On exponential convergence of generic quantum Markov semigroups in a Wasserstein-type distance

We investigate about exponential convergence for generic quantum Markov semigroups using an generalization of the Lipschitz seminorm and a noncommutative analogue of Wasserstein distance. We show turns out to be closely related with classical convergence rate of reductions to diagonal subalgebras of...

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Autores:: Agredo Echeverry, Julian Andres

Tipo de recurso:: Article of investigation

Fecha de publicación:: 2016

Institución:: Escuela Colombiana de Ingeniería Julio Garavito

Repositorio:: Repositorio Institucional ECI

Idioma:: eng

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dc.title.eng.fl_str_mv	On exponential convergence of generic quantum Markov semigroups in a Wasserstein-type distance
title	On exponential convergence of generic quantum Markov semigroups in a Wasserstein-type distance
spellingShingle	On exponential convergence of generic quantum Markov semigroups in a Wasserstein-type distance Semigrupos cuánticos Matemáticas Quantum Markov semigroups Wasserstein distance Exponential convergence Distancia de Wasserstein Semigrupos cuánticos de Markov Convergencia exponencial
title_short	On exponential convergence of generic quantum Markov semigroups in a Wasserstein-type distance
title_full	On exponential convergence of generic quantum Markov semigroups in a Wasserstein-type distance
title_fullStr	On exponential convergence of generic quantum Markov semigroups in a Wasserstein-type distance
title_full_unstemmed	On exponential convergence of generic quantum Markov semigroups in a Wasserstein-type distance
title_sort	On exponential convergence of generic quantum Markov semigroups in a Wasserstein-type distance
dc.creator.fl_str_mv	Agredo Echeverry, Julian Andres
dc.contributor.author.none.fl_str_mv	Agredo Echeverry, Julian Andres
dc.contributor.researchgroup.spa.fl_str_mv	Matemáticas
dc.subject.armarc.none.fl_str_mv	Semigrupos cuánticos Matemáticas
topic	Semigrupos cuánticos Matemáticas Quantum Markov semigroups Wasserstein distance Exponential convergence Distancia de Wasserstein Semigrupos cuánticos de Markov Convergencia exponencial
dc.subject.proposal.spa.fl_str_mv	Quantum Markov semigroups Wasserstein distance Exponential convergence Distancia de Wasserstein Semigrupos cuánticos de Markov Convergencia exponencial
description	We investigate about exponential convergence for generic quantum Markov semigroups using an generalization of the Lipschitz seminorm and a noncommutative analogue of Wasserstein distance. We show turns out to be closely related with classical convergence rate of reductions to diagonal subalgebras of the given generic quantum Markov semigroups.In particular we compute the convergence rates of generic quantum Markov semigroups.
publishDate	2016
dc.date.available.none.fl_str_mv	2016 2021-10-01T17:20:45Z
dc.date.issued.none.fl_str_mv	2016
dc.date.accessioned.none.fl_str_mv	2021-05-05T23:31:12Z 2021-10-01T17:20:45Z
dc.type.spa.fl_str_mv	Artículo de revista
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dc.identifier.doi.none.fl_str_mv	10.12732/ijpam.v107i4.9
dc.identifier.url.none.fl_str_mv	http://dx.doi.org/10.12732/ijpam.v107i4.9
identifier_str_mv	1311-8080 10.12732/ijpam.v107i4.9
url	https://repositorio.escuelaing.edu.co/handle/001/1397 http://dx.doi.org/10.12732/ijpam.v107i4.9
dc.language.iso.spa.fl_str_mv	eng
language	eng
dc.relation.citationedition.eng.fl_str_mv	International Journal of Pure and Applied Mathematics, Volume 107 No. 4 2016.
