{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,4]],"date-time":"2026-03-04T21:39:10Z","timestamp":1772660350391,"version":"3.50.1"},"reference-count":47,"publisher":"Verein zur Forderung des Open Access Publizierens in den Quantenwissenschaften","license":[{"start":{"date-parts":[[2019,6,12]],"date-time":"2019-06-12T00:00:00Z","timestamp":1560297600000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Quantum"],"abstract":"<jats:p>We generalize Kato's adiabatic theorem to nonunitary dynamics with an isospectral generator. This enables us to unify two strong-coupling limits: one driven by fast oscillations under a Hamiltonian, and the other driven by strong damping under a Lindbladian. We discuss the case where both mechanisms are present and provide nonperturbative error bounds. We also analyze the links with the quantum Zeno effect and dynamics.<\/jats:p>","DOI":"10.22331\/q-2019-06-12-152","type":"journal-article","created":{"date-parts":[[2019,6,12]],"date-time":"2019-06-12T13:32:21Z","timestamp":1560346341000},"page":"152","source":"Crossref","is-referenced-by-count":40,"title":["Generalized Adiabatic Theorem and Strong-Coupling Limits"],"prefix":"10.22331","volume":"3","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-4063-1264","authenticated-orcid":false,"given":"Daniel","family":"Burgarth","sequence":"first","affiliation":[{"name":"Center for Engineered Quantum Systems, Dept. of Physics & Astronomy, Macquarie University, 2109 NSW, Australia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9152-6515","authenticated-orcid":false,"given":"Paolo","family":"Facchi","sequence":"additional","affiliation":[{"name":"Dipartimento di Fisica and MECENAS, Universit\u00e0 di Bari, I-70126 Bari, Italy"},{"name":"INFN, Sezione di Bari, I-70126 Bari, Italy"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5257-7309","authenticated-orcid":false,"given":"Hiromichi","family":"Nakazato","sequence":"additional","affiliation":[{"name":"Department of Physics, Waseda University, Tokyo 169-8555, Japan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7214-5685","authenticated-orcid":false,"given":"Saverio","family":"Pascazio","sequence":"additional","affiliation":[{"name":"Dipartimento di Fisica and MECENAS, Universit\u00e0 di Bari, I-70126 Bari, Italy"},{"name":"INFN, Sezione di Bari, I-70126 Bari, Italy"},{"name":"Istituto Nazionale di Ottica (INO-CNR), I-50125 Firenze, Italy"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5314-2780","authenticated-orcid":false,"given":"Kazuya","family":"Yuasa","sequence":"additional","affiliation":[{"name":"Department of Physics, Waseda University, Tokyo 169-8555, Japan"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"9598","published-online":{"date-parts":[[2019,6,12]]},"reference":[{"key":"0","doi-asserted-by":"publisher","unstructured":"Quantum Error Correction, edited by D. A. Lidar and T. A. Brun (Cambridge University Press, New York, 2013).","DOI":"10.1017\/CBO9781139034807"},{"key":"1","doi-asserted-by":"publisher","unstructured":"B. Misra and E. C. G. Sudarshan, The Zeno's Paradox in Quantum Theory, J. Math. Phys. 18, 756 (1977).","DOI":"10.1063\/1.523304"},{"key":"2","doi-asserted-by":"publisher","unstructured":"P. Facchi and S. Pascazio, Quantum Zeno Subspaces, Phys. Rev. Lett. 89, 080401 (2002).","DOI":"10.1103\/PhysRevLett.89.080401"},{"key":"3","doi-asserted-by":"publisher","unstructured":"P. Facchi, Quantum Zeno Effect, Adiabaticity