{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,18]],"date-time":"2025-10-18T10:55:06Z","timestamp":1760784906543,"version":"build-2065373602"},"reference-count":83,"publisher":"MDPI AG","issue":"10","license":[{"start":{"date-parts":[[2020,10,20]],"date-time":"2020-10-20T00:00:00Z","timestamp":1603152000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>In contrast to classical systems, actual implementation of non-Hermitian Hamiltonian dynamics for quantum systems is a challenge because the processes of energy gain and dissipation are based on the underlying Hermitian system\u2013environment dynamics, which are trace preserving. Recently, a scheme for engineering non-Hermitian Hamiltonians as a result of repetitive measurements on an ancillary qubit has been proposed. The induced conditional dynamics of the main system is described by the effective non-Hermitian Hamiltonian arising from the procedure. In this paper, we demonstrate the effectiveness of such a protocol by applying it to physically relevant multi-spin models, showing that the effective non-Hermitian Hamiltonian drives the system to a maximally entangled stationary state. In addition, we report a new recipe to construct a physical scenario where the quantum dynamics of a physical system represented by a given non-Hermitian Hamiltonian model may be simulated. The physical implications and the broad scope potential applications of such a scheme are highlighted.<\/jats:p>","DOI":"10.3390\/e22101184","type":"journal-article","created":{"date-parts":[[2020,10,20]],"date-time":"2020-10-20T20:50:07Z","timestamp":1603227007000},"page":"1184","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":22,"title":["Two-Qubit Entanglement Generation through Non-Hermitian Hamiltonians Induced by Repeated Measurements on an Ancilla"],"prefix":"10.3390","volume":"22","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-2363-7699","authenticated-orcid":false,"given":"Roberto","family":"Grimaudo","sequence":"first","affiliation":[{"name":"Dipartimento di Fisica e Chimica dell\u2019Universit\u00e0 di Palermo, Via Archirafi 36, I-90123 Palermo, Italy"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Antonino","family":"Messina","sequence":"additional","affiliation":[{"name":"Dipartimento di Matematica ed Informatica dell\u2019Universit\u00e0 di Palermo, Via Archirafi 34, I-90123 Palermo, Italy"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3954-0445","authenticated-orcid":false,"given":"Alessandro","family":"Sergi","sequence":"additional","affiliation":[{"name":"Istituto Nazionale di Fisica Nucleare, Sez. di Catania, 95123 Catania, Italy"},{"name":"Dipartimento di Scienze Matematiche e Informatiche, Scienze Fisiche e Scienze della Terra, Universit\u00e0 degli Studi di Messina, viale F. Stagno d\u2019Alcontres 31, 98166 Messina, Italy"},{"name":"Institute of Systems Science, Durban University of Technology, P. O. Box 1334, Durban 4000, South Africa"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8599-4766","authenticated-orcid":false,"given":"Nikolay","family":"Vitanov","sequence":"additional","affiliation":[{"name":"Department of Physics, St. Kliment Ohridski University of Sofia, 5 James Bourchier Boulevard, 1164 Sofia, Bulgaria"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6414-2137","authenticated-orcid":false,"given":"Sergey","family":"Filippov","sequence":"additional","affiliation":[{"name":"Steklov Mathematical Institute of Russian Academy of Sciences, Gubkina St. 8, Moscow 119991, Russia"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2020,10,20]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"204","DOI":"10.1007\/BF01343196","article-title":"Zur Quantentheorie des Atomkernes","volume":"51","author":"Gamow","year":"1928","journal-title":"Z. Phys."},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Moiseyev, N. (2011). Non-Hermitian Quantum Mechanics, Cambridge University Press.","DOI":"10.1017\/CBO9780511976186"},{"key":"ref_3","doi-asserted-by":"crossref","unstructured":"Bender, C.M. (2019). PT-Symmetry: In Quantum and Classical Physics, World Scientific.","DOI":"10.1142\/q0178"},{"key":"ref_4","unstructured":"Cohen-Tannoudji, C. (1968). Cargese Lectures in Physics, Gordon and Breach."