dc.relation.citationendpage.spa.fl_str_mv	925
dc.relation.citationissue.spa.fl_str_mv	4
dc.relation.citationstartpage.spa.fl_str_mv	909
dc.relation.citationvolume.spa.fl_str_mv	107
dc.relation.indexed.spa.fl_str_mv	N/A
dc.relation.ispartofjournal.spa.fl_str_mv	International Journal of Pure and Applied Mathematics
dc.relation.references.eng.fl_str_mv	L. Accardi, F. Fagnola and S. Hachicha, Generic q-Markov semigroups and speed of convergence of q-algorithms, Infin. Dimens. Anal. Quantum Probab. Relat. Top.9, 567 (2006). L. Accardi, S. Kozyrev, Lectures on the qualitative analysis of quantum Markov semigroups in: Quantum interacting particle systems (Trento, 2000), L. Accardi and F. Fagnola, eds., QP–PQ: Quantum Probab. White Noise Anal. 14, World Sci. Publishing, River Edge, NJ, (2002),1195. J. Agredo, A Wasserstein-type Distance to Measure Deviation from Equilibrium of Quantum Markov Semigroups, Open Sys. Information Dyn. 20:2,(2013), 1-20. R. Carbone, Optimal log - Sobolev inequality and hypercontractivity for positive semigroups on M2, Inf.Dim.Anal, Quant Prob and Rel Top 7, (2004), 3-23. R. Carbone, F. Fagnola, Exponential L2 - convergence of quantum Markov semigroups on B(h), Math. Notes 68, (2000), 452-473. R. Carbone, F. Fagnola, S. Hachicha, Generic Quantum Markov Semigroups: the Gaussian Gauge Invariant Case, Open Sys. Information Dyn. 14, (2007), 425-445. R. Carbone, E. Sasso, V. Umanita Decoherence for Quantum Markov Semi-Groups on Matrix Algebras, Ann.Hen. Poninc. 14 (4), (2013), 681-703. M. Chen, From Markov Chains to Non-equilibrium Particle Systems, NJ: World Scientific (2004). M. Chen, Estimation of spectral gap for Markov chains, Acta Math. Sin. 12 (4), (1996), 337-360 A.M. Chebotarev, F. Fagnola, Sufficient conditions for conservativity of minimal quantum dynamical semigroups, J. Funct. Anal. 153 (1998). B. Cloez, Wasserstein decay of one dimensional jump-diffusions, arXiv:1202.1259v2 R. Dudley, Real analysis and probability, Cambridge University Press, Cambridge (2002) F. Fagnola, R. Rebolledo, Lectures on the qualitative analysis of quantum Markov semigroups in: Quantum interacting particle systems (Trento, 2000), QPPQ: Quantum Probab. White Noise Anal. 14, World Sci. Publishing, River Edge, NJ, (2002), 197 - 239. F. Fagnola, V. Umanit`a, Generators of detailed balance quantum Markov semigroups, Inf. Dim. Anal. Quant. Probab. Relat. Top.,10, (2007),335 - 363. F. Fagnola, V. Umanit`a, Generators of KMS Symmetric Markov Semigroups on B(h), Symmetry and Quantum Detailed Balance, Commun. Math. Phys. ,298,(2010), 523 - 547. F. Fagnola, R. Rebolledo, Entropy Production for Quantum Markov Semigroups. Commun. Math. Phys. 335, (2015), 547570. F. Fagnola, R. Rebolledo, Entropy production and detailed balance for a class of quantum Markov semigroups. Open Syst. Inf. Dyn. 22, (2015), 1-14. M. Hairer, A. Stuart and S. Vollmer, Spectral gaps for a Metropolis Hastings algorithm in infinite dimensions, The Annals Aplied Prob., 24 no. 6, Project Euclid , (2014), 2455- 2490. A. Joulin, A new Poisson-type deviation inequality for Markov jump processes with positive Wasserstein curvature, Bernoulli 15 no. 2, (2009), 532-552. A. Joulin, Poisson-type deviation inequalities for curved continuous-time Markov chains, Bernoulli 13 no. 3, (2007), 782-803. Y. Ollivier, A survey of Ricci curvature for metric spaces and Markov chains, Probabilistic approach to geometry, Adv. Stud. Pure Math., 57, Math. Soc. Japan, Tokyo, (2010), 343-363. M. Sammer, Aspects of mass transportation in discrete concentration inequalities, Ph.D. Thesis, Georgia Institute of Technology. (2005), http://smartech.gatech.edu/dspace/handle/1853/7006. C. Villani, Topics in Optimal Transportation, Graduate Studies in Mathematics 58, American Mathematical Society, Providence (2003). M. von Renesse, K. Sturm, Transport inequalities, gradient estimates, entropy, and Ricci curvature, Comm. Pure Appl. Math. 58 (2005), 923-944 . F-Y. Wang, Functional inequalities for the decay of sub-Markov semigroups, Potential Anal.18 1 (2003),1-23.
