{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,18]],"date-time":"2026-01-18T09:57:26Z","timestamp":1768730246740,"version":"3.49.0"},"reference-count":102,"publisher":"MDPI AG","issue":"4","license":[{"start":{"date-parts":[[2018,3,26]],"date-time":"2018-03-26T00:00:00Z","timestamp":1522022400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100003407","name":"MIUR","doi-asserted-by":"publisher","id":[{"id":"10.13039\/501100003407","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>The stabilizing effect of quantum fluctuations on the escape process and the relaxation dynamics from a quantum metastable state are investigated. Specifically, the quantum dynamics of a multilevel bistable system coupled to a bosonic Ohmic thermal bath in strong dissipation regime is analyzed. The study is performed by a non-perturbative method based on the real-time path integral approach of the Feynman-Vernon influence functional. We consider a strongly asymmetric double well potential with and without a monochromatic external driving, and with an out-of-equilibrium initial condition. In the absence of driving we observe a nonmonotonic behavior of the escape time from the metastable region, as a function both of the system-bath coupling coefficient and the temperature. This indicates a stabilizing effect of the quantum fluctuations. In the presence of driving our findings indicate that, as the coupling coefficient    \u03b3    increases, the escape time, initially controlled by the external driving, shows resonant peaks and dips, becoming frequency-independent for higher    \u03b3    values. Moreover, the escape time from the metastable state displays a nonmonotonic behavior as a function of the temperature, the frequency of the driving, and the thermal-bath coupling, which indicates the presence of a quantum noise enhanced stability phenomenon. Finally, we investigate the role of different spectral densities, both in sub-Ohmic and super-Ohmic dissipation regime and for different cutoff frequencies, on the relaxation dynamics from the quantum metastable state. The results obtained indicate that, in the crossover dynamical regime characterized by damped intrawell oscillations and incoherent tunneling, the spectral properties of the thermal bath influence non-trivially the short time behavior and the time scales of the relaxation dynamics from the metastable state.<\/jats:p>","DOI":"10.3390\/e20040226","type":"journal-article","created":{"date-parts":[[2018,3,26]],"date-time":"2018-03-26T12:08:25Z","timestamp":1522066105000},"page":"226","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":16,"title":["Enhancing Metastability by Dissipation and Driving in an Asymmetric Bistable Quantum System"],"prefix":"10.3390","volume":"20","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-6625-3989","authenticated-orcid":false,"given":"Bernardo","family":"Spagnolo","sequence":"first","affiliation":[{"name":"Dipartimento di Fisica e Chimica, Group of Interdisciplinary Theoretical Physics, Universit\u00e0 di Palermo and CNISM, Unit\u00e0 di Palermo, Viale delle Scienze, Edificio 18, I-90128 Palermo, Italy"},{"name":"Istituto Nazionale di Fisica Nucleare, Sezione di Catania, I-95100 Catania, Italy"},{"name":"Radiophysics Department, Lobachevsky State University of Nizhni Novgorod, 603000 Nizhni Novgorod, Russia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Angelo","family":"Carollo","sequence":"additional","affiliation":[{"name":"Dipartimento di Fisica e Chimica, Group of Interdisciplinary Theoretical Physics, Universit\u00e0 di Palermo and CNISM, Unit\u00e0 di Palermo, Viale delle Scienze, Edificio 18, I-90128 Palermo, Italy"},{"name":"Radiophysics Department, Lobachevsky State University of Nizhni Novgorod, 603000 Nizhni Novgorod, Russia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5496-1518","authenticated-orcid":false,"given":"Davide","family":"Valenti","sequence":"additional","affiliation":[{"name":"Dipartimento di Fisica e Chimica, Group of Interdisciplinary Theoretical Physics, Universit\u00e0 di Palermo and CNISM, Unit\u00e0 di Palermo, Viale delle Scienze, Edificio 18, I-90128 Palermo, Italy"},{"name":"Istituto di Biomedicina ed Immunologia Molecolare (IBIM) \u201cAlberto Monroy\u201d, CNR, Via Ugo La Malfa 153, I-90146 Palermo, Italy"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2018,3,26]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"10","DOI":"10.3402\/tellusa.v34i1.10782","article-title":"Stochastic resonance in climatic change","volume":"34","author":"Benzi","year":"1982","journal-title":"Tellus"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"33","DOI":"10.1038\/373033a0","article-title":"Stochastic resonance and the benefits of noise: From ice ages to crayfish and SQUIDs","volume":"373","author":"Wiesenfeld","year":"1995","journal-title":"Nature"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"223","DOI":"10.1103\/RevModPhys.70.223","article-title":"Stochastic resonance","volume":"70","author":"Gammaitoni","year":"1998","journal-title":"Rev. Mod. Phys."