10,493 research outputs found
HOMFLY polynomials, stable pairs and motivic Donaldson-Thomas invariants
Hilbert scheme topological invariants of plane curve singularities are
identified to framed threefold stable pair invariants. As a result, the
conjecture of Oblomkov and Shende on HOMFLY polynomials of links of plane curve
singularities is given a Calabi-Yau threefold interpretation. The motivic
Donaldson-Thomas theory developed by M. Kontsevich and the third author then
yields natural motivic invariants for algebraic knots. This construction is
motivated by previous work of V. Shende, C. Vafa and the first author on the
large duality derivation of the above conjecture.Comment: 59 pages; v2 references added, minor corrections; v3: exposition
improved, proofs expanded, results unchanged, to appear in Comm. Num. Th.
Phy
Steady-State Two Atom Entanglement in a Pumped Cavity
In this paper we explore the possibility of a steady-state entanglement of
two two-level atoms inside a pumped cavity by taking into account cavity
leakage and the spontaneous emission of photons by the atoms. We describe the
system in the dressed state picture in which the coherence is built into the
dressed states while transitions between the dressed states are incoherent. Our
model assumes the vacuum Rabi splitting of the dressed states to be much larger
than any of the decay parameters of the system which allows atom-field
coherence to build up before any decay process takes over. We show that, under
our model, a pumping field cannot entangle two closed two-level atoms inside
the cavity in the steady-state, but a steady-state entanglement can be achieved
with two open two-level atoms.Comment: 19 pages, 5 figure
Classification of free actions on complete intersections of four quadrics
In this paper we classify all free actions of finite groups on Calabi-Yau complete intersection of four quadrics in β 7, up to projective equivalence. We get some examples of smooth Calabi-Yau three-folds with large nonabelian fundamental groups. We also observe the relation between some of these examples and moduli of polarized abelian surfaces. Β© 2011 International Press.postprin
Insulating state and the importance of the spin-orbit coupling in CaCoRhO
We have carried out a comparative theoretical study of the electronic
structure of the novel one-dimensional CaCoRhO and CaFeRhO
systems. The insulating antiferromagnetic state for the CaFeRhO can be
well explained by band structure calculations with the closed shell high-spin
(Fe) and low-spin (Rh) configurations. We
found for the CaCoRhO that the Co has a strong tendency to be
(Co) rather than (Co), and that there is an orbital
degeneracy in the local Co electronic structure. We argue that it is the
spin-orbit coupling which will lift this degeneracy thereby enabling local spin
density approximation + Hubbard U (LSDA+U) band structure calculations to
generate the band gap. We predict that the orbital contribution to the magnetic
moment in CaCoRhO is substantial, i.e. significantly larger than 1
per formula unit. Moreover, we propose a model for the contrasting
intra-chain magnetism in both materials.Comment: 7 pages, 4 figures, and 1 tabl
Generation of frequency multiplexed entangled single photons assisted by the entanglement
We present a scheme to generate the frequency multiplexed entangled (FME)
single photons based on the entanglement between two species atomic mixture
ensemble. The write and reads fields driven according to a certain timing
sequence, the generation of FME single photons can be repeated until success is
achieved. The source might have significant applications in wavelength division
multiplexing quantum key distribution.Comment: 4 pages, 4 figures, submitted to PR
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