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"357","DOI":"10.1016\/0003-4916(58)90007-1","article-title":"Unified theory of nuclear reactions","volume":"5","author":"Feshbach","year":"1958","journal-title":"Ann. Phys."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"287","DOI":"10.1016\/0003-4916(62)90221-X","article-title":"A unified theory of nuclear reactions. II","volume":"19","author":"Feshbach","year":"1962","journal-title":"Ann. Phys."},{"key":"ref_7","first-page":"112","article-title":"On the uncertainty relation between time and energy","volume":"11","author":"Fock","year":"1947","journal-title":"J. Phys. USSR"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"1350163","DOI":"10.1142\/S0217979213501634","article-title":"Non-Hermitian quantum dynamics of a two-level system and models of dissipative environments","volume":"27","author":"Sergi","year":"2013","journal-title":"Int. J. Mod. Phys. B"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"1298","DOI":"10.1080\/09500340.2014.930528","article-title":"Comparison and unification of non-Hermitian and Lindblad approaches with applications to open quantum optical systems","volume":"61","author":"Zloshchastiev","year":"2014","journal-title":"J. Mod. Opt."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"253","DOI":"10.1140\/epjd\/e2015-60384-0","article-title":"Non-Hermitian Hamiltonians and stability of pure states","volume":"69","author":"Zloshchastiev","year":"2015","journal-title":"Eur. Phys. J. D"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"115136","DOI":"10.1103\/PhysRevB.94.115136","article-title":"Quantum-statistical approach to electromagnetic wave propagation and dissipation inside dielectric media and nanophotonic and plasmonic waveguides","volume":"94","author":"Zloshchastiev","year":"2016","journal-title":"Phys. Rev. B"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"1600185","DOI":"10.1002\/andp.201600185","article-title":"Sustainability of environment-assisted energy transfer in quantum photobiological complexes","volume":"529","author":"Zloshchastiev","year":"2017","journal-title":"Ann. Phys."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"1850276","DOI":"10.1142\/S0217979218502764","article-title":"Phase space formulation of density operator for non-Hermitian Hamiltonians and its application in quantum theory of decay","volume":"32","author":"Praxmeyer","year":"2018","journal-title":"Int. J. Mod. Phys. B"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"79","DOI":"10.1007\/s00214-015-1679-6","article-title":"Embedding quantum systems with a non-conserved probability in classical environments","volume":"134","author":"Sergi","year":"2015","journal-title":"Theor. Chem. Acc."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"033835","DOI":"10.1103\/PhysRevA.98.033835","article-title":"Exactly solvable time-dependent pseudo-Hermitian su(1,1) Hamiltonian models","volume":"98","author":"Grimaudo","year":"2018","journal-title":"Phys. Rev. A"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"062108","DOI":"10.1103\/PhysRevA.91.062108","article-title":"Time correlation functions for non-Hermitian quantum systems","volume":"91","author":"Sergi","year":"2015","journal-title":"Phys. Rev. A"},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"033102","DOI":"10.1088\/1742-5468\/2016\/03\/033102","article-title":"Quantum entropy of systems described by non-Hermitian Hamiltonians","volume":"3","author":"Sergi","year":"2016","journal-title":"J. Stat. Mech."},{"key":"ref_18","doi-asserted-by":"crossref","unstructured":"Sergi, A., and Giaquinta, P.V. (2016). Linear quantum entropy and non-Hermitian Hamiltonians. Entropy, 18.","DOI":"10.3390\/e18120451"},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"103904","DOI":"10.1103\/PhysRevLett.100.103904","article-title":"Beam dynamics in PT symmetric optical lattices","volume":"100","author":"Makris","year":"2008","journal-title":"Phys. Rev. Lett."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"1063","DOI":"10.3367\/UFNe.0184.201411b.1177","article-title":"PT-symmetry in optics","volume":"57","author":"Zyablovsky","year":"2014","journal-title":"Phys. Usp."