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Motoko Kotani - One of the best experts on this subject based on the ideXlab platform.
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long time asymptotics of non symmetric random walks on Crystal Lattices
Journal of Functional Analysis, 2017Co-Authors: Satoshi Ishiwata, Hiroshi Kawabi, Motoko KotaniAbstract:Abstract In the present paper, we study long time asymptotics of non-symmetric random walks on Crystal Lattices from a view point of discrete geometric analysis due to Kotani and Sunada [11] , [25] . We observe that the Euclidean metric associated with the standard realization of the Crystal lattice, called the Albanese metric, naturally appears in the asymptotics. In the former half of the present paper, we establish two kinds of (functional) central limit theorems for random walks. We first show that the Brownian motion on the Euclidean space with the Albanese metric appears as the scaling limit of the usual central limit theorem for the random walk. Next we introduce a family of random walks which interpolates between the original non-symmetric random walk and the symmetrized one. We then capture the Brownian motion with a constant drift of the asymptotic direction on the Euclidean space with the Albanese metric associated with the symmetrized random walk through another kind of central limit theorem for the family of random walks. In the latter half of the present paper, we give a spectral geometric proof of the asymptotic expansion of the n-step transition probability for the non-symmetric random walk. This asymptotic expansion is a refinement of the local central limit theorem obtained by Sunada [22] , [23] and is a generalization of the result in [11] for symmetric random walks on Crystal Lattices to non-symmetric cases.
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spectral geometry of Crystal Lattices
2008Co-Authors: Motoko Kotani, Atsusi Katsuda, Tomoyuki Shirai, Yusuke HiguchiAbstract:The aim of this expository article is to exhibit several interesting interactions among geometry, graph theory and probability through a brief survey of a series of our recent work on geometry of Crystal Lattices ([37], [39], [40], [44], [45]). Emphasis is put on the underlying ideas and concepts such as Albanese tori and Albanese maps associated with Crystal Lattices which originate in classical algebraic geometry and Riemannian geometry. Several geometric properties of Crystal Lattices are derived from asymptotic properties of random walks. The spectral theory of transition operators and their magnetic version on Crystal Lattices is also explained with suggestions for further studies ([6], [17], [28], [29]).
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standard realizations of Crystal Lattices via harmonic maps
Transactions of the American Mathematical Society, 2000Co-Authors: Motoko Kotani, Toshikazu SunadaAbstract:An Eells-Sampson type theorem for harmonic maps from a finite weighted graph is employed to characterize the equilibrium configurations of Crystals. It is thus observed that the mimimum principle frames symmetry of Crystals.
Annette Bauerbrandl - One of the best experts on this subject based on the ideXlab platform.
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thermodynamic properties of flufenamic and niflumic acids specific and non specific interactions in solution and in Crystal Lattices mechanism of solvation partitioning and distribution
Journal of Pharmaceutical and Biomedical Analysis, 2007Co-Authors: German L Perlovich, Artem O Surov, Annette BauerbrandlAbstract:Temperature dependency of saturated vapour pressure and the thermochemical characteristics of the fusion process were measured for flufenamic acid and niflumic acid, and thermodynamic functions of sublimation, fusion and evaporation calculated. An approach to split specific and non-specific energetic terms in Crystal Lattices is developed. The melting points of the considered molecules correlate with the ratio between specific and non-specific interactions in Crystal Lattices. Temperature dependencies of the solubility in buffers with pH 2.0 and 7.4, in n-octanol and in n-hexane were measured. The thermodynamic functions of solubility, solvation and transfer processes were deduced. Specific and non-specific solvation terms were distinguished by the transfer from "inert"n-hexane to the other solvents. Comparison of the ratio between specific and non-specific interactions in solid state and in the solutions was carried out. A diagram to analyse energetic terms of partitioning and distribution processes is introduced.
Artem O Surov - One of the best experts on this subject based on the ideXlab platform.
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thermodynamic properties of flufenamic and niflumic acids specific and non specific interactions in solution and in Crystal Lattices mechanism of solvation partitioning and distribution
Journal of Pharmaceutical and Biomedical Analysis, 2007Co-Authors: German L Perlovich, Artem O Surov, Annette BauerbrandlAbstract:Temperature dependency of saturated vapour pressure and the thermochemical characteristics of the fusion process were measured for flufenamic acid and niflumic acid, and thermodynamic functions of sublimation, fusion and evaporation calculated. An approach to split specific and non-specific energetic terms in Crystal Lattices is developed. The melting points of the considered molecules correlate with the ratio between specific and non-specific interactions in Crystal Lattices. Temperature dependencies of the solubility in buffers with pH 2.0 and 7.4, in n-octanol and in n-hexane were measured. The thermodynamic functions of solubility, solvation and transfer processes were deduced. Specific and non-specific solvation terms were distinguished by the transfer from "inert"n-hexane to the other solvents. Comparison of the ratio between specific and non-specific interactions in solid state and in the solutions was carried out. A diagram to analyse energetic terms of partitioning and distribution processes is introduced.