and Dynamical Superselection Rules, in Fundamental Aspects of Quantum Physics, Vol. 17 of QP-PQ: Quantum Probability and White Noise Analysis, edited by L. Accardi and S. Tasaki (World Scientific, Singapore, 2003), pp. 197-221.","DOI":"10.1142\/5213"},{"key":"4","doi-asserted-by":"publisher","unstructured":"E. B. Davies, Markovian Master Equations, Commun. Math. Phys. 39, 91 (1974).","DOI":"10.1007\/BF01608389"},{"key":"5","doi-asserted-by":"publisher","unstructured":"P. Zanardi and L. Campos Venuti, Coherent Quantum Dynamics in Steady-State Manifolds of Strongly Dissipative Systems, Phys. Rev. Lett. 113, 240406 (2014).","DOI":"10.1103\/PhysRevLett.113.240406"},{"key":"6","doi-asserted-by":"publisher","unstructured":"P. Zanardi and L. Campos Venuti, Geometry, Robustness, and Emerging Unitarity in Dissipation-Projected Dynamics, Phys. Rev. A 91, 052324 (2015).","DOI":"10.1103\/PhysRevA.91.052324"},{"key":"7","doi-asserted-by":"publisher","unstructured":"T. Kato, On the Adiabatic Theorem of Quantum Mechanics, J. Phys. Soc. Jpn. 5, 435 (1950).","DOI":"10.1143\/JPSJ.5.435"},{"key":"8","doi-asserted-by":"publisher","unstructured":"W. M. Itano, D. J. Heinzen, J. J. Bollinger, and D. J. Wineland, Quantum Zeno Effect, Phys. Rev. A 41, 2295 (1990).","DOI":"10.1103\/PhysRevA.41.2295"},{"key":"9","doi-asserted-by":"publisher","unstructured":"E. W. Streed, J. Mun, M. Boyd, G. K. Campbell, P. Medley, W. Ketterle, and D. E. Pritchard, Continuous and Pulsed Quantum Zeno Effect, Phys. Rev. Lett. 97, 260402 (2006).","DOI":"10.1103\/PhysRevLett.97.260402"},{"key":"10","doi-asserted-by":"publisher","unstructured":"F. Sch\u00e4fer, I. Herrera, S. Cherukattil, C. Lovecchio, F. S. Cataliotti, F. Caruso, and A. Smerzi, Experimental Realization of Quantum Zeno Dynamics, Nat. Commun. 5, 3194 (2014).","DOI":"10.1038\/ncomms4194"},{"key":"11","doi-asserted-by":"publisher","unstructured":"A. Signoles, A. Facon, D. Grosso, I. Dotsenko, S. Haroche, J.-M. Raimond, M. Brune, and S. Gleyzes, Confined Quantum Zeno Dynamics of a Watched Atomic Arrow, Nat. Phys. 10, 715 (2014).","DOI":"10.1038\/nphys3076"},{"key":"12","doi-asserted-by":"publisher","unstructured":"L. Bretheau, P. Campagne-Ibarcq, E. Flurin, F. Mallet, and B. Huard, Quantum Dynamics of an Electromagnetic Mode that Cannot Contain $N$ Photons, Science 348, 776 (2015).","DOI":"10.1126\/science.1259345"},{"key":"13","doi-asserted-by":"publisher","unstructured":"G. Barontini, L. Hohmann, F. Haas, J. Est\u00e8ve, and J. Reichel, Deterministic Generation of Multiparticle Entanglement by Quantum Zeno Dynamics, Science 349, 1317 (2015).","DOI":"10.1126\/science.aaa0754"},{"key":"14","doi-asserted-by":"publisher","unstructured":"N. Kalb, J. Cramer, D. J. Twitchen, M. Markham, R. Hanson, and T. H. Taminiau, Experimental Creation of Quantum Zeno Subspaces by Repeated Multi-Spin Projections in Diamond, Nat. Commun. 7, 13111 (2016).","DOI":"10.1038\/ncomms13111"},{"key":"15","doi-asserted-by":"publisher","unstructured":"P. Facchi, S. Tasaki, S. Pascazio, H. Nakazato, A. Tokuse, and D. A. Lidar, Control of Decoherence: Analysis and Comparison of Three Different Strategies, Phys. Rev. A 71, 022302 (2005).","DOI":"10.1103\/PhysRevA.71.022302"},{"key":"16","doi-asserted-by":"publisher","unstructured":"P. Facchi and S. Pascazio, Quantum Zeno Dynamics: Mathematical and Physical Aspects, J. Phys. A: Math. Theor. 