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"10E519","DOI":"10.1063\/1.1856276","article-title":"Stochastic resonance in magnetic systems described by Preisach hysteresis model","volume":"97","author":"Mantegna","year":"2005","journal-title":"J. Appl. Phys."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"051123","DOI":"10.1103\/PhysRevE.81.051123","article-title":"Stochastic resonance in a trapping overdamped monostable system","volume":"81","author":"Agudov","year":"2010","journal-title":"Phys. Rev. E"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"114","DOI":"10.1016\/S0378-4371(02)01245-1","article-title":"Role of the noise on the transient dynamics of an ecosystem of interacting species","volume":"315","author":"Spagnolo","year":"2002","journal-title":"Physica A"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"120","DOI":"10.1016\/S0378-4371(02)01173-1","article-title":"Spatio-temporal patterns in population dynamics","volume":"314","author":"Spagnolo","year":"2002","journal-title":"Physica A"},{"key":"ref_8","first-page":"1481","article-title":"Pattern formation and spatial correlation induced by the noise in two competing species","volume":"35","author":"Valenti","year":"2004","journal-title":"Acta Phys. Pol. B"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"L349","DOI":"10.1142\/S0219477505002768","article-title":"Cyclic fluctuations, climatic changes and role of noise in Planktonic Foraminifera in the Mediterranean Sea","volume":"5","author":"Caruso","year":"2005","journal-title":"Fluct. Noise Lett."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"563","DOI":"10.1103\/PhysRevLett.76.563","article-title":"Noise enhanced stability in an unstable system","volume":"76","author":"Mantegna","year":"1996","journal-title":"Phys. Rev. Lett."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"6333","DOI":"10.1103\/PhysRevE.60.6333","article-title":"Decay of unstable equilibrium and nonequilibrium states with inverse probability current taken into account","volume":"60","author":"Agudov","year":"1999","journal-title":"Phys. Rev. E"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"783","DOI":"10.1142\/S0218127498000577","article-title":"Probability distribution of the residence times in periodically fluctuating metastable systems","volume":"8","author":"Mantegna","year":"1998","journal-title":"Int. J. Bifurc. Chaos"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"035102","DOI":"10.1103\/PhysRevE.64.035102","article-title":"Noise-enhanced stability of periodically driven metastable states","volume":"64","author":"Agudov","year":"2001","journal-title":"Phys. Rev. E"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"818","DOI":"10.1103\/PhysRevLett.84.818","article-title":"Noise induced stability in fluctuating, bistable potentials","volume":"84","author":"Mielke","year":"2000","journal-title":"Phys. Rev. Lett."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"061103","DOI":"10.1103\/PhysRevE.69.061103","article-title":"Noise-enhanced stability in fluctuating metastable states","volume":"69","author":"Dubkov","year":"2004","journal-title":"Phys. Rev. E"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"073117","DOI":"10.1063\/1.4959146","article-title":"Stochastic basins of attraction for metastable states","volume":"26","author":"Serdukova","year":"2016","journal-title":"Chaos"},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"2318","DOI":"10.1103\/PhysRevLett.69.2318","article-title":"Resonant activation over a fluctuating barrier","volume":"69","author":"Doering","year":"1992","journal-title":"Phys. Rev. Lett."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"2772","DOI":"10.1103\/PhysRevLett.73.2772","article-title":"Rates of activated processes with fluctuating barriers","volume":"73","author":"Pechukas","year":"1994","journal-title":"Phys. Rev. Lett."