CARABBA, Nicoletta ; University of Luxembourg > Faculty of Science, Technology and Medicine (FSTM) > Department of Physics and Materials Science (DPHYMS)
Hörnedal, Niklas ; University of Luxembourg > Faculty of Science, Technology and Medicine (FSTM) > Department of Physics and Materials Science (DPHYMS)
DEL CAMPO ECHEVARRIA, Adolfo ; University of Luxembourg > Faculty of Science, Technology and Medicine (FSTM) > Department of Physics and Materials Science (DPHYMS) ; Donostia International Physics Center
Co-auteurs externes :
yes
Langue du document :
Anglais
Titre :
Quantum speed limits on operator flows and correlation functions
Date de publication/diffusion :
22 décembre 2022
Titre du périodique :
Quantum
eISSN :
2521-327X
Maison d'édition :
Verein zur Förderung des Open Access Publizierens in den Quantenwissenschaften, Autriche
L. Mandelstam and I. Tamm. The uncertainty relation between energy and time in non-relativistic quantum mechanics. J. Phys. USSR, 9:249, 1945. DOI: https://doi.org/10.1007/978-3-642-74626-0_8.
Norman Margolus and Lev B. Levitin. The maximum speed of dynamical evolution. Physica D: Nonlinear Phenomena, 120(1):188–195, 1998. ISSN 0167-2789. DOI: https://doi.org/10.1016/S0167-2789(98)00054-2. URL https://www.sciencedirect.com/science/ article/pii/S0167278998000542. Proceedings of the Fourth Workshop on Physics and Consumption.
Armin Uhlmann. An energy dispersion estimate. Physics Letters A, 161 (4):329 – 331, 1992. ISSN 0375-9601. DOI: https://doi.org/10.1016/0375-9601(92)90555-Z. URL http://www.sciencedirect.com/science/article/ pii/037596019290555Z.
Francesco Campaioli, Felix A. Pollock, Felix C. Binder, and Kavan Modi. Tightening quantum speed limits for almost all states. Phys. Rev. Lett., 120:060409, Feb 2018. DOI: 10.1103/PhysRevLett.120.060409. URL https://link.aps.org/doi/10.1103/PhysRevLett.120.060409.
J. Anandan and Y. Aharonov. Geometry of quantum evolution. Phys. Rev. Lett., 65: 1697–1700, Oct 1990. DOI: 10.1103/Phys-RevLett.65.1697. URL https://link.aps.org/doi/10.1103/PhysRevLett.65.1697.
Sebastian Deffner and Eric Lutz. Energy–time uncertainty relation for driven quantum systems. Journal of Physics A: Mathematical and Theoretical, 46(33): 335302, jul 2013. DOI: 10.1088/1751-8113/46/33/335302. URL https://doi.org/10.1088/1751-8113/46/33/335302.
Manaka Okuyama and Masayuki Ohzeki. Comment on ‘energy-time uncertainty relation for driven quantum systems’. Journal of Physics A: Mathematical and Theoretical, 51 (31):318001, jun 2018. DOI: 10.1088/1751-8121/aacb90. URL https://doi.org/10.1088/1751-8121/aacb90.
M. M. Taddei, B. M. Escher, L. Davidovich, and R. L. de Matos Filho. Quantum speed limit for physical processes. Phys. Rev. Lett., 110:050402, Jan 2013. DOI: 10.1103/PhysRevLett.110.050402. URL https://link.aps.org/doi/10.1103/PhysRevLett.110.050402.
A. del Campo, I. L. Egusquiza, M. B. Plenio, and S. F. Huelga. Quantum speed limits in open system dynamics. Phys. Rev. Lett., 110:050403, Jan 2013. DOI: 10.1103/PhysRevLett.110.050403. URL https://link.aps.org/doi/10.1103/ PhysRevLett.110.050403.
Sebastian Deffner and Eric Lutz. Quantum speed limit for non-markovian dynamics. Phys. Rev. Lett., 111:010402, Jul 2013. DOI: 10.1103/PhysRevLett.111.010402. URL https://link.aps.org/doi/10.1103/PhysRevLett.111.010402.
Francesco Campaioli, Felix A. Pollock, and Kavan Modi. Tight, robust, and feasible quantum speed limits for open dynamics. Quantum, 3:168, August 2019. ISSN 2521-327X. DOI: 10.22331/q-2019-08-05-168. URL https://doi.org/10.22331/ q-2019-08-05-168.
