QUANTUM DYNAMICAL SEMIGROUPS GENERATED BY NONCOMMUTATIVE UNBOUNDED ELLIPTIC OPERATORS-Reference-Cited by-同舟云学术

QUANTUM DYNAMICAL SEMIGROUPS GENERATED BY NONCOMMUTATIVE UNBOUNDED ELLIPTIC OPERATORS

Published:2006-07 Issue:06 Volume:18 Page:595-617
ISSN:0129-055X
Container-title:Reviews in Mathematical Physics
language:en
Short-container-title:Rev. Math. Phys.

Author:

BAHN CHANGSOO¹,KO CHUL KI²,PARK YONG MOON³

Affiliation:

1. Department of Mathematics, Korean Minjok Leadership Academy, Gangwon-do 225-823, Korea

2. Natural Science Research Institute, Yonsei University, Seoul 120-749, Korea

3. Department of Mathematics, Yonsei University, Seoul 120-749, Korea

Abstract

We study quantum dynamical semigroups generated by noncommutative unbounded elliptic operators which can be written as Lindblad-type unbounded generators. Under appropriate conditions, we first construct the minimal quantum dynamical semigroups for the generators and then use Chebotarev and Fagnola's sufficient conditions for conservativity [1] to show that the semigroups are conservative. We then apply our results to a quantum mechanical system.

Publisher

World Scientific Pub Co Pte Lt

Subject

Mathematical Physics,Statistical and Nonlinear Physics

Link

https://www.worldscientific.com/doi/pdf/10.1142/S0129055X06002759

Reference17 articles.

1. Sufficient Conditions for Conservativity of Minimal Quantum Dynamical Semigroups

2. FEYNMAN–KAC REPRESENTATION AND MARKOV PROPERTY OF SEMIGROUPS GENERATED BY NONCOMMUTATIVE ELLIPTIC OPERATORS

3. Feynman–Kac Representation of Some Noncommutative Elliptic Operators

4. CONSERVATIVE MINIMAL QUANTUM DYNAMICAL SEMIGROUPS GENERATED BY NONCOMMUTATIVE ELLIPTIC OPERATORS

5. REMARKS ON SUFFICIENT CONDITIONS FOR CONSERVATIVITY OF MINIMAL QUANTUM DYNAMICAL SEMIGROUPS

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