41, 493001 (2008).","DOI":"10.1088\/1751-8113\/41\/49\/493001"},{"key":"17","doi-asserted-by":"publisher","unstructured":"T. Petrosky, S. Tasaki, and I. Prigogine, Quantum Zeno Effect, Phys. Lett. A 151, 109 (1990).","DOI":"10.1016\/0375-9601(90)90173-L"},{"key":"18","doi-asserted-by":"publisher","unstructured":"L. S. Schulman, Continuous and Pulsed Observations in the Quantum Zeno Effect, Phys. Rev. A 57, 1509 (1998).","DOI":"10.1103\/PhysRevA.57.1509"},{"key":"19","doi-asserted-by":"publisher","unstructured":"P. Facchi, D. A. Lidar, and S. Pascazio, Unification of Dynamical Decoupling and the Quantum Zeno Effect, Phys. Rev. A 69, 032314 (2004).","DOI":"10.1103\/PhysRevA.69.032314"},{"key":"20","doi-asserted-by":"publisher","unstructured":"K. Koshino and A. Shimizu, Quantum Zeno Effect by General Measurements, Phys. Rep. 412, 191 (2005).","DOI":"10.1016\/j.physrep.2005.03.001"},{"key":"21","doi-asserted-by":"publisher","unstructured":"P. Facchi, H. Nakazato, and S. Pascazio, From the Quantum Zeno to the Inverse Quantum Zeno Effect, Phys. Rev. Lett. 86, 2699 (2001).","DOI":"10.1103\/PhysRevLett.86.2699"},{"key":"22","doi-asserted-by":"publisher","unstructured":"P. Facchi and M. Ligab\u00f2, Quantum Zeno Effect and Dynamics, J. Math. Phys. 51, 022103 (2010).","DOI":"10.1063\/1.3290971"},{"key":"23","doi-asserted-by":"publisher","unstructured":"J. Schwinger, The Algebra of Microscopic Measurement, Proc. Natl. Acad. Sci. USA 45, 1542 (1959).","DOI":"10.1073\/pnas.45.10.1542"},{"key":"24","doi-asserted-by":"publisher","unstructured":"A. Peres, Quantum Theory: Concepts and Methods (Kluwer Academic, New York, 2002).","DOI":"10.1007\/0-306-47120-5"},{"key":"25","doi-asserted-by":"publisher","unstructured":"S. Pascazio, On Noise-Induced Superselection Rules, J. Mod. Opt. 51, 925 (2004).","DOI":"10.1080\/09500340408233606"},{"key":"26","doi-asserted-by":"publisher","unstructured":"K. Macieszczak, M. Gu\u0163\u0103, I. Lesanovsky, and J. P. Garrahan, Towards a Theory of Metastability in Open Quantum Dynamics, Phys. Rev. Lett. 116, 240404 (2016).","DOI":"10.1103\/PhysRevLett.116.240404"},{"key":"27","doi-asserted-by":"publisher","unstructured":"V. V. Albert, B. Bradlyn, M. Fraas, and L. Jiang, Geometry and Response of Lindbladians, Phys. Rev. X 6, 041031 (2016).","DOI":"10.1103\/PhysRevX.6.041031"},{"key":"28","doi-asserted-by":"publisher","unstructured":"J. Marshall, L. Campos Venuti, and P. Zanardi, Noise Suppression via Generalized-Markovian Processes, Phys. Rev. A 96, 052113 (2017).","DOI":"10.1103\/PhysRevA.96.052113"},{"key":"29","doi-asserted-by":"publisher","unstructured":"R. Alicki and K. Lendi, Quantum Dynamical Semigroups and Applications, 2nd ed. (Springer, Berlin, 2007).","DOI":"10.1007\/3-540-70861-8"},{"key":"30","doi-asserted-by":"publisher","unstructured":"D. Chru\u015bci\u0144ski and S. Pascazio, A Brief History of the GKLS Equation, Open Sys. Inf. Dyn. 24, 1740001 (2017).","DOI":"10.1142\/S1230161217400017"},{"key":"31","unstructured":"A. Messiah, Quantum Mechanics (Dover, New York, 2017)."},{"key":"32","doi-asserted-by":"publisher","unstructured":"J. E. Avron, M. Fraas, and G. M. Graf, Adiabatic Response for Lindblad Dynamics, J. Stat. Phys. 148, 800 (2012).","DOI":"10.1007\/s10955-012-0550-6"},{"key":"33","doi-asserted-by":"publisher","unstructured":"J. Schmid, Adiabatic Theorems for General Linear Operators with Time-Independent Domains, Rev. Math. Phys. 31, 1950014 (2019).","DOI":"10.1142\/S0129055X19500144"},{"key":"34","unstructured":"E. B. Davies, One-Parameter Semigroups (Academic Press, San Diego, 1980)."