Luis Pedro García-Pintos and Adolfo del Campo. Quantum speed limits under continuous quantum measurements. New Journal of Physics, 21(3):033012, mar 2019. DOI: 10.1088/1367-2630/ab099e. URL https://doi.org/10.1088/1367-2630/ab099e.
B. Shanahan, A. Chenu, N. Margolus, and A. del Campo. Quantum speed limits across the quantum-to-classical transition. Phys. Rev. Lett., 120:070401, Feb 2018. DOI: 10.1103/PhysRevLett.120.070401. URL https://link.aps.org/doi/10.1103/PhysRevLett.120.070401.
Manaka Okuyama and Masayuki Ohzeki. Quantum speed limit is not quantum. Phys. Rev. Lett., 120:070402, Feb 2018. DOI: 10.1103/PhysRevLett.120.070402. URL https://link.aps.org/doi/10.1103/PhysRevLett.120.070402.
Naoto Shiraishi, Ken Funo, and Keiji Saito. Speed limit for classical stochastic processes. Phys. Rev. Lett., 121:070601, Aug 2018. DOI: 10.1103/PhysRevLett.121.070601. URL https://link.aps.org/doi/10.1103/PhysRevLett.121.070601.
Sebastian Deffner and Steve Campbell. Quantum speed limits: from heisenberg’s uncertainty principle to optimal quantum control. Journal of Physics A: Mathematical and Theoretical, 50(45): 453001, oct 2017. DOI: 10.1088/1751-8121/aa86c6. URL https://doi.org/10. 1088/1751-8121/aa86c6.
S. Lloyd. Ultimate physical limits to computation. Nature, 406(6799):1047–1054, 2000. DOI: https://doi.org/10.1038/35023282.
Seth Lloyd. Computational capacity of the universe. Phys. Rev. Lett., 88:237901, May 2002. DOI: 10.1103/PhysRevLett.88.237901. URL https://link.aps.org/doi/10.1103/PhysRevLett.88.237901.
Vittorio Giovannetti, Seth Lloyd, and Lorenzo Maccone. Advances in quantum metrology. Nature Photonics, 5(4):222–229, 2011. ISSN 1749-4893. DOI: 10.1038/npho-ton.2011.35. URL https://doi.org/10.1038/nphoton.2011.35.
M. Beau and A. del Campo. Nonlinear quantum metrology of many-body open systems. Phys. Rev. Lett., 119:010403, Jul 2017. DOI: 10.1103/PhysRevLett.119.010403. URL https://link.aps.org/doi/10.1103/PhysRevLett.119.010403.
T. Caneva, M. Murphy, T. Calarco, R. Fazio, S. Montangero, V. Giovannetti, and G. E. Santoro. Optimal control at the quantum speed limit. Phys. Rev. Lett., 103:240501, Dec 2009. DOI: 10.1103/PhysRevLett.103.240501. URL https://link.aps.org/doi/10.1103/PhysRevLett.103.240501.
Gerhard C. Hegerfeldt. Driving at the quantum speed limit: Optimal control of a two-level system. Phys. Rev. Lett., 111:260501, Dec 2013. DOI: 10.1103/PhysRevLett.111.260501. URL https://link.aps.org/doi/10.1103/PhysRevLett.111.260501.
Ken Funo, Jing-Ning Zhang, Cyril Chatou, Kihwan Kim, Masahito Ueda, and Adolfo del Campo. Universal work fluctuations during shortcuts to adiabaticity by counterdiabatic driving. Phys. Rev. Lett., 118:100602, Mar 2017. DOI: 10.1103/PhysRevLett.118.100602. URL https://link.aps.org/doi/10.1103/PhysRevLett.118.100602.
Steve Campbell and Sebastian Deffner. Trade-off between speed and cost in shortcuts to adiabaticity. Phys. Rev. Lett., 118:100601, Mar 2017. DOI: 10.1103/PhysRevLett.118.100601. URL https://link.aps.org/doi/10.1103/ PhysRevLett.118.100601.
Sahar Alipour, Aurelia Chenu, Ali T. Rezakhani, and Adolfo del Campo. Shortcuts to Adiabaticity in Driven Open Quantum Systems: Balanced Gain and Loss and Non-Markovian Evolution. Quantum, 4:336, September 2020. ISSN 2521-327X. DOI: 10.22331/q-2020-09-28-336. URL https://doi.org/10.22331/q-2020-09-28-336.
