17,518 research outputs found
Orbifolds and Finite Group Representations
We present our recent understanding on resolutions of Gorenstein orbifolds,
which involves the finite group representation theory. We shall concern only
the quotient singularity of hypersurface type. The abelian group for
-type hypersurface quotient singularity of dimension is introduced. For
, the structure of Hilbert scheme of group orbits and crepant resolutions
of -singularity are obtained. The flop procedure of 4-folds is
explicitly constructed through the process.Comment: 20 pages, Latex, 26 figures including 24 postscript; minor changes
for clearer presentation, references updated, typos correcte
Breakdown of local convertibility through Majorana modes in a quantum quench
The local convertibility of quantum states, measured by the R\'enyi entropy,
is concerned with whether or not a state can be transformed into another state,
using only local operations and classical communications. We found that in the
one-dimensional Kitaev chain with quenched chemical potential , the
convertibility between the state for and that for ,
depends on the quantum phases of the system ( is a perturbation).
This is similar to the adiabatic case where the ground state is considered.
Specifically, when the quenched system has edge modes and the subsystem size
for the partition is much larger than the correlation length of the Majorana
fermions which forms the edge modes, the quenched state is locally
inconvertible. We give a physical interpretation for the result, based on
analyzing the interactions between the two subsystems for various partitions.
Our work should help to better understand the many-body phenomena in
topological systems and also the entanglement properties in the Majorana
fermionic quantum computation.Comment: 8 pages, 5 figures, accepted by Physical Review
On Hypersurface Quotient Singularity of Dimension 4
We consider geometrical problems on Gorenstein hypersurface orbifolds of
dimension through the theory of Hilbert scheme of group orbits. For
a linear special group acting on \CZ^n, we study the -Hilbert scheme,
\hl^G(\CZ^n), and crepant resolutions of \CZ^n/G for =the -type
abelian group . For , we obtain the explicit structure of
\hl^{A_r(4)}(\CZ^4). The crepant resolutions of \CZ^4/A_r(4) are
constructed through their relation with \hl^{A_r(4)}(\CZ^4), and the
connections between these crepant resolutions are found by the "flop" procedure
of 4-folds. We also make some primitive discussion on \hl^G(\CZ^n) for the
= alternating group {\goth A}_{n+1} of degree with the standard
representation on \CZ^n; the detailed structure of \hl^{{\goth A}_4}(\CZ^3)
is explicitly constructed.Comment: 27 pages, Latex, 11 figures, Some reorganizations and improvement of
presentations, Typos corrected, Arguments of Theorem 1 of section 3 in the
earlier version are refined with clearer explanation for the justification of
contradicting statement appeared in a published journal literature by some
other autho
Multiple Disk Gaps and Rings Generated by a Single Super-Earth: II. Spacings, Depths, and Number of Gaps, with Application to Real Systems
ALMA has found multiple dust gaps and rings in a number of protoplanetary
disks in continuum emission at millimeter wavelengths. The origin of such
structures is in debate. Recently, we documented how one super-Earth planet can
open multiple (up to five) dust gaps in a disk with low viscosity
(). In this paper, we examine how the positions, depths,
and total number of gaps opened by one planet depend on input parameters, and
apply our results to real systems. Gap locations (equivalently, spacings) are
the easiest metric to use when making comparisons between theory and
observations, as positions can be robustly measured. We fit the locations of
gaps empirically as functions of planet mass and disk aspect ratio. We find
that the locations of the double gaps in HL Tau and TW Hya, and of all three
gaps in HD 163296, are consistent with being opened by a sub-Saturn mass
planet. This scenario predicts the locations of other gaps in HL Tau and TW
Hya, some of which appear consistent with current observations. We also show
how the Rossby wave instability may develop at the edges of several gaps and
result in multiple dusty vortices, all caused by one planet. A planet as low in
mass as Mars may produce multiple dust gaps in the terrestrial planet forming
region.Comment: 16 pages; ApJ accepte
Multiple Disk Gaps and Rings Generated by a Single Super-Earth
We investigate the observational signatures of super-Earths (i.e.,
Earth-to-Neptune mass planets) in their natal disks of gas and dust. Combining
two-fluid global hydrodynamics simulations with a radiative transfer code, we
calculate the distributions of gas and of sub-mm-sized dust in a disk perturbed
by a super-Earth, synthesizing images in near-infrared scattered light and the
mm-wave thermal continuum for direct comparison with observations. In low
viscosity gas (), a super-Earth opens two annular gaps
to either side of its orbit by the action of Lindblad torques. This double gap
and its associated gas pressure gradients cause dust particles to be dragged by
gas into three rings: one ring sandwiched between the two gaps, and two rings
located at the gap edges farthest from the planet. Depending on system
parameters, additional rings may manifest for a single planet. A double gap
located at tens of AUs from a host star in Taurus can be detected in the dust
continuum by the Atacama Large Millimeter Array (ALMA) at an angular resolution
of ~0".03 after two hours of integration. Ring and gap features persist in a
variety of background disk profiles, last for thousands of orbits, and change
their relative positions and dimensions depending on the speed and direction of
planet migration. Candidate double gaps have been observed by ALMA in systems
like HL Tau (D5 and D6) and TW Hya (at 37 and 43 AU); we submit that each
double gap is carved by one super-Earth in nearly inviscid gas.Comment: 23 pages, 1 table, 14 figures, ApJ accepte
Can the 750-GeV diphoton resonance be the singlet Higgs boson of custodial Higgs triplet model?
The observation of diphoton excess around the mass of 750 GeV in LHC Run-II
motivates us to consider whether the singlet Higgs boson in the custodial Higgs
triplet model can serve as a good candidate because an earlier study of
comprehensive parameter scan shows that it can have the right mass in the
viable mass spectra. By assuming the singlet Higgs mass at 750 GeV, its total
width less than 50 GeV and imposing constraints from the LHC 8-TeV data, we
identify an approximately linear region on the plane along
which the exotic Higgs boson masses satisfy a specific hierarchy and have lower
possible spectra, where denotes the triplet vacuum expectation value
and is the mixing angle between the singlet Higgs boson and the
standard model-like Higgs boson. Although the diphoton decay rate can be
enhanced by charged Higgs bosons running in the loop in this region, it is
mostly orders of magnitude smaller than that required for the observed
production rate, except for the small region when the diphoton
fusion production mechanism becomes dominant. Nonetheless, this part of
parameter space suffers from the problems of breakdown of perturbativity and
large uncertainties in the photon parton distribution function of proton.Comment: 14 pages, 2 figures, and 2 tables; bugs in numerical calculations
fixed, and discussions and conclusions changed; typo corrected; 16 pages,
expanded with more detailed discussions, updated figures and tables, version
to appear in the journa
Extracting entangled qubits from Majorana fermions in quantum dot chains through the measurement of parity
We propose a scheme for extracting entangled charge qubits from quantum-dot
chains that support zero-energy edge modes. The edge mode is composed of
Majorana fermions localized at the ends of each chain. The qubit, logically
encoded in double quantum dots, can be manipulated through tunneling and
pairing interactions between them. The detailed form of the entangled state
depends on both the parity measurement (an even or odd number) of the
boundary-site electrons in each chain and the teleportation between the chains.
The parity measurement is realized through the dispersive coupling of
coherent-state microwave photons to the boundary sites, while the teleportation
is performed via Bell measurements. Our scheme illustrates \emph{localizable
entanglement} in a fermionic system, which serves feasibly as a quantum
repeater under realistic experimental conditions, as it allows for finite
temperature effect and is robust against disorders, decoherence and
quasi-particle poisoning.Comment: Accepted by Scientific Report
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