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spelling	Agredo Echeverry, Julian Andresb5187d47185154d6d2aff006b295b884600Matemáticas2021-05-05T23:31:12Z2021-10-01T17:20:45Z20162021-10-01T17:20:45Z20161311-8080https://repositorio.escuelaing.edu.co/handle/001/139710.12732/ijpam.v107i4.9http://dx.doi.org/10.12732/ijpam.v107i4.9We investigate about exponential convergence for generic quantum Markov semigroups using an generalization of the Lipschitz seminorm and a noncommutative analogue of Wasserstein distance. We show turns out to be closely related with classical convergence rate of reductions to diagonal subalgebras of the given generic quantum Markov semigroups.In particular we compute the convergence rates of generic quantum Markov semigroups.Investigamos la convergencia exponencial de semigrupos cuánticos genéricos de Markov utilizando una generalización de la seminorma de Lipschitz y un análogo no conmutativo de la distancia de Wasserstein. Se demuestra que está estrechamente relacionado con la tasa de convergencia clásica de las reducciones a las subálgebras diagonales de los semigrupos de Markov genéricos dados, y en particular se calculan las tasas de convergencia de los semigrupos de Markov genéricos.J. Agredo Department of Mathematics National University of Colombia and Department of Mathematics Colombian School of Engineering Julio Garavito Bogotá, COLOMBIAapplication/pdfengPublicaciones académicas Ltd.https://ijpam.eu/contents/2016-107-4/9/On exponential convergence of generic quantum Markov semigroups in a Wasserstein-type distanceArtículo de revistainfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_2df8fbb1Textinfo:eu-repo/semantics/articlehttp://purl.org/redcol/resource_type/ARThttp://purl.org/coar/version/c_970fb48d4fbd8a85International Journal of Pure and Applied Mathematics, Volume 107 No. 4 2016.9254909107N/AInternational Journal of Pure and Applied MathematicsL. Accardi, F. Fagnola and S. Hachicha, Generic q-Markov semigroups and speed of convergence of q-algorithms, Infin. Dimens. Anal. Quantum Probab. Relat. Top.9, 567 (2006).L. Accardi, S. Kozyrev, Lectures on the qualitative analysis of quantum Markov semigroups in: Quantum interacting particle systems (Trento, 2000), L. Accardi and F. Fagnola, eds., QP–PQ: Quantum Probab. White Noise Anal. 14, World Sci. Publishing, River Edge, NJ, (2002),1195.J. Agredo, A Wasserstein-type Distance