dimension
by assigning a Berry phase defined on closed circles around the gap closing
points in the parameter space of momentum and a transition driving parameter.
While the topological property of the system is generally
characterized by a topological invariant, we identify that it
has a correspondence to the quantized Berry phase protected by the
particle-hole symmetry, and then give a proper definition of Berry phase to the
phase transition point. By applying our scheme to some specific models of class
D and DIII, we demonstrate that the topological phase transition can be well
characterized by the Berry phase of the transition point, which reflects the
change of Berry phases of topologically different phases across the phase
transition point.Comment: 6 pages, 5 figure
Winding numbers of phase transition points for one-dimensional topological systems
We study topological properties of phase transition points of one-dimensional
topological quantum phase transitions by assigning winding numbers defined on
closed circles around the gap closing points in the parameter space of momentum
and a transition driving parameter, which overcomes the problem of ill
definition of winding numbers on the transition points. By applying our scheme
to the extended Kitaev model and extended Su-Schrieffer-Heeger model, we
demonstrate that the topological phase transition can be well characterized by
winding numbers of transition points, which reflect the change of the winding
number of topologically different phases across the phase transition points.Comment: 5 pages, 5 figure
The Mid-Infrared Extinction Law and its Variation in the Coalsack Nebula
In recent years the wavelength dependence of interstellar extinction from the
ultraviolet (UV), optical, through the near- and mid-infrared (IR) has been
studied extensively. Although it is well established that the UV/optical
extinction law varies significantly among the different lines of sight, it is
not clear how the IR extinction varies among various environments. In this
work, using the color-excess method and taking red giants as the extinction
tracer, we determine the interstellar extinction Alambda in the four
Spitzer/IRAC bands of the Coalsack nebula, a nearby starless dark cloud, based
on the data obtained from the 2MASS and Spitzer/GLIMPSE surveys. We select five
individual regions across the nebula that span a wide variety of physical
conditions, ranging from diffuse, translucent to dense environments, as traced
by the visual extinction, the Spitzer/MIPS 24micron emission, and CO emission.
We find that Alambda/AKs, the mid-IR extinction relative to AKs, decreases from
diffuse to dense environments, which may be explained in terms of ineffective
dust growth in dense regions. The mean extinction (relative to AKs) is
calculated for the four IRAC bands as well, which exhibits a flat mid-IR
extinction law, consistent with previous determinations for other regions. The
extinction in the IRAC 4.5micron band is anomalously high, much higher than
that of the other three IRAC bands. It cannot be explained in terms of CO and
CO2 ices. The mid-IR extinction in the four IRAC bands have also been derived
for four representative regions in the Coalsack Globule 2 which respectively
exhibit strong ice absorption, moderate or weak ice absorption, and very weak
or no ice absorption. The derived mid-IR extinction curves are all flat, with
Alambda/AKs increasing with the decrease of the H2O ice absorption optical
depth.Comment: 39 pages, 13 figures, accepted by Ap
- …