Preduals of semigroup algebras

For a locally compact group G, the measure convolution algebra M(G) carries a natural coproduct. In previous work, we showed that the canonical predual C 0(G) of M(G) is the unique predual which makes both the product and the coproduct on M(G) weak*-continuous. Given a discrete semigroup S, the convolution algebra ℓ 1(S) also carries a coproduct. In this paper we examine preduals for ℓ 1(S) making both the product and the coproduct weak*-continuous. Under certain conditions on S, we show that ℓ 1(S) has a unique such predual. Such S include the free semigroup on finitely many generators. In general, however, this need not be the case even for quite simple semigroups and we construct uncountably many such preduals on ℓ 1(S) when S is either ℤ+×ℤ or (ℕ,⋅)

Distinct subpopulations of enteric neuronal progenitors defined by time of development, sympathoadrenal lineage markers and Mash-1-dependence

Enteric and sympathetic neurons have previously been proposed to be lineally related. We present independent lines of evidence that suggest that enteric neurons arise from at least two lineages, only one of which expresses markers in common with sympathoadrenal cells. In the rat, sympathoadrenal markers are expressed, in the same order as in sympathetic neurons, by a subset of enteric neuronal precursors, which also transiently express tyrosine hydroxylase. If this precursor pool is eliminated in vitro by complement-mediated lysis, enteric neurons continue to develop; however, none of these are serotonergic. In the mouse, the Mash-1−/− mutation, which eliminates sympathetic neurons, also prevents the development of enteric serotonergic neurons. Other enteric neuronal populations, however, including those that contain calcitonin gene related peptide are present. Enteric tyrosine hydroxylase-containing cells co-express Mash-1 and are eliminated by the Mash-1−/− mutation, consistent with the idea that in the mouse, as in the rat, these precursors generate serotonergic neurons. Serotonergic neurons are generated early in development, while calcitonin gene related peptide-containing enteric neurons are generated much later. These data suggest that enteric neurons are derived from at least two progenitor lineages. One transiently expresses sympathoadrenal markers, is Mash-1-dependent, and generates early-born enteric neurons, some of which are serotonergic. The other is Mash-1-independent, does not express sympathoadrenal markers, and generates late-born enteric neurons, some of which contain calcitonin gene related peptide

Solid-state electronic spin coherence time approaching one second

Solid-state electronic spin systems such as nitrogen-vacancy (NV) color centers in diamond are promising for applications of quantum information, sensing, and metrology. However, a key challenge for such solid-state systems is to realize a spin coherence time that is much longer than the time for quantum spin manipulation protocols. Here we demonstrate an improvement of more than two orders of magnitude in the spin coherence time ($T_2$) of NV centers compared to previous measurements: $T_2 \approx 0.5$ s at 77 K, which enables $\sim 10^7$ coherent NV spin manipulations before decoherence. We employed dynamical decoupling pulse sequences to suppress NV spin decoherence due to magnetic noise, and found that $T_2$ is limited to approximately half of the longitudinal spin relaxation time ($T_1$) over a wide range of temperatures, which we attribute to phonon-induced decoherence. Our results apply to ensembles of NV spins and do not depend on the optimal choice of a specific NV, which could advance quantum sensing, enable squeezing and many-body entanglement in solid-state spin ensembles, and open a path to simulating a wide range of driven, interaction-dominated quantum many-body Hamiltonians

Coupled SDW and Superconducting Order in FFLO State of CeCoIn5_5

The mechanism of incommensurate (IC) spin-density-wave (SDW) order observed in the Flude-Ferrell-Larkin-Ovchinnikov (FFLO) phase of CeCoIn$_5$ is discussed on the basis of new mode-coupling scheme among IC-SDW order, two superconducting orders of FFLO with B$_{1{\rm g}}$ ($d_{x^{2}-y^{2}}$) symmetry and $\pi$-pairing of odd-parity. Unlike the mode-coupling schemes proposed by Kenzelmann et al, Sciencexpress, 21 August (2008), that proposed in the present Letter can offer a simple explanation for why the IC-SDW order is observed only in FFLO phase and the IC wave vector is rather robust against the magnetic field.Comment: 3pages, 1 figure, accepted for publication in J. Phys. Soc. Jpn., Vol.77 (2008), No.1

Light Rays at Optical Black Holes in Moving Media

Light experiences a non-uniformly moving medium as an effective gravitational field, endowed with an effective metric tensor $\tilde{g}^{\mu \nu}=\eta^{\mu \nu}+(n^2-1)u^\mu u^\nu$, $n$ being the refractive index and $u^\mu$ the four-velocity of the medium. Leonhardt and Piwnicki [Phys. Rev. A {\bf 60}, 4301 (1999)] argued that a flowing dielectric fluid of this kind can be used to generate an 'optical black hole'. In the Leonhardt-Piwnicki model, only a vortex flow was considered. It was later pointed out by Visser [Phys. Rev. Lett. {\bf 85}, 5252 (2000)] that in order to form a proper optical black hole containing an event horizon, it becomes necessary to add an inward radial velocity component to the vortex flow. In the present paper we undertake this task: we consider a full spiral flow, consisting of a vortex component plus a radially infalling component. Light propagates in such a dielectric medium in a way similar to that occurring around a rotating black hole. We calculate, and show graphically, the effective potential versus the radial distance from the vortex singularity, and show that the spiral flow can always capture light in both a positive, and a negative, inverse impact parameter interval. The existence of a genuine event horizon is found to depend on the strength of the radial flow, relative to the strength of the azimuthal flow. A limitation of our fluid model is that it is nondispersive.Comment: 30 pages, LaTeX, 4 ps figures. Expanded discussion especially in section 6; 5 new references. Version to appear in Phys. Rev.

Giant Spin Seebeck Effect through an Interface Organic Semiconductor

Interfacing an organic semiconductor C60 with a non-magnetic metallic thin film (Cu or Pt) has created a novel heterostructure that is ferromagnetic at ambient temperature, while its interface with a magnetic metal (Fe or Co) can tune the anisotropic magnetic surface property of the material. Here, we demonstrate that sandwiching C60 in between a magnetic insulator (Y3Fe5O12: YIG) and a non-magnetic, strong spin-orbit metal (Pt) promotes highly efficient spin current transport via the thermally driven spin Seebeck effect (SSE). Experiments and first principles calculations consistently show that the presence of C60 reduces significantly the conductivity mismatch between YIG and Pt and the surface perpendicular magnetic anisotropy of YIG, giving rise to enhanced spin mixing conductance across YIG/C60/Pt interfaces. As a result, a 600% increase in the SSE voltage (VLSSE) has been realized in YIG/C60/Pt relative to YIG/Pt. Temperature-dependent SSE voltage measurements on YIG/C60/Pt with varying C60 layer thicknesses also show an exponential increase in VLSSE at low temperatures below 200 K, resembling the temperature evolution of spin diffusion length of C60. Our study emphasizes the important roles of the magnetic anisotropy and the spin diffusion length of the intermediate layer in the SSE in YIG/C60/Pt structures, providing a new pathway for developing novel spin-caloric materials