• Title, Summary, Keyword: covariant representation

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RECONSTRUCTION THEOREM FOR STATIONARY MONOTONE QUANTUM MARKOV PROCESSES

  • Heo, Jae-Seong;Belavkin, Viacheslav P.;Ji, Un Cig
    • Bulletin of the Korean Mathematical Society
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    • v.49 no.1
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    • pp.63-74
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    • 2012
  • Based on the Hilbert $C^*$-module structure we study the reconstruction theorem for stationary monotone quantum Markov processes from quantum dynamical semigroups. We prove that the quantum stochastic monotone process constructed from a covariant quantum dynamical semigroup is again covariant in the strong sense.

GROUND STATES OF A COVARIANT SEMIGROUP C-ALGEBRA

  • Jang, Sun Young;Ahn, Jieun
    • Journal of the Chungcheong Mathematical Society
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    • v.33 no.3
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    • pp.339-349
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    • 2020
  • Let P ⋊ ℕx be a semidirect product of an additive semigroup P = {0, 2, 3, ⋯ } by a multiplicative positive natural numbers semigroup ℕx. We consider a covariant semigroup C-algebra 𝓣(P ⋊ ℕx) of the semigroup P ⋊ ℕx. We obtain the condition that a state on 𝓣(P ⋊ ℕx) can be a ground state of the natural C-dynamical system (𝓣(P ⋊ ℕx), ℝ, σ).

NEWTONIAN COSMOLOGICAL PERTURBATIONS

  • Hwang, Jai-Chan
    • Publications of The Korean Astronomical Society
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    • v.7 no.1
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    • pp.107-148
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    • 1992
  • This paper presents a cosmological perturbation analysis in a Newtonian framework, using the Newtonian multi component version of the relativistic covariant equations. This work considers the fully nonlinear evolution of the perturbations, and is generalized to multicomponent systems and imperfect fluids. Known nonlinear solutions are presented in a general framework. Quasi-nonlinear analysis, considering both the compressible and rotational modes, is presented, including cases already known in the literature. The Fourier space representation of the conservation equations is also derived in a general context, with various decompositions of the velocity field. Commonly accepted cosmogonical frameworks are critically examined in the context of nonlinear evolution. This work may be regarded as the Newtonian counterpart of a recently presented general relativistic covariant formulation.

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