Ken Funo, Neill Lambert, and Franco Nori. General bound on the performance of counter-diabatic driving acting on dissipative spin systems. Phys. Rev. Lett., 127:150401, Oct 2021. DOI: 10.1103/PhysRevLett.127.150401. URL https://link.aps.org/doi/10.1103/PhysRevLett.127.150401.
Marin Bukov, Dries Sels, and Anatoli Polkovnikov. Geometric speed limit of accessible many-body state preparation. Phys. Rev. X, 9:011034, Feb 2019. DOI: 10.1103/PhysRevX.9.011034. URL https://link.aps.org/doi/10.1103/PhysRevX.9.011034.
Keisuke Suzuki and Kazutaka Takahashi. Performance evaluation of adiabatic quantum computation via quantum speed limits and possible applications to many-body systems. Phys. Rev. Research, 2:032016, Jul 2020. DOI: 10.1103/PhysRevResearch.2.032016. URL https://link.aps.org/doi/10.1103/PhysRevResearch.2.032016.
Adolfo del Campo. Probing quantum speed limits with ultracold gases. Phys. Rev. Lett., 126:180603, May 2021. DOI: 10.1103/PhysRevLett.126.180603. URL https://link.aps.org/doi/10.1103/PhysRevLett.126.180603.
Zongping Gong and Ryusuke Hamazaki. Bounds in nonequilibrium quantum dynamics. International Journal of Modern Physics B, 36(31):2230007, 2022. DOI: 10.1142/S0217979222300079. URL https: //doi.org/10.1142/S0217979222300079.
Jun Jing, Lian-Ao Wu, and Adolfo del Campo. Fundamental speed limits to the generation of quantumness. Scientific Reports, 6(1):38149, Nov 2016. ISSN 2045-2322. DOI: 10.1038/srep38149. URL https://doi.org/10.1038/srep38149.
Iman Marvian, Robert W. Spekkens, and Paolo Zanardi. Quantum speed limits, coherence, and asymmetry. Phys. Rev. A, 93:052331, May 2016. DOI: 10.1103/Phys-RevA.93.052331. URL https://link.aps.org/doi/10.1103/PhysRevA.93.052331.
Brij Mohan, Siddhartha Das, and Arun Kumar Pati. Quantum speed limits for information and coherence. New Journal of Physics, 24(6):065003, jun 2022. DOI: 10.1088/1367-2630/ac753c. URL https://doi.org/10.1088/1367-2630/ac753c.
Francesco Campaioli, Chang shui Yu, Felix A Pollock, and Kavan Modi. Resource speed limits: maximal rate of resource variation. New Journal of Physics, 24(6):065001, jun 2022. DOI: 10.1088/1367-2630/ac7346. URL https://doi.org/10.1088/1367-2630/ac7346.
Todd R. Gingrich, Jordan M. Horowitz, Nikolay Perunov, and Jeremy L. England. Dissipation bounds all steady-state current fluctuations. Phys. Rev. Lett., 116:120601, Mar 2016. DOI: 10.1103/PhysRevLett.116.120601. URL https://link.aps.org/doi/10.1103/PhysRevLett.116.120601.
Yoshihiko Hasegawa. Thermodynamic uncertainty relation for general open quantum systems. Phys. Rev. Lett., 126:010602, Jan 2021. DOI: 10.1103/PhysRevLett.126.010602. URL https://link.aps.org/doi/10.1103/PhysRevLett.126.010602.
Schuyler B. Nicholson, Luis Pedro García-Pintos, Adolfo del Campo, and Jason R. Green. Time–information uncertainty relations in thermodynamics. Nature Physics, 16(12):1211–1215, Dec 2020. ISSN 1745-2481. DOI: 10.1038/s41567-020-0981-y. URL https://doi.org/10.1038/ s41567-020-0981-y.
Van Tuan Vo, Tan Van Vu, and Yoshihiko Hasegawa. Unified approach to classical speed limit and thermodynamic uncertainty relation. Phys. Rev. E, 102:062132, Dec 2020. DOI: 10.1103/PhysRevE.102.062132. URL https://link.aps.org/doi/10. 1103/PhysRevE.102.062132.
