Representation of SO(3) Group by a Maximally Entangled State

A representation of the SO(3) group is mapped into a maximally entangled two qubit state according to literatures. To show the evolution of the entangled state, a model is set up on an maximally entangled electron pair, two electrons of which pass independently through a rotating magnetic field. It is found that the evolution path of the entangled state in the SO(3) sphere breaks an odd or even number of times, corresponding to the double connectedness of the SO(3) group. An odd number of breaks leads to an additional $\pi$ phase to the entangled state, but an even number of breaks does not. A scheme to trace the evolution of the entangled state is proposed by means of entangled photon pairs and Kerr medium, allowing observation of the additional $\pi$ phase.Comment: 4 pages, 3 figure

Rapid "Turn-on" of type 1 AGN in a quiescent early type galaxy SDSS1115+0544

We present a detailed study of a transient in the center of SDSS1115+0544 based on the extensive UV, optical, mid-IR light curves (LC) and spectra over 1200 days. The host galaxy is a quiescent early type galaxy at $z$ = 0.0899 with a blackhole mass of $2\times10^7M_\odot$. The transient underwent a 2.5 magnitude brightening over $\sim120$ days, reaching a peak $V$-band luminosity (extinction corrected) of $-20.9$ magnitude, then fading 0.5 magnitude over 200 days, settling into a plateau of $>600$ days. Following the optical brightening are the significant mid-IR flares at $3.4$ and $4.5\mu$m, with a peak time delay of $\sim180$ days. The mid-IR LCs are explained as the echo of UV photons by a dust medium with a radius of $5\times10^{17}$ cm, consistent with $\rm E(B-V)$ of 0.58 inferred from the spectra. This event is very energetic with an extinction corrected $L_{bol} \sim 4\times10^{44}$ erg s$^{-1}$. Optical spectra over 400 days in the plateau phase revealed newly formed broad H$\alpha, \beta$ emission with a FWHM of $\sim3750$ km s$^{-1}$ and narrow coronal lines such as [Fe VII], [Ne V]. This flare also has a steeply rising UV continuum, detected by multi-epoch $Swift$ data at $+700$ to $+900$ days post optical peak. The broad Balmer lines and the UV continuum do not show significant temporal variations. The slow evolving LCs over 1200 days, the constant Balmer lines and UV continuum at late-times rule out TDE and SN IIn as the physical model for this event. We propose that this event is a `turn-on' AGN, transitioning from a quiescent state to a type 1 AGN with a sub-Eddington accretion rate of $0.017M_\odot$/yr. This change occurred on a very short time scale of $\sim 120- 200$ days. The discovery of such a rapid `turn-on' AGN poses challenges to accretion disk theories and may indicate such event is not extremely rare.Comment: Comments are welcome. Emails to the first author. Accepted for publication in Ap

Multifunctional in vivo vascular imaging using near-infrared II fluorescence

In vivo real-time epifluorescence imaging of mouse hindlimb vasculatures in the second near-infrared region (NIR-II, 1.1~1.4 microns) is performed using single-walled carbon nanotubes (SWNTs) as fluorophores. Both high spatial resolution (~30 microns) and temporal resolution (<200 ms/frame) for small vessel imaging are achieved 1-3 mm deep in the tissue owing to the beneficial NIR-II optical window that affords deep anatomical penetration and low scattering. This spatial resolution is unattainable by traditional NIR imaging (NIR-I, 0.75~0.9 microns) or microscopic computed tomography (micro-CT), while the temporal resolution far exceeds scanning microscopic imaging techniques. Arterial and venous vessels are unambiguously differentiated using a dynamic contrast-enhanced NIR-II imaging technique based on their distinct hemodynamics. Further, the deep tissue penetration, high spatial and temporal resolution of NIR-II imaging allow for precise quantifications of blood velocity in both normal and ischemic femoral arteries, which are beyond the capability of ultrasonography at lower blood velocity.Comment: 33 pages, 5 main text figures, 6 supporting figures and 2 tables; Published online at Nature Medicine, 201

Darboux transformation for two component derivative nonlinear Schr\"odinger equation

In this paper, we consider the two component derivative nonlinear Schr\"{o}dinger equation and present a simple Darboux transformation for it. By iterating this Darboux transformation, we construct a compact representation for the $N-$soliton solutions.Comment: 12 pages, 2 figure

Projected wave functions for fractionalized phases of quantum spin systems

Gutzwiller projection allows a construction of an assortment of variational wave functions for strongly correlated systems. For quantum spin S=1/2 models, Gutzwiller-projected wave functions have resonating-valence-bond structure and may represent states with fractional quantum numbers for the excitations. Using insights obtained from field-theoretical descriptions of fractionalization in two dimensions, we construct candidate wave functions of fractionalized states by projecting specific superconducting states. We explicitly demonstrate the presence of topological order in these states.Comment: 10 pages, 3 figure

Fractionalization in an Easy-axis Kagome Antiferromagnet

We study an antiferromagnetic spin-1/2 model with up to third nearest-neighbor couplings on the Kagome lattice in the easy-axis limit, and show that its low-energy dynamics are governed by a four site XY ring exchange Hamiltonian. Simple ``vortex pairing'' arguments suggest that the model sustains a novel fractionalized phase, which we confirm by exactly solving a modification of the Hamiltonian including a further four-site interaction. In this limit, the system is a featureless ``spin liquid'', with gaps to all excitations, in particular: deconfined S^z=1/2 bosonic ``spinons'' and Ising vortices or ``visons''. We use an Ising duality transformation to express vison correlators as non-local strings in terms of the spin operators, and calculate the string correlators using the ground state wavefunction of the modified Hamiltonian. Remarkably, this wavefunction is exactly given by a kind of Gutzwiller projection of an XY ferromagnet. Finally, we show that the deconfined spin liquid state persists over a finite range as the additional four-spin interaction is reduced, and study the effect of this reduction on the dynamics of spinons and visons.Comment: best in color but readable in B+

The emission positions of kHz QPOs and Kerr spacetime influence

Based the Alfven wave oscillation model (AWOM) and relativistic precession model (RPM) for twin kHz QPOs, we estimate the emission positions of most detected kHz QPOs to be at r=18+-3 km (R/15km) except Cir X-1 at r = 30\+-5 km (R/15km). For the proposed Keplerian frequency as an upper limit to kHz QPO, the spin effects in Kerr Spacetime are discussed, which have about a 5% (2%) modification for that of the Schwarzchild case for the spin frequency of 1000 (400) Hz.The application to the four typical QPO sources, Cir X-1, Sco X-1, SAX J1808.4-3658 and XTE 1807-294, is mentioned.Comment: Science China, Physics, Mechanics & Astronomy, 2010, 53, NO.

Singularly Perturbed Monotone Systems and an Application to Double Phosphorylation Cycles

The theory of monotone dynamical systems has been found very useful in the modeling of some gene, protein, and signaling networks. In monotone systems, every net feedback loop is positive. On the other hand, negative feedback loops are important features of many systems, since they are required for adaptation and precision. This paper shows that, provided that these negative loops act at a comparatively fast time scale, the main dynamical property of (strongly) monotone systems, convergence to steady states, is still valid. An application is worked out to a double-phosphorylation ``futile cycle'' motif which plays a central role in eukaryotic cell signaling.Comment: 21 pages, 3 figures, corrected typos, references remove