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"083604","DOI":"10.1103\/PhysRevLett.110.083604","article-title":"PT Symmetry with a System of Three-Level Atoms","volume":"110","author":"Hang","year":"2013","journal-title":"Phys. Rev. Lett."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"1139","DOI":"10.1038\/nphys3842","article-title":"Anti-parity-time symmetry with flying atoms","volume":"12","author":"Peng","year":"2017","journal-title":"Nat. Phys."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"123601","DOI":"10.1103\/PhysRevLett.117.123601","article-title":"Observation of Parity-Time Symmetry in Optically Induced Atomic Lattices","volume":"117","author":"Zhang","year":"2016","journal-title":"Phys. Rev. Lett."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"234101","DOI":"10.1103\/PhysRevLett.110.234101","article-title":"Observation of Asymmetric Transport in Structures with Active Nonlinearities","volume":"110","author":"Bender","year":"2013","journal-title":"Phys. Rev. Lett."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"387","DOI":"10.1038\/nature22404","article-title":"Robust wireless power transfer using a nonlinear parity-time-symmetric circuit","volume":"546","author":"Assawaworrarit","year":"2017","journal-title":"Nature"},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"2182","DOI":"10.1038\/s41467-018-04690-y","article-title":"Observation of an anti-PT-symmetric exceptional point and energy-difference conserving dynamics in electrical circuit resonators","volume":"9","author":"Choi","year":"2018","journal-title":"Nat. Commun."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"024101","DOI":"10.1103\/PhysRevLett.108.024101","article-title":"PT Symmetry and Spontaneous Symmetry Breaking in a Microwave Billiard","volume":"108","author":"Bittner","year":"2012","journal-title":"Phys. Rev. Lett."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"173","DOI":"10.1119\/1.4789549","article-title":"Observation of PT phase transition in a simple mechanical system","volume":"81","author":"Bender","year":"2013","journal-title":"Am. J. Phys."},{"key":"ref_29","first-page":"031042","article-title":"PT-Symmetric Acoustics","volume":"4","author":"Zhu","year":"2014","journal-title":"Phys. Rev. X"},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"3398","DOI":"10.1038\/ncomms4398","article-title":"Non-reciprocal and highly nonlinear active acoustic metamaterials","volume":"5","author":"Popa","year":"2014","journal-title":"Nat. Commun."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"5905","DOI":"10.1038\/ncomms6905","article-title":"An invisible acoustic sensor based on parity-time symmetry","volume":"6","author":"Fleury","year":"2015","journal-title":"Nat. Commun."},{"key":"ref_32","doi-asserted-by":"crossref","unstructured":"Holevo, A.S. (2012). Quantum Systems, Channels, Information: A Mathematical Introduction, De Gruyter.","DOI":"10.1515\/9783110273403"},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"210","DOI":"10.1007\/s10958-019-04418-3","article-title":"Quantum mappings and characterization of entangled quantum states","volume":"241","author":"Filippov","year":"2019","journal-title":"J. Math. Sci."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"010301","DOI":"10.1103\/PhysRevA.90.010301","article-title":"Entanglement sensitivity to signal attenuation and amplification","volume":"90","author":"Filippov","year":"2014","journal-title":"Phys. Rev. A"},{"key":"ref_35","doi-asserted-by":"crossref","unstructured":"Znojil, M. (2020). Theory of Response to Perturbations in Non-Hermitian Systems Using Five-Hilbert-Space Reformulation of Unitary Quantum Mechanics. Entropy, 22.","DOI":"10.3390\/e22010080"},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"230404","DOI":"10.1103\/PhysRevLett.101.230404","article-title":"Naimark-Dilated PT-Symmetric Brachistochrone","volume":"101","author":"Samsonov","year":"2008","journal-title":"Phys. Rev. Lett."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"190401","DOI":"10.1103\/PhysRevLett.119.190401","article-title":"Information Retrieval and Criticality in Parity-Time-Symmetric Systems","volume":"119","author":"Kawabata","year":"2017","journal-title":"Phys. Rev. Lett."