Non-commutative Markov chains and multi-analytic operators

Rolf Gohm

doi:10.48550/arXiv.0902.3445

Non-commutative Markov chains and multi-analytic operators

Rolf Gohm

Adran Ffiseg

Allbwn ymchwil: Cyfraniad at gyfnodolyn › Erthygl › adolygiad gan gymheiriaid

10 Dyfyniadau (Scopus)

134 Wedi eu Llwytho i Lawr (Pure)

Crynodeb

We study a model of repeated interaction between quantum systems which can be thought of as a non-commutative Markov chain. It is shown that there exists an outgoing Cuntz scattering system associated to this model which induces an input–output formalism with a transfer function corresponding to a multi-analytic operator, in the sense of multivariate operator theory. Finally we show that observability for this system is closely related to the scattering theory of non-commutative Markov chains.

Iaith wreiddiol	Saesneg
Tudalennau (o-i)	275-288
Nifer y tudalennau	14
Cyfnodolyn	Journal of Mathematical Analysis and Applications
Cyfrol	364
Rhif cyhoeddi	1
Dynodwyr Gwrthrych Digidol (DOIs)	https://doi.org/10.48550/arXiv.0902.3445 https://doi.org/10.1016/j.jmaa.2009.11.021
Statws	Cyhoeddwyd - 01 Ebr 2010

Mynediad at Ddogfen

10.48550/arXiv.0902.3445
10.1016/j.jmaa.2009.11.021Trwydded: Aneglur 1

Non-commutative Markov chains and multi-analytic operatorsFersiwn derfynol wedi’i chyhoeddi, 267 KBTrwydded: Aneglur 2

Cysylltiad parhaol

Dolen barhaus

Ffeiliau eraill a chysylltiadau

Dolen i’r cyhoeddiad yn Scopus

1 Wedi Gorffen

Quantum Control : Approach Based on Scattering Theory for Non-commutative Markov Chains
Gohm, R. (Prif Ymchwilydd)
Engineering & Physical Sciences Research Council
01 Meh 2009 → 31 Mai 2012
Prosiect: Ymchwil a ariannwyd yn allanol

Dyfynnu hyn

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title = "Non-commutative Markov chains and multi-analytic operators",

abstract = "We study a model of repeated interaction between quantum systems which can be thought of as a non-commutative Markov chain. It is shown that there exists an outgoing Cuntz scattering system associated to this model which induces an input–output formalism with a transfer function corresponding to a multi-analytic operator, in the sense of multivariate operator theory. Finally we show that observability for this system is closely related to the scattering theory of non-commutative Markov chains.",

keywords = "Characteristic function, Input-output formalism, Linear system, Multi-analytic operator, Multivariate operator theory, Non-commutative Markov chain, Observability, Open quantum system, Outgoing Cuntz scattering system, Quantum control, Repeated interaction, Row contraction, Scattering theory, Transfer function",

author = "Rolf Gohm",

note = "Journal of Mathematical Analysis and Applications, Volume 364, Issue 1, 1 April 2010, Pages 275-288",

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doi = "10.48550/arXiv.0902.3445",

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AB - We study a model of repeated interaction between quantum systems which can be thought of as a non-commutative Markov chain. It is shown that there exists an outgoing Cuntz scattering system associated to this model which induces an input–output formalism with a transfer function corresponding to a multi-analytic operator, in the sense of multivariate operator theory. Finally we show that observability for this system is closely related to the scattering theory of non-commutative Markov chains.

KW - Characteristic function

KW - Input-output formalism

KW - Linear system

KW - Multi-analytic operator

KW - Multivariate operator theory

KW - Non-commutative Markov chain

KW - Observability

KW - Open quantum system

KW - Outgoing Cuntz scattering system

KW - Quantum control

KW - Repeated interaction

KW - Row contraction

KW - Scattering theory

KW - Transfer function

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DO - 10.48550/arXiv.0902.3445

M3 - Article

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VL - 364

SP - 275

EP - 288

JO - Journal of Mathematical Analysis and Applications

JF - Journal of Mathematical Analysis and Applications

IS - 1

ER -

Non-commutative Markov chains and multi-analytic operators

Crynodeb

Mynediad at Ddogfen

Cysylltiad parhaol

Ffeiliau eraill a chysylltiadau

Ôl bys

Prosiectau

Quantum Control : Approach Based on Scattering Theory for Non-commutative Markov Chains

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