525 research outputs found

    Fusion of implementers for spinors on the circle

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    We consider the space of odd spinors on the circle, and a decomposition into spinors supported on either the top or on the bottom half of the circle. If an operator preserves this decomposition, and acts on the bottom half in the same way as a second operator acts on the top half, then the fusion of both operators is a third operator acting on the top half like the first, and on the bottom half like the second. Fusion restricts to the Banach Lie group of restricted orthogonal operators, which supports a central extension of implementers on a Fock space. In this article, we construct a lift of fusion to this central extension. Our construction uses Tomita-Takesaki theory for the Clifford-von Neumann algebras of the decomposed space of spinors. Our motivation is to obtain an operator-algebraic model for the basic central extension of the loop group of the spin group, on which the fusion of implementers induces a fusion product in the sense considered in the context of transgression and string geometry. In upcoming work we will use this model to construct a fusion product on a spinor bundle on the loop space of a string manifold, completing a construction proposed by Stolz and Teichner.Comment: 49 page

    N√°vrh konceptu univerz√°ln√≠ho mont√°Ňĺn√≠ho stroje s vyuŇĺit√≠m koncepce Industry 4.0

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    The aim of the thesis is to present the concept of the assembly device, which is based on the equipment already implemented. The concept involves deploying collaborative robots to increase the efficiency of the assembly cycle. The primary goal is to use time that is used in conventional equipment only for handling device operations. Collaborative activity reduces worker downtime, and this timeframe is significant in terms of process.Smyslem pr√°ce je pŇôedstaven√≠ konceptu mont√°Ňĺn√≠ho zaŇô√≠zen√≠, kter√Ĺ vych√°z√≠ ze zaŇô√≠zen√≠ jiŇĺ implementovan√©ho. Koncept pońć√≠t√° s nasazen√≠m kolaborativn√≠ch robotŇĮ pro zv√ĹŇ°en√≠ efektivity mont√°Ňĺn√≠ho cyklu. Prim√°rn√≠m c√≠lem je vyuŇĺit√≠ ńćasu, kter√Ĺ je v konvenńćn√≠m zaŇô√≠zen√≠ vyuŇĺit pouze pro manipulańćn√≠ √ļkony zaŇô√≠zen√≠. Kolaborativn√≠ ńćinnost redukuje prostoje pracovn√≠ka, pŇôińćemŇĺ tento ńćasov√Ĺ r√°mec je z hlediska procesu v√Ĺznamn√Ĺ

    Quantum Brownian motion in a Landau level

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    Motivated by questions about the open-system dynamics of topological quantum matter, we investigated the quantum Brownian motion of an electron in a homogeneous magnetic field. When the Fermi length lF=‚ĄŹ/(vFmeff)l_F=\hbar/(v_Fm_{\text{eff}}) becomes much longer than the magnetic length lB=(‚ĄŹc/eB)1/2l_B=(\hbar c/eB)^{1/2}, then the spatial coordinates X,YX,Y of the electron cease to commute, [X,Y]=ilB2[X,Y]=il_B^2. As a consequence, localization of the electron becomes limited by Heisenberg uncertainty, and the linear bath-electron coupling becomes unconventional. Moreover, because the kinetic energy of the electron is quenched by the strong magnetic field, the electron has no energy to give to or take from the bath, and so the usual connection between frictional forces and dissipation no longer holds. These two features make quantum Brownian motion topological, in the regime lF‚ČęlBl_F\gg l_B, which is at the verge of current experimental capabilities. We model topological quantum Brownian motion in terms of an unconventional operator Langevin equation derived from first principles, and solve this equation with the aim of characterizing diffusion. While diffusion in the noncommutative plane turns out to be conventional, with the mean displacement squared being proportional to tőĪt^\alpha and őĪ=1\alpha=1, there is an exotic regime for the proportionality constant in which it is directly proportional to the friction coefficient and inversely proportional to the square of the magnetic field: in this regime, friction helps diffusion and the magnetic field suppresses all fluctuations. We also show that quantum tunneling can be completely suppressed in the noncommutative plane for suitably designed metastable potential wells, a feature that might be worth exploiting for storage and protection of quantum information