},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"567","DOI":"10.5890\/DNC.2020.12.010","article-title":"One-particle approximation as a simple playground for irreversible quantum evolution","volume":"9","author":"Teretenkov","year":"2020","journal-title":"Discontinuity Nonlinearity Complex."},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"080404","DOI":"10.1103\/PhysRevLett.123.080404","article-title":"Simulating Broken PT-Symmetric Hamiltonian Systems by Weak Measurement","volume":"123","author":"Huang","year":"2019","journal-title":"Phys. Rev. Lett."},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"878","DOI":"10.1126\/science.aaw8205","article-title":"Observation of parity-time symmetry breaking in a single-spin system","volume":"364","author":"Wu","year":"2019","journal-title":"Science"},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"022113","DOI":"10.1103\/PhysRevA.95.022113","article-title":"Quantum evolution in the stroboscopic limit of repeated measurements","volume":"95","author":"Luchnikov","year":"2017","journal-title":"Phys. Rev. A"},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"1467","DOI":"10.1103\/PhysRevA.42.1467","article-title":"Non-Hermitian evolution of two-level quantum systems","volume":"42","author":"Dattoli","year":"1990","journal-title":"Phys. Rev. A"},{"key":"ref_43","doi-asserted-by":"crossref","first-page":"587","DOI":"10.1088\/0034-4885\/41\/4\/003","article-title":"Decay theory of unstable quantum systems","volume":"41","author":"Fonda","year":"1978","journal-title":"Rep. Prog. Phys."},{"key":"ref_44","doi-asserted-by":"crossref","first-page":"3603","DOI":"10.1088\/0022-3700\/14\/19\/012","article-title":"Time-dependent theory of non-Hermitian Schr\u00f6dinger equation: Application to multiphoton-induced ionisation decay of atoms","volume":"14","author":"Faisal","year":"1981","journal-title":"J. Phys. B At. Mol. Phys."},{"key":"ref_45","doi-asserted-by":"crossref","first-page":"10","DOI":"10.1103\/PhysRevA.42.10","article-title":"Non-Hermitian quantum dynamics","volume":"42","author":"Baker","year":"1990","journal-title":"Phys. Rev. A"},{"key":"ref_46","doi-asserted-by":"crossref","first-page":"060101","DOI":"10.1103\/PhysRevA.83.060101","article-title":"Wave-packet evolution in non-Hermitian quantum systems","volume":"83","author":"Graefe","year":"2011","journal-title":"Phys. Rev. A"},{"key":"ref_47","doi-asserted-by":"crossref","first-page":"062122","DOI":"10.1103\/PhysRevA.99.062122","article-title":"Experimental demonstration of a digital quantum simulation of a general PT-symmetric system","volume":"99","author":"Wen","year":"2019","journal-title":"Phys. Rev. A"},{"key":"ref_48","doi-asserted-by":"crossref","first-page":"1880","DOI":"10.1103\/PhysRev.129.1880","article-title":"Relaxation phenomena in spin and harmonic oscillator systems","volume":"129","author":"Rau","year":"1963","journal-title":"Phys. Rev."},{"key":"ref_49","doi-asserted-by":"crossref","first-page":"040401","DOI":"10.1103\/PhysRevLett.108.040401","article-title":"Master Equations for Correlated Quantum Channels","volume":"108","author":"Giovannetti","year":"2012","journal-title":"Phys. Rev. Lett."},{"key":"ref_50","doi-asserted-by":"crossref","first-page":"032111","DOI":"10.1103\/PhysRevA.96.032111","article-title":"Divisibility of quantum dynamical maps and collision models","volume":"96","author":"Filippov","year":"2017","journal-title":"Phys. Rev. A"},{"key":"ref_51","doi-asserted-by":"crossref","first-page":"012114","DOI":"10.1103\/PhysRevA.101.012114","article-title":"Quantum master equations for a system interacting with a quantum gas in the low-density limit and for the semiclassical collision model","volume":"101","author":"Filippov","year":"2020","journal-title":"Phys. Rev. A"},{"key":"ref_52","doi-asserted-by":"crossref","first-page":"038110","DOI":"10.1088\/0031-8949\/82\/03\/038110","article-title":"Conceptual aspects of-symmetry and pseudo-Hermiticity: A status report","volume":"82","author":"Mostafazadeh","year":"2010","journal-title":"Phys. Scr."},{"key":"ref_53","doi-asserted-by":"crossref","first-page":"1191","DOI":"10.1142\/S0219887810004816","article-title":"Pseudo-Hermitian representation of quantum mechanics","volume":"7","author":"Mostafazadeh","year":"2010","journal-title":"Int. J. Geom. Methods Mod. Phys."