to Measure Deviation from Equilibrium of Quantum Markov Semigroups, Open Sys. Information Dyn. 20:2,(2013), 1-20.R. Carbone, Optimal log - Sobolev inequality and hypercontractivity for positive semigroups on M2, Inf.Dim.Anal, Quant Prob and Rel Top 7, (2004), 3-23.R. Carbone, F. Fagnola, Exponential L2 - convergence of quantum Markov semigroups on B(h), Math. Notes 68, (2000), 452-473.R. Carbone, F. Fagnola, S. Hachicha, Generic Quantum Markov Semigroups: the Gaussian Gauge Invariant Case, Open Sys. Information Dyn. 14, (2007), 425-445.R. Carbone, E. Sasso, V. Umanita Decoherence for Quantum Markov Semi-Groups on Matrix Algebras, Ann.Hen. Poninc. 14 (4), (2013), 681-703.M. Chen, From Markov Chains to Non-equilibrium Particle Systems, NJ: World Scientific (2004).M. Chen, Estimation of spectral gap for Markov chains, Acta Math. Sin. 12 (4), (1996), 337-360A.M. Chebotarev, F. Fagnola, Sufficient conditions for conservativity of minimal quantum dynamical semigroups, J. Funct. Anal. 153 (1998).B. Cloez, Wasserstein decay of one dimensional jump-diffusions, arXiv:1202.1259v2R. Dudley, Real analysis and probability, Cambridge University Press, Cambridge (2002)F. Fagnola, R. Rebolledo, Lectures on the qualitative analysis of quantum Markov semigroups in: Quantum interacting particle systems (Trento, 2000), QPPQ: Quantum Probab. White Noise Anal. 14, World Sci. Publishing, River Edge, NJ, (2002), 197 - 239.F. Fagnola, V. Umanit`a, Generators of detailed balance quantum Markov semigroups, Inf. Dim. Anal. Quant. Probab. Relat. Top.,10, (2007),335 - 363.F. Fagnola, V. Umanit`a, Generators of KMS Symmetric Markov Semigroups on B(h), Symmetry and Quantum Detailed Balance, Commun. Math. Phys. ,298,(2010), 523 - 547.F. Fagnola, R. Rebolledo, Entropy Production for Quantum Markov Semigroups. Commun. Math. Phys. 335, (2015), 547570.F. Fagnola, R. Rebolledo, Entropy production and detailed balance for a class of quantum Markov semigroups. Open Syst. Inf. Dyn. 22, (2015), 1-14.M. Hairer, A. Stuart and S. Vollmer, Spectral gaps for a Metropolis Hastings algorithm in infinite dimensions, The Annals Aplied Prob., 24 no. 6, Project Euclid , (2014), 2455- 2490.A. Joulin, A new Poisson-type deviation inequality for Markov jump processes with positive Wasserstein curvature, Bernoulli 15 no. 2, (2009), 532-552.A. Joulin, Poisson-type deviation inequalities for curved continuous-time Markov