    Grassmannians of Lagrangian Polarizations

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    This paper is an introduction to polarizations in the symplectic and orthogonal settings. They arise in association to a triple of compatible structures on a real vector space, consisting of an inner product, a symplectic form, and a complex structure. A polarization is a decomposition of the complexified vector space into the eigenspaces of the complex structure; this information is equivalent to the specification of a compatible triple. When either a symplectic form or inner product is fixed, one obtains a Grassmannian of polarizations. We give an exposition of this circle of ideas, emphasizing the symmetry of the symplectic and orthogonal settings, and allowing the possibility that the underlying vector spaces are infinite-dimensional. This introduction would be useful for those interested in applications of polarizations to representation theory, loop groups, complex geometry, moduli spaces, quantization, and conformal field theory

    A Fermionic Grunsky operator

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    To a conformal map ff from the disk D\mathbb{D} into the complex plane onto a domain with rectifiable Ahlfors-regular boundary, we associate a new kind of Grunsky operator on the Hardy space of the unit disk. This is analogous to the classical Grunsky operator, which itself can be viewed as an operator on Bergman or Dirichlet space. We show that the pull-back of the Smirnov space of the complement of f(D)f(\mathbb{D}) by ff is the graph of the Grunsky operator. We also characterize those domains with rectifiable Ahlfors-regular boundaries such that the Grunsky operator is Hilbert-Schmidt. In particular, we show that if the Grunsky operator is Hilbert-Schmidt, then f(D)f(\mathbb{D}) is a Weil-Petersson quasidisk. The formulations of the results and proofs make essential use of a geometric treatment of Smirnov space as a space of half-order differentials

    Design and construction of the prototype of universal semi-automatic equipment for the automotive industry

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    KonŇ°trukcia poloautomatick√©ho zariadenia DCR 231 predstavuje pre spolońćnosŇ• Mubea v dlhodobom hńĺadisku n√°kladov√ļ √ļsporu, ktor√° rastie s ńćasom akt√≠vneho vyuŇĺ√≠vania zariadenia. Zariadenie je koncipovan√© ako univerz√°lny n√°stroj na automatiz√°ciu v√Ĺrobn√©ho kroku nas√ļvania trubińćky do vn√ļtorn√©ho priemeru trubkov√Ĺch stabiliz√°torov. Nas√ļvanie trubińćky do oboch koncov stabilizańćnej tyńće prispeje k zv√ĹŇ°eniu pevnosti t√Ĺchto koncov√Ĺch oblast√≠ stabiliz√°tora, vyuŇĺitie spevnenia len na koncoch stabilizańćnej tyńće prispieva k redukci√≠ hmotnosti stabiliz√°tora, ktor√° ńćiastkovo prispieva k celkovej redukci√≠ hmotnosti n√°pravy vozidla. V glob√°lnej mierke teda zariadenie prispieva k zn√≠Ňĺeniu n√°kladov spojen√Ĺch s uŇĺ√≠van√≠m automobilu.Construction of semi-automatic equipment DCR 231 means for company Mubea saving money in long-range target. This economy profit rises with time period of the equipment active usage. The equipment is designed as a universal tool of automatic production step for inserting reinforcement tubes into tubular stabilizer bars. Inserting of these tubes into the both stabilizer ends brings higher strength of supported areas. Benefit of stabilizer bar reinforcement only on its ends is a lower mass leads to reduction of the whole axle mass. The equipment in global scale helps to reduce the costs connected with daily vehicle usage.

    Microbial protein out of thin air : fixation of nitrogen gas by an autotrophic hydrogen-oxidizing bacterial enrichment

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    For the production of edible microbial protein (MP), ammonia generated by the Haber-Bosch process or reclaimed ammonia from waste streams is typically considered as the nitrogen source. These processes for ammonia production are highly energy intensive. In this study, the potential for using nitrogen gas (N-2) as a direct nitrogen source for MP production by hydrogen-oxidizing bacteria (HOB) was evaluated. The use of N-2 versus ammonium as nitrogen source during the enrichment process resulted in differentiation of the bacterial community composition of the enrichments. A few previously unknown potential N-2-fixing HOB taxa (i.e., representatives of the genus Azonexus and the family Comamonadaceae) dominated the enrichments. The biomass yield of a N-2-fixing HOB enrichment was 30-50% lower than that of the ammonium-based HOB enrichment from the same inoculum source. The dried biomass of N-2-fixing HOB had a high protein content (62.0 +/- 6.3%) and an essential amino acid profile comparable to MP from ammonium-based HOB. MP from N-2-fixing HOB could potentially be produced in situ without entailing the emissions caused by ammonia production and transportation by conventional means. It could be a promising substitute for N-2-fixing protein-rich soybean because it has 70% higher protein content and double energy conversion efficiency from solar energy to biomass
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