Chul Ki Ko
Yonsei University
Network
Latest external collaboration on country level. Dive into details by clicking on the dots.
Publication
Featured researches published by Chul Ki Ko.
Journal of Mathematical Physics | 2003
Changsoo Bahn; Chul Ki Ko; Yong Moon Park
Employing the construction method of Dirichlet forms on standard forms of von Neumann algebras developed in Infinite Dimensional Analysis, Quantum Probability and Related Topics, 2000, Vol. 3, No. 1, pp. 1–14 (Ref. 1), we construct Dirichlet forms and associated symmetric Markovian semigroups on CCR algebras with respect to quasi-free states. More precisely, let A(h0) be the CCR algebra over a complex separable pre-Hilbert space h0 and let ω be a quasi-free state on A(h0). For any normalized admissible function f and complete orthonormal system (CONS) {gn}⊂h0, we construct a Dirichlet form and corresponding symmetric Markovian semigroup on the natural standard form associated to the GNS representation of (A(h0),ω). It turns out that the form is independent of admissible function f and CONS {gn} chosen. By analyzing the spectrum of the generator (Dirichlet operator) of the semigroup, we show that the semigroup is ergodic and tends to the equilibrium exponentially fast.
Journal of Mathematical Physics | 2004
Chul Ki Ko; Yong Moon Park
For a given quasi-free state on the CCR algebra over one dimensional Hilbert space, a family of Markovian semigroups which leave the quasi-free state invariant is constructed by means of noncommutative elliptic operators and Dirichlet forms on von Neumann algebras. The generators (Dirichlet operators) of the semigroups are analyzed and the spectrums together with eigenspaces are found. When restricted to a maximal Abelian subalgebra, the semigroups are reduced to a unique Markovian semigroup of classical Ornstein–Uhlenbeck process.
Reviews in Mathematical Physics | 2003
Changsoo Bahn; Chul Ki Ko; Yong Moon Park
We extend the construction of Dirichlet forms and symmetric Markovian semigroups on standard forms of von Neumann algebras given in [1] to the case of ℤ2-graded von Neumann algebras. As an application of the extension, we construct symmetric Markovian semigroups on CAR algebras with respect to gauge invariant quasi-free states and also investigate detailed properties such as ergodicity of the semigroups.
Infinite Dimensional Analysis, Quantum Probability and Related Topics | 2013
Chul Ki Ko; Hyun Jae Yoo
We investigate the limit distributions of the discrete time quantum random walks on lattice spaces via a spectral analysis of concretely given self-adjoint operators. We discuss the interacting Fock spaces associated with the limit distributions. Thereby, we represent the moments of the limit distribution by vacuum expectation of the monomials of the Fock operator. We get formulas not only for one-dimensional walks but also for high-dimensional walks.
Journal of Mathematical Physics | 2007
Chul Ki Ko
For a bounded generator G of a weakly*-continuous, completely positive, KMS-symmetric Markovian semigroup on a von Neumann algebra M acting on a separable Hilbert space H, let H be the operator induced by G via the symmetric embedding of M into H. We decompose the Dirichlet form associated with H into a direct integral of forms whose associated generators are divergences of derivations. Moreover, if the derivations are inner, then the Dirichlet form can be written as the form given by Park [Infinite Dimen. Anal. Quantum Probab., Relat. Top. 3, 1 (2000); 8, 179 (2005)].
Quantum Information Processing | 2018
Chul Ki Ko; Norio Konno; Etsuo Segawa; Hyun Jae Yoo
We consider the support of the limit distribution of the Grover walk on crystal lattices with the linear scaling. The orbit of the Grover walk is denoted by the parametric plot of the pseudo-velocity of the Grover walk in the wave space. The region of the orbit is the support of the limit distribution. In this paper, we compute the regions of the orbits for the triangular, hexagonal and kagome lattices. We show every outer frame of the support is described by an ellipse. The shape of the ellipse depends only on the realization of the fundamental lattice of the crystal lattice in
Infinite Dimensional Analysis, Quantum Probability and Related Topics | 2016
Chul Ki Ko; Etsuo Segawa; Hyun Jae Yoo
Infinite Dimensional Analysis, Quantum Probability and Related Topics | 2015
Chul Ki Ko; Sang Don Park; Hyun Jae Yoo
\mathbb {R}^2
Reviews in Mathematical Physics | 2006
Changsoo Bahn; Chul Ki Ko; Yong Moon Park
Kodai Mathematical Journal | 2013
Chul Ki Ko; Hyun Jae Yoo
R2.