528 research outputs found

    A Meinardus theorem with multiple singularities

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    Meinardus proved a general theorem about the asymptotics of the number of weighted partitions, when the Dirichlet generating function for weights has a single pole on the positive real axis. Continuing \cite{GSE}, we derive asymptotics for the numbers of three basic types of decomposable combinatorial structures (or, equivalently, ideal gas models in statistical mechanics) of size nn, when their Dirichlet generating functions have multiple simple poles on the positive real axis. Examples to which our theorem applies include ones related to vector partitions and quantum field theory. Our asymptotic formula for the number of weighted partitions disproves the belief accepted in the physics literature that the main term in the asymptotics is determined by the rightmost pole.Comment: 26 pages. This version incorporates the following two changes implied by referee's remarks: (i) We made changes in the proof of Proposition 1; (ii) We provided an explanation to the argument for the local limit theorem. The paper is tentatively accepted by "Communications in Mathematical Physics" journa

    Random combinatorial structures: the convergent case

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    This paper studies the distribution of the component spectrum of combinatorial structures such as uniform random forests, in which the classical generating function for the numbers of (irreducible) elements of the different sizes converges at the radius of convergence; here, this property is expressed in terms of the expectations of independent random variables Zj, j ≥ 1, whose joint distribution, conditional on the event that Σnj=1 jZj = n, gives the distribution of the component spectrum for a random structure of size n. For a large class of such structures, we show that the component spectrum is asymptotically composed of Zj components of small sizes j, j ≥ 1, with the remaining part, of size close to n, being made up of a single, giant component

    Impurity-induced tuning of quantum well states in spin-dependent resonant tunneling

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    We report exact model calculations of the spin-dependent tunneling in double magnetic tunnel junctions in the presence of impurities in the well. We show that the impurity can tune selectively the spin channels giving rise to a wide variety of interesting and novel transport phenomena. The tunneling magnetoresistance, the spin polarization and the local current can be dramatically enhanced or suppressed by impurities. The underlying mechanism is the impurity-induced shift of the quantum well states (QWS) which depends on the impurity potential, impurity position and the symmetry of the QWS.Comment: 4 pages, 4 figures, submitted to Phys. Rev. Let

    Cosmochemical Derivation of the Composition of Chondrite Material.

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    第2回極域科学シンポジウム/第34回南極隕石シンポジウム 11月17日(木) 国立国語研究所 2階講

    Ordinary Chondrites and the Origin of the Earth

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    第3回極域科学シンポジウム/第35回南極隕石シンポジウム 11月29日(木)、30日(金) 国立国語研究所 2階講
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