},{"key":"ref_54","doi-asserted-by":"crossref","first-page":"947","DOI":"10.1088\/0034-4885\/70\/6\/R03","article-title":"Making sense of non-Hermitian Hamiltonians","volume":"70","author":"Bender","year":"2007","journal-title":"Rep. Prog. Phys."},{"key":"ref_55","doi-asserted-by":"crossref","first-page":"012123","DOI":"10.1103\/PhysRevA.93.012123","article-title":"Dynamical invariants for pseudo-Hermitian Hamiltonians","volume":"93","author":"Simeonov","year":"2016","journal-title":"Phys. Rev. A"},{"key":"ref_56","doi-asserted-by":"crossref","first-page":"013845","DOI":"10.1103\/PhysRevA.96.013845","article-title":"Pseudo-Hermitian Landau-Zener-St\u00fcckelberg-Majorana model","volume":"96","author":"Torosov","year":"2017","journal-title":"Phys. Rev. A"},{"key":"ref_57","doi-asserted-by":"crossref","first-page":"309","DOI":"10.1103\/PhysRev.112.309","article-title":"Linear antiferromagnetic chain with anisotropic coupling","volume":"112","author":"Orbach","year":"1958","journal-title":"Phys. Rev."},{"key":"ref_58","doi-asserted-by":"crossref","first-page":"022108","DOI":"10.1103\/PhysRevA.94.022108","article-title":"Exactly solvable time-dependent models of two interacting two-level systems","volume":"94","author":"Grimaudo","year":"2016","journal-title":"Phys. Rev. A"},{"key":"ref_59","doi-asserted-by":"crossref","first-page":"175301","DOI":"10.1088\/1751-8121\/aa5fb6","article-title":"Spin-1\/2 sub-dynamics nested in the quantum dynamics of two coupled qutrits","volume":"50","author":"Grimaudo","year":"2017","journal-title":"J. Phys. A"},{"key":"ref_60","doi-asserted-by":"crossref","first-page":"242","DOI":"10.1016\/j.aop.2018.03.012","article-title":"Time evolution of a pair of distinguishable interacting spins subjected to controllable and noisy magnetic fields","volume":"392","author":"Grimaudo","year":"2017","journal-title":"Ann. Phys. (N. Y.)"},{"key":"ref_61","doi-asserted-by":"crossref","first-page":"042330","DOI":"10.1103\/PhysRevA.98.042330","article-title":"Cooling of many-body systems via selective interactions","volume":"98","author":"Grimaudo","year":"2018","journal-title":"Phys. Rev. A"},{"key":"ref_62","doi-asserted-by":"crossref","first-page":"102147","DOI":"10.1016\/j.rinp.2019.02.083","article-title":"Dynamics of quantum discord of two coupled spin-1\/2\u2019s subjected to time-dependent magnetic fields","volume":"13","author":"Grimaudo","year":"2019","journal-title":"Results Phys."},{"key":"ref_63","doi-asserted-by":"crossref","first-page":"174416","DOI":"10.1103\/PhysRevB.99.174416","article-title":"Coupling-assisted Landau-Majorana-St\u00fcckelberg-Zener transition in a system of two interacting spin qubits","volume":"99","author":"Grimaudo","year":"2019","journal-title":"Phys. Rev. B"},{"key":"ref_64","doi-asserted-by":"crossref","first-page":"214406","DOI":"10.1103\/PhysRevB.99.214406","article-title":"Landau-Majorana-St\u00fcckelberg-Zener dynamics driven by coupling for two interacting qutrit systems","volume":"99","author":"Grimaudo","year":"2019","journal-title":"Phys. Rev. B"},{"key":"ref_65","doi-asserted-by":"crossref","first-page":"024004","DOI":"10.1088\/1402-4896\/ab4305","article-title":"Dynamics of a harmonic oscillator coupled with a Glauber amplifier","volume":"95","author":"Grimaudo","year":"2019","journal-title":"Phys. Scr."},{"key":"ref_66","doi-asserted-by":"crossref","unstructured":"Ghiu, I., Grimaudo, R., Mihaescu, T., Isar, A., and Messina, A. (2020). Quantum Correlation Dynamics in Controlled Two-Coupled-Qubit Systems. Entropy, 22.","DOI":"10.3390\/e22070785"},{"key":"ref_67","doi-asserted-by":"crossref","first-page":"064301","DOI":"10.1103\/PhysRevA.81.064301","article-title":"Berezinskii-Kosterlitz-Thouless transition uncovered by the fidelity susceptibility in the model","volume":"81","author":"Wang","year":"2010","journal-title":"Phys. Rev. A"},{"key":"ref_68","doi-asserted-by":"crossref","first-page":"042302","DOI":"10.1103\/PhysRevA.84.042302","article-title":"Quantum entanglement and quantum phase transition in the model with staggered Dzyaloshinskii-Moriya interaction","volume":"84","author":"Ma","year":"2011","journal-title":"Phys. Rev. A"},{"key":"ref_69","doi-asserted-by":"crossref","first-page":"052112","DOI":"10.1103\/PhysRevA.83.052112","article-title":"Quantum and classical correlations in the one-dimensional model with Dzyaloshinskii-Moriya interaction","volume":"83","author":"Liu","year":"2011","journal-title":"Phys. Rev. A"},{"key":"ref_70","doi-asserted-by":"crossref","first-page":"033092","DOI":"10.1103\/PhysRevResearch.2.033092","article-title":"Dzyaloshinskii-Moriya and dipole-dipole interactions affect coupling-based Landau-Majorana-St\u00fcckelberg-Zener transitions","volume":"2","author":"Grimaudo","year":"2020","journal-title":"Phys. Rev. Res."