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Decomposition of Dirichlet forms associated to unbounded Dirichlet operators
고철기 대한수학회 2009 대한수학회보 Vol.46 No.2
In [8], the author decomposed the Dirichlet form associated to a bounded generator G of a weakly^*-continuous, completely positive, KMS-symmetric Markovian semigroup on a von Neumann algebra M. The aim of this paper is to extend $G$ to the unbounded generator using the bimodule structure and derivations.
Schrödinger uncertainty relation for the monotone triple skew information
고철기,유현재 대한수학회 2017 대한수학회보 Vol.54 No.1
We get a Schr\"odinger uncertainty relation for the monotone triple skew information which was introduced by Yanagi and Kajihara. This information extends the monotone pair skew information as well as Wigner-Yanase-Dyson skew information.
이온증착된 Al-1% Si 박막의 내구성과 미세조직에 미치는 Cu 첨가의 영향
고철기,김재갑,조경수,김헌도 대한금속재료학회(대한금속학회) 1991 대한금속·재료학회지 Vol.29 No.3
Al-1%Si thin films with a small amount of copper were deposited on SiO₂ in a single wafer magnetron-sputtering system, followed by BPSG(boro-phospho-silicate glass) deposition. Hillock, grain size variations and etchability of metal films were investigated scanning electron and optical microscopes. Cross-sectional transmission electron microscopy analysis showed that CuAl₂ precipitated along the interface of BPSG and the metal film in as-deposit condition and they were show redistributed homogeneously after annealing treatment. These results were consistent with those obtained from AES and RBS. Electromigration tests were conducted for the metal films with 0.5% and 2% copper contents. The increase in electromigration resistance may be attributed to the homogeneous redistribution of copper in Al-1%Si-X%Cu metal films.
Quantum Markovian semigroups on quantum spin systems: Glauber dynamics
최베니,고철기,박용문 대한수학회 2008 대한수학회지 Vol.45 No.4
We study a class of KMS-symmetric quantum Markovian semigroups on a quantum spin system (A, γ, ω), where A is a quasi-local algebra, γ is a strongly continuous one parameter group of *-automorphisms of A and ω is a Gibbs state on A. The semigroups can be considered as the extension of semigroups on the nontrivial abelian subalgebra. Let H be a Hilbert space corresponding to the GNS representation constructed from ω. Using the general construction method of Dirichlet form developed in [8], we construct the symmetric Markovian semigroup {Tt}t≥0 on H. The semigroup {Tt}t≥0 acts separately on two subspaces Hd and Hod of H, where Hd is the diagonal subspace and Hod is the off-diagonal subspace, H = Hd Hod. The restriction of the semigroup {Tt}t≥0 on Hd is Glauber dynamics, and for any η∈ Hod, Ttη decays to zero exponentially fast as t approaches to the infinity. We study a class of KMS-symmetric quantum Markovian semigroups on a quantum spin system (A, γ, ω), where A is a quasi-local algebra, γ is a strongly continuous one parameter group of *-automorphisms of A and ω is a Gibbs state on A. The semigroups can be considered as the extension of semigroups on the nontrivial abelian subalgebra. Let H be a Hilbert space corresponding to the GNS representation constructed from ω. Using the general construction method of Dirichlet form developed in [8], we construct the symmetric Markovian semigroup {Tt}t≥0 on H. The semigroup {Tt}t≥0 acts separately on two subspaces Hd and Hod of H, where Hd is the diagonal subspace and Hod is the off-diagonal subspace, H = Hd Hod. The restriction of the semigroup {Tt}t≥0 on Hd is Glauber dynamics, and for any η∈ Hod, Ttη decays to zero exponentially fast as t approaches to the infinity.
Construction of unbounded Dirichlet Forms on Standard forms of von Neumann Algebras
반창수,고철기 대한수학회 2002 대한수학회지 Vol.39 No.6
We extend the construction of Dirichlet forms and Mar-koviansemigroups on standard forms of von Neumann algebra given incite{Pa1} to the case of unbounded operators affiliated with thevon Neumann algebra. We then apply our result to give Dirichletforms associated to the momentum and position operators on quantummechanical systems.
Conservative minimal quantum dynamical semigroups generated by noncommutative elliptic operators
반창호,고철기 대한수학회 2005 대한수학회지 Vol.42 No.6
By employing Chebotarev and Fagnola's sufficient conditions for conservativity of minimal quantum dynamical semigroups \cite{CF1, CF2}, we construct the conservative minimal quantum dynamical semigroups generated by noncommutative elliptic operators in the sense of \cite{BP}. We apply our results to concrete examples.
초미세소자의 다층배선에서 Spin - On Glass 를 이용한 저온 평탄화 기술
최동규,고철기 한국화학공학회 1991 Korean Chemical Engineering Research(HWAHAK KONGHA Vol.29 No.3
반도체 소자의 고집적화를 위한 다층배선구조에서 spin-on glass(SOG)를 이용한 저온 평탄화공정이 연구되었다. 이층배선구조에 SOG를 적용한 결과 금지대, V-홈, 공동의 문제를 해결할 수 있었고, SOG를 420℃에서 열처리를 했을 때 SOG막은 10-27%의 체적수축율을 보였으며 열처리전 보다 막내에 잔존하는 수분과 유기물의 함량이 줄어들었다. 전기적 특성은 2㎹/㎝의 절연파괴 전압과 30fA/㎠의 누설전류를 보였으며, 그 밖에 낮은 via 저항(≤0.2Ω/via)과 1×10^9 dyne/㎠의 인장응력, 80%의 평탄화율을 보였다. Low temperature planarization technology using spin-on glass(SOG) was studied in the multilevel interconnection structures to increase the integration density of semiconductor device. The problems of forbidden gabs, V-grooves and voids between metal line steps were solved as a result of SOG application in double level metallization structure. SOG film showed 10-20% volume shrinkage after SOG film was cured in 420℃ for 30 minutes, and it has less water and organic matter than before curing. 2㎹/㎝ breakdown voltage and 30fA/㎠ leakage current were also obtained from the semiconductor parameter analyzer. In addition, this process showed low via resistance(≤0.2Ω/via), 1×10^9 dyne/㎠ tensile stress and 80% degree of planarization.