Quantum dynamical semigroups generated by noncommutative unbounded elliptic operators

Changsoo Bahn; Chul Ki Ko; Yong Moon Park

doi:10.1142/S0129055X06002759

Quantum dynamical semigroups generated by noncommutative unbounded elliptic operators

Changsoo Bahn, Chul Ki Ko, Yong Moon Park

University College

Research output: Contribution to journal › Article › peer-review

1 Citation (Scopus)

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.

Original language	English
Pages (from-to)	595-617
Number of pages	23
Journal	Reviews in Mathematical Physics
Volume	18
Issue number	6
DOIs	https://doi.org/10.1142/S0129055X06002759
Publication status	Published - 2006 Jul

Bibliographical note

Funding Information:
The authors would like to thank their anonymous referees for suggestions to improve the paper. This work was supported by Korea Research Foundation Grant (KRF-2003-005-00010, KRF-2003-005-C00011).

All Science Journal Classification (ASJC) codes

Statistical and Nonlinear Physics
Mathematical Physics

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10.1142/S0129055X06002759

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title = "Quantum dynamical semigroups generated by noncommutative unbounded elliptic operators",

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.",

keywords = "Conservativity, Noncommutative elliptic operators, Quantum dynamical semigroups, Quantum mechanical system",

author = "Changsoo Bahn and Ko, {Chul Ki} and Park, {Yong Moon}",

note = "Funding Information: The authors would like to thank their anonymous referees for suggestions to improve the paper. This work was supported by Korea Research Foundation Grant (KRF-2003-005-00010, KRF-2003-005-C00011).",

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doi = "10.1142/S0129055X06002759",

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T1 - Quantum dynamical semigroups generated by noncommutative unbounded elliptic operators

AU - Bahn, Changsoo

AU - Ko, Chul Ki

AU - Park, Yong Moon

N1 - Funding Information: The authors would like to thank their anonymous referees for suggestions to improve the paper. This work was supported by Korea Research Foundation Grant (KRF-2003-005-00010, KRF-2003-005-C00011).

PY - 2006/7

Y1 - 2006/7

N2 - 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.

AB - 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.

KW - Conservativity

KW - Noncommutative elliptic operators

KW - Quantum dynamical semigroups

KW - Quantum mechanical system

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SP - 595

EP - 617

JO - Reviews in Mathematical Physics

JF - Reviews in Mathematical Physics

IS - 6

ER -

Quantum dynamical semigroups generated by noncommutative unbounded elliptic operators

Abstract

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