Etsuo Segawa - One of the best experts on this subject based on the ideXlab platform.
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Central Limit Theorems for Open Quantum Random Walks on the Crystal Lattices
Journal of Statistical Physics, 2019Co-Authors: Chul Ki Ko, Norio Konno, Etsuo Segawa, Hyun Jae YooAbstract:We consider the open quantum random walks on the Crystal Lattices and investigate the central limit theorems for the walks. On the integer Lattices the open quantum random walks satisfy the central limit theorems as was shown by Attal et al (Ann Henri Poincare 16(1):15–43, 2015). In this paper we prove the central limit theorems for the open quantum random walks on the Crystal Lattices. We then provide with some examples for the Hexagonal Lattices. We also develop the Fourier analysis on the Crystal Lattices. This leads to construct the so called dual processes for the open quantum random walks. It amounts to get Fourier transform of the probability densities, and it is very useful when we compute the characteristic functions of the walks. In this paper we construct the dual processes for the open quantum random walks on the Crystal Lattices providing with some examples.
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central limit theorems for open quantum random walks on the Crystal Lattices
arXiv: Mathematical Physics, 2018Co-Authors: Norio Konno, Etsuo Segawa, Hyun Jae YooAbstract:We consider the open quantum random walks on the Crystal Lattices and investigate the central limit theorems for the walks. On the integer Lattices the open quantum random walks satisfy the central limit theorems as was shown by Attal, {\it et al}. In this paper we prove the central limit theorems for the open quantum random walks on the Crystal Lattices. We then provide with some examples for the Hexagonal Lattices. We also develop the Fourier analysis on the Crystal Lattices. This leads to construct the so called dual processes for the open quantum random walks. It amounts to get Fourier transform of the probability densities, and it is very useful when we compute the characteristic functions of the walks. In this paper we construct the dual processes for the open quantum random walks on the Crystal Lattices providing with some examples.
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spectral and asymptotic properties of grover walks on Crystal Lattices
Journal of Functional Analysis, 2014Co-Authors: Yusuke Higuchi, Norio Konno, Iwao Sato, Etsuo SegawaAbstract:Abstract We propose a twisted Szegedy walk for estimating the limit behavior of a discrete-time quantum walk on a Crystal lattice, an infinite abelian covering graph, whose notion was introduced by [14] . First, we show that the spectrum of the twisted Szegedy walk on the quotient graph can be expressed by mapping the spectrum of a twisted random walk onto the unit circle. Secondly, we show that the spatial Fourier transform of the twisted Szegedy walk on a finite graph with appropriate parameters becomes the Grover walk on its infinite abelian covering graph. Finally, as an application, we show that if the Betti number of the quotient graph is strictly greater than one, then localization is ensured with some appropriated initial state. We also compute the limit density function for the Grover walk on Z d with flip flop shift, which implies the coexistence of linear spreading and localization. We partially obtain the abstractive shape of the limit density function: the support is within the d -dimensional sphere of radius 1 / d , and 2 d singular points reside on the sphere's surface.
Yusuke Higuchi - One of the best experts on this subject based on the ideXlab platform.
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spectral and asymptotic properties of grover walks on Crystal Lattices
Journal of Functional Analysis, 2014Co-Authors: Yusuke Higuchi, Norio Konno, Iwao Sato, Etsuo SegawaAbstract:Abstract We propose a twisted Szegedy walk for estimating the limit behavior of a discrete-time quantum walk on a Crystal lattice, an infinite abelian covering graph, whose notion was introduced by [14] . First, we show that the spectrum of the twisted Szegedy walk on the quotient graph can be expressed by mapping the spectrum of a twisted random walk onto the unit circle. Secondly, we show that the spatial Fourier transform of the twisted Szegedy walk on a finite graph with appropriate parameters becomes the Grover walk on its infinite abelian covering graph. Finally, as an application, we show that if the Betti number of the quotient graph is strictly greater than one, then localization is ensured with some appropriated initial state. We also compute the limit density function for the Grover walk on Z d with flip flop shift, which implies the coexistence of linear spreading and localization. We partially obtain the abstractive shape of the limit density function: the support is within the d -dimensional sphere of radius 1 / d , and 2 d singular points reside on the sphere's surface.
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spectral geometry of Crystal Lattices
2008Co-Authors: Motoko Kotani, Atsusi Katsuda, Tomoyuki Shirai, Yusuke HiguchiAbstract:The aim of this expository article is to exhibit several interesting interactions among geometry, graph theory and probability through a brief survey of a series of our recent work on geometry of Crystal Lattices ([37], [39], [40], [44], [45]). Emphasis is put on the underlying ideas and concepts such as Albanese tori and Albanese maps associated with Crystal Lattices which originate in classical algebraic geometry and Riemannian geometry. Several geometric properties of Crystal Lattices are derived from asymptotic properties of random walks. The spectral theory of transition operators and their magnetic version on Crystal Lattices is also explained with suggestions for further studies ([6], [17], [28], [29]).