},{"key":"ref_71","unstructured":"Boyd, R. (2008). Nonlinear Optics, Academic Press. [3rd ed.]."},{"key":"ref_72","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/0370-1573(90)90089-K","article-title":"Laser-induced continuum structure","volume":"190","author":"Knight","year":"1990","journal-title":"Phys. Rep."},{"key":"ref_73","doi-asserted-by":"crossref","first-page":"741","DOI":"10.1103\/PhysRevA.56.741","article-title":"Population transfer by delayed pulses via continuum states","volume":"56","author":"Vitanov","year":"1997","journal-title":"Phys. Rev. A"},{"key":"ref_74","doi-asserted-by":"crossref","first-page":"R46","DOI":"10.1103\/PhysRevA.58.R46","article-title":"Population trapping and laser-induced continuum structure in helium: Experiment and theory","volume":"58","author":"Halfmann","year":"1998","journal-title":"Phys. Rev. A"},{"key":"ref_75","doi-asserted-by":"crossref","first-page":"243","DOI":"10.1002\/lpor.200810055","article-title":"Quantum-optical analogies using photonic structures","volume":"3","author":"Longhi","year":"2009","journal-title":"Laser Photon. Rev."},{"key":"ref_76","doi-asserted-by":"crossref","first-page":"192","DOI":"10.1038\/nphys1515","article-title":"Observation of parity\u2013time symmetry in optics","volume":"6","author":"Ruter","year":"2010","journal-title":"Nat. Phys."},{"key":"ref_77","doi-asserted-by":"crossref","first-page":"093902","DOI":"10.1103\/PhysRevLett.103.093902","article-title":"Observation of PT-Symmetry Breaking in Complex Optical Potentials","volume":"103","author":"Guo","year":"2009","journal-title":"Phys. Rev. Lett."},{"key":"ref_78","doi-asserted-by":"crossref","first-page":"052103","DOI":"10.1103\/PhysRevA.99.052103","article-title":"Analytically solvable 2 \u00d7 2 PT-symmetry dynamics from su(1,1)-symmetry problems","volume":"99","author":"Grimaudo","year":"2019","journal-title":"Phys. Rev. A"},{"key":"ref_79","doi-asserted-by":"crossref","first-page":"8919","DOI":"10.1063\/1.478811","article-title":"Mixed quantum-classical dynamics","volume":"110","author":"Kapral","year":"1999","journal-title":"J. Chem. Phys."},{"key":"ref_80","doi-asserted-by":"crossref","first-page":"2885","DOI":"10.1021\/jp0037899","article-title":"Quantum-classical dynamics in a classical bath","volume":"105","author":"Kapral","year":"2001","journal-title":"J. Phys. Chem. A"},{"key":"ref_81","doi-asserted-by":"crossref","first-page":"5805","DOI":"10.1063\/1.1400129","article-title":"Statistical mechanics of quantum-classical systems","volume":"115","author":"Nielsen","year":"2001","journal-title":"J. Chem. Phys."},{"key":"ref_82","doi-asserted-by":"crossref","unstructured":"Sergi, A., Hanna, G., Grimaudo, R., and Messina, A. (2018). Quasi-Lie brackets and the breaking of time-translation symmetry for quantum systems embedded in classical baths. Symmetry, 10.","DOI":"10.3390\/sym10100518"},{"key":"ref_83","doi-asserted-by":"crossref","first-page":"402","DOI":"10.3390\/physics1030029","article-title":"Proposal of a computational approach for simulating thermal bosonic fields in phase space","volume":"1","author":"Sergi","year":"2019","journal-title":"Physics"}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/22\/10\/1184\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T10:24:54Z","timestamp":1760178294000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/22\/10\/1184"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,10,20]]},"references-count":83,"journal-issue":{"issue":"10","published-online":{"date-parts":[[2020,10]]}},"alternative-id":["e22101184"],"URL":"https:\/\/doi.org\/10.3390\/e22101184","relation":{},"ISSN":["1099-4300"],"issn-type":[{"type":"electronic","value":"1099-4300"}],"subject":[],"published":{"date-parts":[[2020,10,20]]}}}