On quantum vertex algebras and their modules

We give a survey on the developments in a certain theory of quantum vertex algebras, including a conceptual construction of quantum vertex algebras and their modules and a connection of double Yangians and Zamolodchikov-Faddeev algebras with quantum vertex algebras.Comment: 18 pages; contribution to the proceedings of the conference in honor of Professor Geoffrey Maso

Modules-at-infinity for quantum vertex algebras

This is a sequel to \cite{li-qva1} and \cite{li-qva2} in a series to study vertex algebra-like structures arising from various algebras such as quantum affine algebras and Yangians. In this paper, we study two versions of the double Yangian $DY_{\hbar}(sl_{2})$, denoted by $DY_{q}(sl_{2})$ and $DY_{q}^{\infty}(sl_{2})$ with $q$ a nonzero complex number. For each nonzero complex number $q$, we construct a quantum vertex algebra $V_{q}$ and prove that every $DY_{q}(sl_{2})$-module is naturally a $V_{q}$-module. We also show that $DY_{q}^{\infty}(sl_{2})$-modules are what we call $V_{q}$-modules-at-infinity. To achieve this goal, we study what we call $\S$-local subsets and quasi-local subsets of \Hom (W,W((x^{-1}))) for any vector space $W$, and we prove that any $\S$-local subset generates a (weak) quantum vertex algebra and that any quasi-local subset generates a vertex algebra with $W$ as a (left) quasi module-at-infinity. Using this result we associate the Lie algebra of pseudo-differential operators on the circle with vertex algebras in terms of quasi modules-at-infinity.Comment: Latex, 48 page

Eruption of a multi-flux-rope system in solar active region 12673 leading to the two largest flares in Solar Cycle 24

Solar active region (AR) 12673 in 2017 September produced two largest flares in Solar Cycle 24: the X9.3 flare on September 06 and the X8.2 flare on September 10. We attempt to investigate the evolutions of the two great flares and their associated complex magnetic system in detail. Aided by the NLFFF modeling, we identify a double-decker flux rope configuration above the polarity inversion line (PIL) in the AR core region. The north ends of these two flux ropes were rooted in a negative- polarity magnetic patch, which began to move along the PIL and rotate anticlockwise before the X9.3 flare on September 06. The strong shearing motion and rotation contributed to the destabilization of the two magnetic flux ropes, of which the upper one subsequently erupted upward due to the kink-instability. Then another two sets of twisted loop bundles beside these ropes were disturbed and successively erupted within 5 minutes like a chain reaction. Similarly, multiple ejecta components were detected to consecutively erupt during the X8.2 flare occurring in the same AR on September 10. We examine the evolution of the AR magnetic fields from September 03 to 06 and find that five dipoles emerged successively at the east of the main sunspot. The interactions between these dipoles took place continuously, accompanied by magnetic flux cancellations and strong shearing motions. In AR 12673, significant flux emergence and successive interactions between the different emerging dipoles resulted in a complex magnetic system, accompanied by the formations of multiple flux ropes and twisted loop bundles. We propose that the eruptions of a multi-flux-rope system resulted in the two largest flares in Solar Cycle 24.Comment: 10 pages, 8 figures. To be published in A&

Type I Planet Migration in Nearly Laminar Disks

We describe 2D hydrodynamic simulations of the migration of low-mass planets ($\leq 30 M_{\oplus}$) in nearly laminar disks (viscosity parameter $\alpha < 10^{-3}$) over timescales of several thousand orbit periods. We consider disk masses of 1, 2, and 5 times the minimum mass solar nebula, disk thickness parameters of $H/r = 0.035$ and 0.05, and a variety of $\alpha$ values and planet masses. Disk self-gravity is fully included. Previous analytic work has suggested that Type I planet migration can be halted in disks of sufficiently low turbulent viscosity, for $\alpha \sim 10^{-4}$. The halting is due to a feedback effect of breaking density waves that results in a slight mass redistribution and consequently an increased outward torque contribution. The simulations confirm the existence of a critical mass ($M_{cr} \sim 10 M_{\oplus}$) beyond which migration halts in nearly laminar disks. For \alpha \ga 10^{-3}, density feedback effects are washed out and Type I migration persists. The critical masses are in good agreement with the analytic model of Rafikov (2002). In addition, for \alpha \la 10^{-4} steep density gradients produce a vortex instability, resulting in a small time-varying eccentricity in the planet's orbit and a slight outward migration. Migration in nearly laminar disks may be sufficiently slow to reconcile the timescales of migration theory with those of giant planet formation in the core accretion model.Comment: 3 figures, accepted to ApJ