Luis Pedro García-Pintos, Schuyler B. Nicholson, Jason R. Green, Adolfo del Campo, and Alexey V. Gorshkov. Unifying quantum and classical speed limits on observables. Phys. Rev. X, 12: 011038, Feb 2022. DOI: 10.1103/Phys-RevX.12.011038. URL https://link.aps.org/doi/10.1103/PhysRevX.12.011038.
Brij Mohan and Arun Kumar Pati. Quantum speed limits for observables. Phys. Rev. A, 106:042436, Oct 2022. DOI: 10.1103/PhysRevA.106.042436. URL https://link.aps.org/doi/10.1103/PhysRevA.106.042436.
A.M. Perelomov. Integrable Systems of Classical Mechanics and Lie Algebras Volume I. Birkhäuser Basel, 1990. DOI: https://doi.org/10.1007/978-3-0348-9257-5.
Franz J. Wegner. Flow equations for hamiltonians. Physics Reports, 348 (1):77–89, 2001. ISSN 0370-1573. DOI: https://doi.org/10.1016/S0370-1573(00)00136-8. URL https://www.sciencedirect.com/science/ article/pii/S0370157300001368.
Pablo M. Poggi. Geometric quantum speed limits and short-time accessibility to unitary operations. Phys. Rev. A, 99: 042116, Apr 2019. DOI: 10.1103/Phys-RevA.99.042116. URL https://link.aps.org/doi/10.1103/PhysRevA.99.042116.
Raam Uzdin. Resources needed for non-unitary quantum operations. Journal of Physics A: Mathematical and Theoretical, 46(14):145302, mar 2013. DOI: 10.1088/1751-8113/46/14/145302. URL https://doi.org/10.1088%2F1751-8113% 2F46%2F14%2F145302.
Raam Uzdin and Ronnie Kosloff. Speed limits in liouville space for open quantum systems. EPL (Europhysics Letters), 115 (4):40003, aug 2016. DOI: 10.1209/0295-5075/115/40003. URL https://doi.org/10.1209/0295-5075/115/40003.
C. W. von Keyserlingk, Tibor Rakovszky, Frank Pollmann, and S. L. Sondhi. Operator hydrodynamics, otocs, and entanglement growth in systems without conservation laws. Phys. Rev. X, 8: 021013, Apr 2018. DOI: 10.1103/Phys-RevX.8.021013. URL https://link.aps. org/doi/10.1103/PhysRevX.8.021013.
Vedika Khemani, Ashvin Vishwanath, and David A. Huse. Operator spreading and the emergence of dissipative hydrodynamics under unitary evolution with conservation laws. Phys. Rev. X, 8: 031057, Sep 2018. DOI: 10.1103/Phys-RevX.8.031057. URL https://link.aps.org/doi/10.1103/PhysRevX.8.031057.
Adam Nahum, Sagar Vijay, and Jeongwan Haah. Operator spreading in random unitary circuits. Phys. Rev. X, 8: 021014, Apr 2018. DOI: 10.1103/Phys-RevX.8.021014. URL https://link.aps.org/doi/10.1103/PhysRevX.8.021014.
Sarang Gopalakrishnan, David A. Huse, Vedika Khemani, and Romain Vasseur. Hydrodynamics of operator spreading and quasiparticle diffusion in interacting integrable systems. Phys. Rev. B, 98: 220303, Dec 2018. DOI: 10.1103/Phys-RevB.98.220303. URL https://link.aps.org/doi/10.1103/PhysRevB.98.220303.
Tibor Rakovszky, Frank Pollmann, and C. W. von Keyserlingk. Diffusive hydrodynamics of out-of-time-ordered correlators with charge conservation. Phys. Rev. X, 8:031058, Sep 2018. DOI: 10.1103/Phys-RevX.8.031058. URL https://link.aps.org/doi/10.1103/PhysRevX.8.031058.
Leonard Susskind. Computational complexity and black hole horizons. Fortschritte der Physik, 64(1):24–43, 2016. DOI: https://doi.org/10.1002/prop.201500092. URL https://onlinelibrary.wiley.com/doi/abs/10.1002/prop.201500092.
Adam R. Brown, Daniel A. Roberts, Leonard Susskind, Brian Swingle, and Ying Zhao. Holographic complexity equals bulk action? Phys. Rev. Lett., 116:191301, May 2016. DOI: 10.1103/PhysRevLett.116.191301. URL https://link.aps.org/doi/10.1103/PhysRevLett.116.191301.