},{"key":"35","doi-asserted-by":"publisher","unstructured":"C. Cohen\u2010Tannoudji, J. Dupont\u2010Roc, and G. Grynberg, Atom-Photon Interactions: Basic Process and Appilcations (Wiley, Weinheim, 1998).","DOI":"10.1002\/9783527617197"},{"key":"36","unstructured":"N. G. Van Kampen, Stochastic Processes in Physics and Chemistry, 2nd ed. (Elsevier, Amsterdam, 1992)."},{"key":"37","doi-asserted-by":"publisher","unstructured":"R. Azouit, A. Sarlette, and P. Rouchon, Adiabatic Elimination for Open Quantum Systems with Effective Lindblad Master Equations, in 2016 IEEE 55th Conference on Decision and Control (CDC), Dec. 2016, pp. 4559-4565.","DOI":"10.1109\/CDC.2016.7798963"},{"key":"38","doi-asserted-by":"publisher","unstructured":"G. Dirr and U. Helmke, Lie Theory for Quantum Control, GAMM-Mitt. 31, 59 (2008).","DOI":"10.1002\/gamm.200890003"},{"key":"39","doi-asserted-by":"crossref","unstructured":"Z. K. Minev, S. O. Mundhada, S. Shankar, P. Reinhold, R. Guti\u00e9rrez-J\u00e1uregui, R. J. Schoelkopf, M. Mirrahimi, H. J. Carmichael, and M. H. Devoret, To Catch and Reverse a Quantum Jump Mid-Flight, arXiv:1803.00545 [quant-ph] (2018).","DOI":"10.1038\/s41586-019-1287-z"},{"key":"40","doi-asserted-by":"publisher","unstructured":"T. Kato, Perturbation Theory for Linear Operators, 2nd ed. (Springer, Berlin, 1980).","DOI":"10.1007\/978-3-642-66282-9"},{"key":"41","unstructured":"M. M. Wolf, ``Quantum Channels & Operations: Guided Tour,'' URL: https:\/\/www-m5.ma.tum.de\/foswiki\/pub\/M5\/Allgemeines\/MichaelWolf\/QChannelLecture.pdf."},{"key":"42","doi-asserted-by":"publisher","unstructured":"B. Baumgartner, H. Narnhofer, and W. Thirring, Analysis of Quantum Semigroups with GKS-Lindblad Generators: I. Simple Generators, J. Phys. A: Math. Theor. 41, 065201 (2008).","DOI":"10.1088\/1751-8113\/41\/6\/065201"},{"key":"43","doi-asserted-by":"publisher","unstructured":"B. Baumgartner and H. Narnhofer, Analysis of Quantum Semigroups with GKS-Lindblad Generators: II. General, J. Phys. A: Math. Theor. 41, 395303 (2008).","DOI":"10.1088\/1751-8113\/41\/39\/395303"},{"key":"44","doi-asserted-by":"publisher","unstructured":"B. Baumgartner and H. Narnhofer, The Structures of State Space Concerning Quantum Dynamical Semigroups, Rev. Math. Phys. 24, 1250001 (2012).","DOI":"10.1142\/S0129055X12500018"},{"key":"45","unstructured":"V. V. Albert, Lindbladians with Multiple Steady States: Theory and Applications, Ph.D. Thesis, Yale University, Connecticut, 2017, available at arXiv:1802.00010 [quant-ph]."},{"key":"46","unstructured":"R. A. Horn and C. R. Johnson, Matrix Analysis, 2nd ed. (Cambridge University Press, Cambridge, 2012)."}],"container-title":["Quantum"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/quantum-journal.org\/papers\/q-2019-06-12-152\/pdf\/","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"}],"deposited":{"date-parts":[[2019,6,12]],"date-time":"2019-06-12T13:32:25Z","timestamp":1560346345000},"score":1,"resource":{"primary":{"URL":"https:\/\/quantum-journal.org\/papers\/q-2019-06-12-152\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,6,12]]},"references-count":47,"URL":"https:\/\/doi.org\/10.22331\/q-2019-06-12-152","archive":["CLOCKSS"],"relation":{},"ISSN":["2521-327X"],"issn-type":[{"value":"2521-327X","type":"electronic"}],"subject":[],"published":{"date-parts":[[2019,6,12]]},"article-number":"152"}}