chains, Bernoulli 13 no. 3, (2007), 782-803.Y. Ollivier, A survey of Ricci curvature for metric spaces and Markov chains, Probabilistic approach to geometry, Adv. Stud. Pure Math., 57, Math. Soc. Japan, Tokyo, (2010), 343-363.M. Sammer, Aspects of mass transportation in discrete concentration inequalities, Ph.D. Thesis, Georgia Institute of Technology. (2005), http://smartech.gatech.edu/dspace/handle/1853/7006.C. Villani, Topics in Optimal Transportation, Graduate Studies in Mathematics 58, American Mathematical Society, Providence (2003).M. von Renesse, K. Sturm, Transport inequalities, gradient estimates, entropy, and Ricci curvature, Comm. Pure Appl. Math. 58 (2005), 923-944 .F-Y. Wang, Functional inequalities for the decay of sub-Markov semigroups, Potential Anal.18 1 (2003),1-23.info:eu-repo/semantics/openAccesshttp://purl.org/coar/access_right/c_abf2Semigrupos cuánticosMatemáticasQuantum Markov semigroupsWasserstein distanceExponential convergenceDistancia de WassersteinSemigrupos cuánticos de MarkovConvergencia exponencialLICENSElicense.txttext/plain1881https://repositorio.escuelaing.edu.co/bitstream/001/1397/1/license.txt5a7ca94c2e5326ee169f979d71d0f06eMD51open accessORIGINALON EXPONENTIAL CONVERGENCE OF GENERIC.pdfapplication/pdf175007https://repositorio.escuelaing.edu.co/bitstream/001/1397/2/ON%20EXPONENTIAL%20CONVERGENCE%20OF%20GENERIC.pdf8f70ef7881ec552adf678aa517980582MD52open accessTEXTON EXPONENTIAL CONVERGENCE OF GENERIC.pdf.txtON EXPONENTIAL CONVERGENCE OF GENERIC.pdf.txtExtracted texttext/plain27761https://repositorio.escuelaing.edu.co/bitstream/001/1397/3/ON%20EXPONENTIAL%20CONVERGENCE%20OF%20GENERIC.pdf.txt48cc7fa23f8b248cbfbe6aa9d5facbe7MD53open accessTHUMBNAILON EXPONENTIAL CONVERGENCE OF GENERIC.pdf.jpgON EXPONENTIAL CONVERGENCE OF GENERIC.pdf.jpgGenerated Thumbnailimage/jpeg9715https://repositorio.escuelaing.edu.co/bitstream/001/1397/4/ON%20EXPONENTIAL%20CONVERGENCE%20OF%20GENERIC.pdf.jpg2fde78c00edc932fc13703ea2d4f4ce0MD54open access001/1397oai:repositorio.escuelaing.edu.co:001/13972021-10-01 17:22:38.007open accessRepositorio Escuela Colombiana de Ingeniería Julio