2,692 research outputs found
The Coulomb Branch Formula for Quiver Moduli Spaces
In recent series of works, by translating properties of multi-centered
supersymmetric black holes into the language of quiver representations, we
proposed a formula that expresses the Hodge numbers of the moduli space of
semi-stable representations of quivers with generic superpotential in terms of
a set of invariants associated to `single-centered' or `pure-Higgs' states. The
distinguishing feature of these invariants is that they are independent of the
choice of stability condition. Furthermore they are uniquely determined by the
-genus of the moduli space. Here, we provide a self-contained summary
of the Coulomb branch formula, spelling out mathematical details but leaving
out proofs and physical motivations.Comment: 24 pages. v2: final version; minor changes, including a new diagra
Generalized quiver mutations and single-centered indices
Quiver quantum mechanics is invariant under Seiberg duality. A mathematical
consequence is that the cohomology of the Higgs branch moduli space is
invariant under mutations of the quiver. The Coulomb branch formula, on the
other hand, conjecturally expresses the Poincar\'e / Dolbeault polynomial of
the Higgs branch moduli space in terms of certain quantities known as
single-centered indices. In this work we determine the transformations of these
single-centered indices under mutations. Moreover, we generalize these
mutations to quivers whose nodes carry single-centered indices different from
unity. Although the Higgs branch description of these generalized quivers is
currently unknown, the Coulomb branch formula is conjectured to be invariant
under generalized mutations.Comment: 33 pages, 1 figure; a mathematica notebook using an updated version
of the CoulombHiggs.m package released along with our previous work
arXiv:1302.5498 is included as ancillary file; v2: refs added, one extra
paragraph in sec 2.
On the Coulomb and Higgs branch formulae for multi-centered black holes and quiver invariants
In previous work we have shown that the equivariant index of multi-centered
N=2 black holes localizes on collinear configurations along a fixed axis. Here
we provide a general algorithm for enumerating such collinear configurations
and computing their contribution to the index. We apply this machinery to the
case of black holes described by quiver quantum mechanics, and give a
systematic prescription -- the Coulomb branch formula -- for computing the
cohomology of the moduli space of quiver representations. For quivers without
oriented loops, the Coulomb branch formula is shown to agree with the Higgs
branch formula based on Reineke's result for stack invariants, even when the
dimension vector is not primitive. For quivers with oriented loops, the Coulomb
branch formula parametrizes the Poincar\'e polynomial of the quiver moduli
space in terms of single-centered (or pure-Higgs) BPS invariants, which are
conjecturally independent of the stability condition (i.e. the choice of
Fayet-Iliopoulos parameters) and angular-momentum free. To facilitate further
investigation we provide a Mathematica package "CoulombHiggs.m" implementing
the Coulomb and Higgs branch formulae.Comment: 45 pages, 1 figure; v2 (after publication in JHEP): New recursion
scheme introduced in Note Added, 4.31-4.34; Appendix updated to document new
features of the Mathematica package "CoulombHiggs.m" v2.0, available along
with example files from the submission source, or from
http://www.lpthe.jussieu.fr/~pioline/computing.htm
Higher order nonclassicalities in a codirectional nonlinear optical coupler: Quantum entanglement, squeezing and antibunching
Higher order nonclassical properties of fields propagating through a
codirectional asymmetric nonlinear optical coupler which is prepared by
combining a linear wave guide and a nonlinear (quadratic) wave guide operated
by second harmonic generation are studied. A completely quantum mechanical
description is used here to describe the system. Closed form analytic solutions
of Heisenberg's equations of motion for various modes are used to show the
existence of higher order antibunching, higher order squeezing, higher order
two-mode and multi-mode entanglement in the asymmetric nonlinear optical
coupler. It is also shown that nonclassical properties of light can transfer
from a nonlinear wave guide to a linear wave guide.Comment: 9 pages 5 figure
NMR solution structure of a chymotrypsin inhibitor from the Taiwan cobra Naja naja atra
The Taiwan cobra (Naja naja atra) chymotrypsin inhibitor (NACI) consists of 57 amino acids and is related to other Kunitz-type inhibitors such as bovine pancreatic trypsin inhibitor (BPTI) and Bungarus fasciatus fraction IX (BF9), another chymotrypsin inhibitor. Here we present the solution structure of NACI. We determined the NMR structure of NACI with a root-mean-square deviation of 0.37 Å for the backbone atoms and 0.73 Å for the heavy atoms on the basis of 1,075 upper distance limits derived from NOE peaks measured in its NOESY spectra. To investigate the structural characteristics of NACI, we compared the three-dimensional structure of NACI with BPTI and BF9. The structure of the NACI protein comprises one 310-helix, one α-helix and one double-stranded antiparallel β-sheet, which is comparable with the secondary structures in BPTI and BF9. The RMSD value between the mean structures is 1.09 Å between NACI and BPTI and 1.27 Å between NACI and BF9. In addition to similar secondary and tertiary structure, NACI might possess similar types of protein conformational fluctuations as reported in BPTI, such as Cys14–Cys38 disulfide bond isomerization, based on line broadening of resonances from residues which are mainly confined to a region around the Cys14–Cys38 disulfide bond
Interplay between quantum Zeno and anti-Zeno effects in a non-degenerate hyper-Raman nonlinear optical coupler
Quantum Zeno and anti-Zeno effects are studied in an asymmetric nonlinear
optical coupler composed of a probe waveguide and a system waveguide. The
system is a nonlinear waveguide operating under non-degenerate hyper-Raman
process, while both the pump modes in the system are constantly interacting
with the probe waveguide. The effect of the presence of probe on the temporal
evolution of the system in terms of the number of photons in Stokes and
anti-Stokes modes as well as phonon number is quantified as Zeno parameter. The
negative (positive) values of the Zeno parameter in the specific mode are
considered as the signatures of the quantum Zeno (anti-Zeno)effect in that mode
of the system. It is observed that the phase mismatch in Stokes and anti-Stokes
generation processes can be controlled to induce a transition between quantum
Zeno and anti-Zeno effects for both off-resonant and resonant hyper-Raman
process. However, in case of off-resonant hyper-Raman process in the system
waveguide, the frequency detuning parameters can also be used analogously to
cause the desired crossover. Further, the general nature of the physical system
and the perturbative technique used here allowed us to analytically study the
possibilities of observing quantum Zeno and anti-Zeno effects in a large number
of special cases, including situations where the process is spontaneous,
partially spontaneous and/or the system is operated under degenerate
hyper-Raman process, or a simple Raman process.Comment: Dynamics of quantum Zeno and anti-Zeno effect is studied analytically
in a nonlinear optical coupler which is very general in natur
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