Measurement-induced entanglement of two superconducting qubits

We study the problem of two superconducting quantum qubits coupled via a resonator. If only one quanta is present in the system and the number of photons in the resonator is measured with a null result, the qubits end up in an entangled Bell state. Here we look at one source of errors in this quantum nondemolition scheme due to the presence of more than one quanta in the resonator, previous to the measurement. By analyzing the structure of the conditional Hamiltonian with arbitrary number of quanta, we show that the scheme is remarkably robust against these type of errors.Comment: 4 pages, 2 figure

The Origin of the Magnetic Fields of the Universe: The Plasma Astrophysics of the Free Energy of the Universe

(abridged) The interpretation of Faraday rotation measure maps of AGNs within galaxy clusters has revealed regions, $\sim 50-100$ kpc, that are populated with large, $\sim 30 \mu$ G magnetic fields. The magnetic energy of these coherent regions is $\sim 10^{59-60}$ ergs, and the total magnetic energy over the whole cluster ($\sim 1$ Mpc across) is expected to be even larger. A sequence of physical processes that are responsible for the production, redistribution and dissipation of these magnetic fields is proposed. These fields are associated with single AGNs within the cluster and therefore with all galaxies during their AGN phase, simply because only the central supermassive black holes ($\sim 10^8 M_{\odot}$) have an accessible energy, $\sim 10^{61}$ ergs. We propose an $\alpha-\Omega$ dynamo process in an accretion disk. The disk rotation naturally provides a large winding number, $\sim 10^{11}$ turns, sufficient to make both large gain and large flux. The helicity of the dynamo can be generated by the differential plume rotation derived from star-disk collisions. This helicity generation process has been demonstrated in the laboratory and the dynamo gain was simulated numerically. A liquid sodium analog of the dynamo is being built. Speculations are that the back reaction of the saturated dynamo will lead to the formation of a force-free magnetic helix, which will carry the energy and flux of the dynamo away from the accretion disk and redistribute the field within the clusters and galaxy walls. The magnetic reconnection of a small fraction of this energy logically is the source of the AGN luminosity, and the remainder of the field energy should then dominate the free energy of the present-day universe.Comment: invited review at the 2000 APS/DPP meeting, Quebec, 11 pages, 7 color figs (.jpg

Type I planet migration in nearly laminar disks - long term behavior

We carry out 2-D high resolution numerical simulations of type I planet migration with different disk viscosities. We find that the planet migration is strongly dependent on disk viscosities. Two kinds of density wave damping mechanisms are discussed. Accordingly, the angular momentum transport can be either viscosity dominated or shock dominated, depending on the disk viscosities. The long term migration behavior is different as well. Influences of the Rossby vortex instability on planet migration are also discussed. In addition, we investigate very weak shock generation in inviscid disks by small mass planets and compare the results with prior analytic results.Comment: Accepted for publication in Ap

Temperature-dependent compressibility in graphene and two-dimensional systems

We calculate the finite temperature compressibility for two-dimensional semiconductor systems, monolayer graphene, and bilayer graphene within the Hartree-Fock approximation. We find that the calculated temperature dependent compressibility including exchange energy is non-monotonic. In 2D systems at low temperatures the inverse compressibility decreases first with increasing temperature, but after reaching a minimum it increases as temperature is raised further. At high enough temperatures the negative compressibility of low density systems induced by the exchange energy becomes positive due to the dominance of the finite temperature kinetic energy. The inverse compressibility in monolayer graphene is always positive and its temperature dependence appears to be reverse of the 2D semiconductor systems, i.e., it increases first with temperature and then decreases at high temperatures. The inverse compressibility of bilayer graphene shows the same non-monotonic behavior as ordinary 2D systems, but at high temperatures it approaches a constant which is smaller than the value of the non-interacting bilayer graphene. We find the leading order temperature correction to the compressibility within Hartree-Fock approximation to be $T^2 \ln T$ at low temperatures for all three systems.Comment: 19 pages, 9 figure