Poisson boundaries of discrete quantum groups

Reiji Tomatsu

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Displaying similar documents to “Poisson boundaries of discrete quantum groups”

A characterization of coboundary Poisson Lie groups and Hopf algebras

Stanisław Zakrzewski (1997)

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We show that a Poisson Lie group (G,π) is coboundary if and only if the natural action of G×G on M=G is a Poisson action for an appropriate Poisson structure on M (the structure turns out to be the well known $π_{+}$ ). We analyze the same condition in the context of Hopf algebras. A quantum analogue of the $π_{+}$ structure on SU(N) is described in terms of generators and relations as an example.

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J. Donin, D. Gurevich, S. Majid (1993)

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Deformation on phase space.

Oscar Arratia, M.ª Angeles Martín Mínguez, María Angeles del Olmo (2002)

RACSAM

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El trabajo que presentamos constituye una revisión de varios procedimientos de cuantización basados en un espacio de fases clásico M. Estos métodos consideran a la mecánica cuántica como una "deformación" de la mecánica clásica por medio de la "transformación" del álgebra conmutativa C(M) en una nueva álgebra no conmutativa C(M). Todas estas ideas conducen de modo natural a los grupos cuánticos como deformación (o cuantización en un sentido amplio) de los grupos de Poisson-Lie, lo cual...

Quantization of pencils with a gl-type Poisson center and braided geometry

Dimitri Gurevich, Pavel Saponov (2011)

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We consider Poisson pencils, each generated by a linear Poisson-Lie bracket and a quadratic Poisson bracket corresponding to a so-called Reflection Equation Algebra. We show that any bracket from such a Poisson pencil (and consequently, the whole pencil) can be restricted to any generic leaf of the Poisson-Lie bracket. We realize a quantization of these Poisson pencils (restricted or not) in the framework of braided affine geometry. Also, we introduce super-analogs of all these Poisson...

Boltzmann distributed quantum steady states and their classical limit.

Peter A. Markowich (1994)

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A Quantum Corrected Poisson-Nernst-Planck Model for Biological Ion Channels

Jinn-Liang Liu (2015)

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A quantum corrected Poisson-Nernst-Planck (QCPNP) model is proposed for simulating ionic currents through biological ion channels by taking into account both classical and quantum mechanical effects. A generalized Gummel algorithm is also presented for solving the model system. Compared with the experimental results of X-ray crystallography, it is shown that the quantum PNP model is more accurate than the classical model in predicting the average number of ions in the channel pore. Moreover,...

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Quantum integrable systems

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A boundary integral Poisson-Boltzmann solvers package for solvated bimolecular simulations

Weihua Geng (2015)

Molecular Based Mathematical Biology

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Numerically solving the Poisson-Boltzmann equation is a challenging task due to the existence of the dielectric interface, singular partial charges representing the biomolecule, discontinuity of the electrostatic field, infinite simulation domains, etc. Boundary integral formulation of the Poisson-Boltzmann equation can circumvent these numerical challenges and meanwhile conveniently use the fast numerical algorithms and the latest high performance computers to achieve combined improvement...

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Asymptotic Analysis of a Schrödinger-Poisson System with Quantum Wells and Macroscopic Nonlinearities in Dimension 1

Faraj, A. (2010)

Serdica Mathematical Journal

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2000 Mathematics Subject Classification: 35Q02, 35Q05, 35Q10, 35B40. We consider the stationary one dimensional Schrödinger-Poisson system on a bounded interval with a background potential describing a quantum well. Using a partition function which forces the particles to remain in the quantum well, the limit h®0 in the nonlinear system leads to a uniquely solved nonlinear problem with concentrated particle density. It allows to conclude about the convergence of the solution. ...