Garavitorepositorio.eci@escuelaing.edu.coU0kgVVNURUQgSEFDRSBQQVJURSBERUwgR1JVUE8gREUgUEFSRVMgRVZBTFVBRE9SRVMgREUgTEEgQ09MRUNDScOTTiAiUEVFUiBSRVZJRVciLCBPTUlUQSBFU1RBIExJQ0VOQ0lBLgoKQXV0b3Jpem8gYSBsYSBFc2N1ZWxhIENvbG9tYmlhbmEgZGUgSW5nZW5pZXLDrWEgSnVsaW8gR2FyYXZpdG8gcGFyYSBwdWJsaWNhciBlbCB0cmFiYWpvIGRlIGdyYWRvLCBhcnTDrWN1bG8sIHZpZGVvLCAKY29uZmVyZW5jaWEsIGxpYnJvLCBpbWFnZW4sIGZvdG9ncmFmw61hLCBhdWRpbywgcHJlc2VudGFjacOzbiB1IG90cm8gKGVuICAgIGFkZWxhbnRlIGRvY3VtZW50bykgcXVlIGVuIGxhIGZlY2hhIAplbnRyZWdvIGVuIGZvcm1hdG8gZGlnaXRhbCwgeSBsZSBwZXJtaXRvIGRlIGZvcm1hIGluZGVmaW5pZGEgcXVlIGxvIHB1YmxpcXVlIGVuIGVsIHJlcG9zaXRvcmlvIGluc3RpdHVjaW9uYWwsIAplbiBsb3MgdMOpcm1pbm9zIGVzdGFibGVjaWRvcyBlbiBsYSBMZXkgMjMgZGUgMTk4MiwgbGEgTGV5IDQ0IGRlIDE5OTMsIHkgZGVtw6FzIGxleWVzIHkganVyaXNwcnVkZW5jaWEgdmlnZW50ZQphbCByZXNwZWN0bywgcGFyYSBmaW5lcyBlZHVjYXRpdm9zIHkgbm8gbHVjcmF0aXZvcy4gRXN0YSBhdXRvcml6YWNpw7NuIGVzIHbDoWxpZGEgcGFyYSBsYXMgZmFjdWx0YWRlcyB5IGRlcmVjaG9zIGRlIAp1c28gc29icmUgbGEgb2JyYSBlbiBmb3JtYXRvIGRpZ2l0YWwsIGVsZWN0csOzbmljbywgdmlydHVhbDsgeSBwYXJhIHVzb3MgZW4gcmVkZXMsIGludGVybmV0LCBleHRyYW5ldCwgeSBjdWFscXVpZXIgCmZvcm1hdG8gbyBtZWRpbyBjb25vY2lkbyBvIHBvciBjb25vY2VyLgpFbiBtaSBjYWxpZGFkIGRlIGF1dG9yLCBleHByZXNvIHF1ZSBlbCBkb2N1bWVudG8gb2JqZXRvIGRlIGxhIHByZXNlbnRlIGF1dG9yaXphY2nDs24gZXMgb3JpZ2luYWwgeSBsbyBlbGFib3LDqSBzaW4gCnF1ZWJyYW50YXIgbmkgc3VwbGFudGFyIGxvcyBkZXJlY2hvcyBkZSBhdXRvciBkZSB0ZXJjZXJvcy4gUG9yIGxvIHRhbnRvLCBlcyBkZSBtaSBleGNsdXNpdmEgYXV0b3LDrWEgeSwgZW4gY29uc2VjdWVuY2lhLCAKdGVuZ28gbGEgdGl0dWxhcmlkYWQgc29icmUgw6lsLiBFbiBjYXNvIGRlIHF1ZWphIG8gYWNjacOzbiBwb3IgcGFydGUgZGUgdW4gdGVyY2VybyByZWZlcmVudGUgYSBsb3MgZGVyZWNob3MgZGUgYXV0b3Igc29icmUgCmVsIGRvY3VtZW50byBlbiBjdWVzdGnDs24sIGFzdW1pcsOpIGxhIHJlc3BvbnNhYmlsaWRhZCB0b3RhbCB5IHNhbGRyw6kgZW4gZGVmZW5zYSBkZSBsb3MgZGVyZWNob3MgYXF1w60gYXV0b3JpemFkb3MuIEVzdG8gCnNpZ25pZmljYSBxdWUsIHBhcmEgdG9kb3MgbG9zIGVmZWN0b3MsIGxhIEVzY3VlbGEgYWN0w7phIGNvbW8gdW4gdGVyY2VybyBkZSBidWVuYSBmZS4KVG9kYSBwZXJzb25hIHF1ZSBjb25zdWx0ZSBlbCBSZXBvc2l0b3JpbyBJbnN0aXR1Y2lvbmFsIGRlIGxhIEVzY3VlbGEsIGVsIENhdMOhbG9nbyBlbiBsw61uZWEgdSBvdHJvIG1lZGlvIGVsZWN0csOzbmljbywgCnBvZHLDoSBjb3BpYXIgYXBhcnRlcyBkZWwgdGV4dG8sIGNvbiBlbCBjb21wcm9taXNvIGRlIGNpdGFyIHNpZW1wcmUgbGEgZnVlbnRlLCBsYSBjdWFsIGluY2x1eWUgZWwgdMOtdHVsbyBkZWwgdHJhYmFqbyB5IGVsIAphdXRvci5Fc3RhIGF1dG9yaXphY2nDs24gbm8gaW1wbGljYSByZW51bmNpYSBhIGxhIGZhY3VsdGFkIHF1ZSB0ZW5nbyBkZSBwdWJsaWNhciB0b3RhbCBvIHBhcmNpYWxtZW50ZSBsYSBvYnJhIGVuIG90cm9zIAptZWRpb3MuRXN0YSBhdXRvcml6YWNpw7NuIGVzdMOhIHJlc3BhbGRhZGEgcG9yIGxhcyBmaXJtYXMgZGVsIChsb3MpIGF1dG9yKGVzKSBkZWwgZG9jdW1lbnRvLiAKU8OtIGF1dG9yaXpvIChhbWJvcykK

On exponential convergence of generic quantum Markov semigroups in a Wasserstein-type distance

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