scholarly journals Sufficient Conditions for Conservativity of Minimal Quantum Dynamical Semigroups

1998 ◽  
Vol 153 (2) ◽  
pp. 382-404 ◽  
Author(s):  
A.M Chebotarev ◽  
F Fagnola
Keyword(s):  
Sufficient Conditions ◽  
Quantum Dynamical ◽  
Quantum Dynamical Semigroups

scholarly journals REMARKS ON SUFFICIENT CONDITIONS FOR CONSERVATIVITY OF MINIMAL QUANTUM DYNAMICAL SEMIGROUPS

2005 ◽  
Vol 17 (07) ◽  
pp. 745-768 ◽  
Author(s):  
CHANGSOO BAHN ◽  
CHUL KI KO ◽  
YONG MOON PARK
Keyword(s):  
Sufficient Conditions ◽  
Heavy Ion ◽  
Elliptic Operators ◽  
Heavy Ion Collision ◽  
Quantum Dynamical Semigroup ◽  
Quantum Dynamical ◽  
Dynamical Semigroup ◽  
Quantum Dynamical Semigroups ◽  
Ion Collision

We have obtained sufficient conditions for conservativity of minimal quantum dynamical semigroup by modifying and extending the method used in [1]. Our criterion for conservativity can be considered as a complement to Chebotarev and Fagnola's conditions [1]. In order to show that our conditions are useful, we apply our results to concrete examples (models of heavy ion collision and noncommutative elliptic operators).

scholarly journals QUANTUM DYNAMICAL SEMIGROUPS GENERATED BY NONCOMMUTATIVE UNBOUNDED ELLIPTIC OPERATORS

2006 ◽  
Vol 18 (06) ◽  
pp. 595-617
Author(s):  
CHANGSOO BAHN ◽  
CHUL KI KO ◽  
YONG MOON PARK
Keyword(s):  
Mechanical System ◽  
Sufficient Conditions ◽  
Elliptic Operators ◽  
Quantum Mechanical ◽  
Quantum Mechanical System ◽  
Quantum Dynamical ◽  
Quantum Dynamical Semigroups

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.

scholarly journals Quantum Dynamical Semigroups and Decoherence

2011 ◽  
Vol 2011 ◽  
pp. 1-16 ◽  
Author(s):  
Mario Hellmich
Keyword(s):  
Banach Spaces ◽  
Sufficient Conditions ◽  
Splitting Theorem ◽  
Quantum Dynamical Semigroup ◽  
Quantum Dynamical ◽  
Dynamical Semigroup ◽  
Quantum Dynamical Semigroups

We prove a version of the Jacobs-de Leeuw-Glicksberg splitting theorem for weak*continuous one-parameter semigroups on dual Banach spaces. This result is applied to give sufficient conditions for a quantum dynamical semigroup to display decoherence. The underlying notion of decoherence is that introduced by Blanchard and Olkiewicz (2003). We discuss this notion in some detail.

scholarly journals Entropic Fluctuations of Quantum Dynamical Semigroups

2013 ◽  
Vol 154 (1-2) ◽  
pp. 153-187 ◽  
Author(s):  
V. Jakšić ◽  
C.-A. Pillet ◽  
M. Westrich
Keyword(s):  
Quantum Dynamical ◽  
Quantum Dynamical Semigroups
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