Adam R. Brown, Daniel A. Roberts, Leonard Susskind, Brian Swingle, and Ying Zhao. Complexity, action, and black holes. Phys. Rev. D, 93:086006, Apr 2016. DOI: 10.1103/PhysRevD.93.086006. URL https://link.aps.org/doi/10.1103/ PhysRevD.93.086006.
Shira Chapman, Michal P. Heller, Hugo Marrochio, and Fernando Pastawski. Toward a definition of complexity for quantum field theory states. Phys. Rev. Lett., 120:121602, Mar 2018. DOI: 10.1103/PhysRevLett.120.121602. URL https://link.aps.org/doi/10.1103/PhysRevLett.120.121602.
J. Molina-Vilaplana and A. del Campo. Complexity functionals and complexity growth limits in continuous mera circuits. Journal of High Energy Physics, 2018(8): 12, Aug 2018. ISSN 1029-8479. DOI: 10.1007/JHEP08(2018)012. URL https://doi.org/10.1007/JHEP08(2018)012.
Niklas Hörnedal, Nicoletta Carabba, Apollonas S. Matsoukas-Roubeas, and Adolfo del Campo. Ultimate speed limits to the growth of operator complexity. Communications Physics, 5(1):207, Aug 2022. ISSN 2399-3650. DOI: 10.1038/s42005-022-00985-1. URL https://doi.org/10.1038/ s42005-022-00985-1.
Daniel E. Parker, Xiangyu Cao, Alexander Avdoshkin, Thomas Scaffidi, and Ehud Altman. A universal operator growth hypothesis. Phys. Rev. X, 9: 041017, Oct 2019. DOI: 10.1103/Phys-RevX.9.041017. URL https://link.aps.org/doi/10.1103/PhysRevX.9.041017.
J.L.F. Barbón, E. Rabinovici, R. Shir, and R. Sinha. On the evolution of operator complexity beyond scrambling. J. High Energ. Phys., 2019(10):264, October 2019. ISSN 1029-8479. DOI: 10.1007/JHEP10(2019)264. URL https://doi.org/10.1007/JHEP10(2019)264.
E. Rabinovici, A. Sánchez-Garrido, R. Shir, and J. Sonner. Operator complexity: a journey to the edge of Krylov space. J. High Energ. Phys., 2021(6): 62, June 2021. ISSN 1029-8479. DOI: 10.1007/JHEP06(2021)062. URL https://doi.org/10.1007/JHEP06(2021)062.
Pawel Caputa, Javier M. Magan, and Dim-itrios Patramanis. Geometry of Krylov Complexity. arXiv:2109.03824, September 2021. URL http://arxiv.org/abs/2109.03824.
Ryogo Kubo. Statistical-mechanical theory of irreversible processes. i. general theory and simple applications to magnetic and conduction problems. Journal of the Physical Society of Japan, 12(6):570–586, 1957. DOI: 10.1143/JPSJ.12.570. URL https://doi.org/10.1143/JPSJ.12.570.
Gal Ness, Manolo R. Lam, Wolfgang Alt, Dieter Meschede, Yoav Sagi, and Andrea Alberti. Observing crossover between quantum speed limits. Science Advances, 7 (52):eabj9119, 2021. DOI: 10.1126/sci-adv.abj9119. URL https://www.science.org/doi/abs/10.1126/sciadv.abj9119.
Philipp Hauke, Markus Heyl, Luca Tagliacozzo, and Peter Zoller. Measuring multipartite entanglement through dynamic susceptibilities. Nature Physics, 12(8):778–782, 2016. DOI: 10.1038/nphys3700. URL https://doi.org/10.1038/nphys3700.
Xiaoguang Wang, Zhe Sun, and Z. D. Wang. Operator fidelity susceptibility: An indicator of quantum criticality. Phys. Rev. A, 79:012105, Jan 2009. DOI: 10.1103/Phys-RevA.79.012105. URL https://link.aps.org/doi/10.1103/PhysRevA.79.012105.
Ole Andersson. Holonomy in Quantum Information Geometry. PhD thesis, Stockholm University, 2019.
Gal Ness, Andrea Alberti, and Yoav Sagi. Quantum speed limit for states with a bounded energy spectrum. Phys. Rev. Lett., 129:140403, Sep 2022. DOI: 10.1103/PhysRevLett.129.140403. URL https://link.aps.org/doi/10.1103/PhysRevLett.129.140403.
Lev B. Levitin and Tommaso Toffoli. Fundamental limit on the rate of quantum dynamics: The unified bound is tight. Phys. Rev. Lett., 103:160502, Oct 2009. DOI: 10.1103/PhysRevLett.103.160502. URL https://link.aps.org/doi/10.1103/PhysRevLett.103.160502.
Anatoly Dymarsky and Michael Smolkin. Krylov complexity in conformal field theory. Phys. Rev. D, 104:L081702, Oct 2021. DOI: 10.1103/PhysRevD.104.L081702. URL https://link.aps.org/doi/10.1103/ PhysRevD.104.L081702.
Álvaro M. Alhambra, Jonathon Riddell, and Luis Pedro García-Pintos. Time evolution of correlation functions in quantum many-body systems. Phys. Rev. Lett., 124:110605, Mar 2020. DOI: 10.1103/PhysRevLett.124.110605. URL https://link.aps.org/doi/10.1103/PhysRevLett.124.110605.
Mark E. Tuckerman. Statistical Mechanics: Theory and Molecular Simulation. Oxford University Press, 2010. DOI: https://doi.org/10.1002/anie.201105752.
Masahito Ueda. Fundamentals and New Frontiers of Bose-Einstein Condensation. WORLD SCIENTIFIC, 2010. DOI: 10.1142/7216. URL https://www.worldscientific.com/doi/abs/10.1142/7216.
Gene F. Mazenko. Nonequilibrium Statistical Mechanics. John Wiley Sons, 2006. ISBN 9783527618958. DOI: https://doi.org/10.1002/9783527618958.
G.E. Pake. Paramagnetic Resonance: An Introductory Monograph. Number v. 1 in Frontiers in physics. W.A. Benjamin, 1962. URL https://books.google.lu/books?id=B8pEAAAAIAAJ.
Marlon Brenes, Silvia Pappalardi, John Goold, and Alessandro Silva. Multipartite entanglement structure in the eigenstate thermalization hypothesis. Phys. Rev. Lett., 124:040605, Jan 2020. DOI: 10.1103/PhysRevLett.124.040605. URL https://link.aps.org/doi/10.1103/PhysRevLett.124.040605.
Samuel L. Braunstein, Carlton M. Caves, and G.J. Milburn. Generalized uncertainty relations: Theory, examples, and lorentz invariance. Annals of Physics, 247(1): 135–173, 1996. ISSN 0003-4916. DOI: https://doi.org/10.1006/aphy.1996.0040. URL https://www.sciencedirect.com/science/article/pii/ S0003491696900408.
Vittorio Giovannetti, Seth Lloyd, and Lorenzo Maccone. Quantum limits to dynamical evolution. Phys. Rev. A, 67: 052109, May 2003. DOI: 10.1103/Phys-RevA.67.052109. URL https://link.aps. org/doi/10.1103/PhysRevA.67.052109.
Vittorio Giovannetti, Seth Lloyd, and Lorenzo Maccone. The speed limit of quantum unitary evolution. Journal of Optics B: Quantum and Semiclassical Optics, 6(8): S807–S810, jul 2004. DOI: 10.1088/1464-4266/6/8/028. URL https://doi.org/10.1088/1464-4266/6/8/028.
A. del Campo, J. Molina-Vilaplana, and J. Sonner. Scrambling the spectral form factor: Unitarity constraints and exact results. Phys. Rev. D, 95:126008, Jun 2017. DOI: 10.1103/PhysRevD.95.126008. URL https://link.aps.org/doi/10.1103/PhysRevD.95.126008.
Zhenyu Xu, Aurelia Chenu, Tomaž Prosen, and Adolfo del Campo. Thermofield dynamics: Quantum chaos versus decoherence. Phys. Rev. B, 103:064309, Feb 2021. DOI: 10.1103/PhysRevB.103.064309. URL https://link.aps.org/doi/10.1103/PhysRevB.103.064309.
Manaka Okuyama and Masayuki Ohzeki. Comment on ‘energy-time uncertainty relation for driven quantum systems’. Journal of Physics A: Mathematical and Theoretical, 51 (31):318001, jun 2018. DOI: 10.1088/1751-8121/aacb90. URL https://dx.doi.org/10.1088/1751-8121/aacb90.