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"3025","DOI":"10.1103\/PhysRevLett.84.3025","article-title":"Experimental investigation of resonant activation","volume":"84","author":"Mantegna","year":"2000","journal-title":"Phys. Rev. Lett."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"3479","DOI":"10.1103\/PhysRevE.54.3479","article-title":"Resonant activation in a bistable system","volume":"54","author":"Marchi","year":"1996","journal-title":"Phys. Rev. E"},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"034001","DOI":"10.1088\/1478-3975\/7\/3\/034001","article-title":"Resonant activation in polymer translocation: New insights into escape dynamics of molecules driven by an oscillating field","volume":"7","author":"Pizzolato","year":"2010","journal-title":"Phys. Biol."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"041122","DOI":"10.1103\/PhysRevE.83.041122","article-title":"Resonant activation in piecewise linear asymmetric potentials","volume":"83","author":"Fiasconaro","year":"2011","journal-title":"Phys. Rev. E"},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"3915","DOI":"10.1103\/PhysRevE.47.3915","article-title":"Nonlinear Relaxation in the presence of an Absorbing Barrier","volume":"47","author":"Ciuchi","year":"1993","journal-title":"Phys. Rev. E"},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"022101","DOI":"10.1103\/PhysRevE.65.022101","article-title":"Suppression of noise in nonlinear systems subjected to strong periodic driving","volume":"65","author":"Pankratov","year":"2002","journal-title":"Phys. Rev. E"},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"177001","DOI":"10.1103\/PhysRevLett.93.177001","article-title":"Suppression of timing errors in short overdamped Josephson junctions","volume":"93","author":"Pankratov","year":"2004","journal-title":"Phys Rev Lett."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"052501","DOI":"10.1103\/PhysRevB.81.052501","article-title":"Optimal fast single-pulse readout of qubits","volume":"81","author":"Pankratov","year":"2010","journal-title":"Phys. Rev. B"},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"162501","DOI":"10.1063\/1.3582615","article-title":"Fine tuning of phase qubit parameters for optimization of fast single-pulse readout","volume":"98","author":"Pankratov","year":"2011","journal-title":"Appl. Phys. Lett."},{"key":"ref_28","first-page":"1745","article-title":"Langevin Approach to L\u00e9vy flights in fixed potentials: Exact results for stationary probability distributions","volume":"38","author":"Dubkov","year":"2007","journal-title":"Acta Phys. Pol. B"},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"211","DOI":"10.1103\/PhysRevLett.46.211","article-title":"Influence of Dissipation on Quantum Tunneling in Macroscopic Systems","volume":"46","author":"Caldeira","year":"1981","journal-title":"Phys. Rev. Lett."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1103\/RevModPhys.59.1","article-title":"Dynamics of the dissipative two-state system","volume":"59","author":"Leggett","year":"1987","journal-title":"Rev. Mod. Phys."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"229","DOI":"10.1016\/S0370-1573(98)00022-2","article-title":"Driven quantum tunneling","volume":"304","author":"Grifoni","year":"1998","journal-title":"Phys. Rep."},{"key":"ref_32","doi-asserted-by":"crossref","unstructured":"Weiss, U. (2012). Quantum Dissipative Systems, World Scientific. [4th ed.].","DOI":"10.1142\/9789814374927"},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"268","DOI":"10.1002\/anie.200390099","article-title":"Quantum Tunneling of Magnetization and Related Phenomena in Molecular Materials","volume":"42","author":"Gatteschi","year":"2003","journal-title":"Angew. Chem. Int. Ed."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"789","DOI":"10.1038\/35071024","article-title":"Quantum computing in molecular magnets","volume":"410","author":"Leuenberger","year":"2001","journal-title":"Nature"},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"163","DOI":"10.1016\/S0301-0104(98)00354-1","article-title":"Laser driven hydrogen tunneling in a dissipative environment","volume":"240","author":"Naundorf","year":"1999","journal-title":"Chem. Phys."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"43","DOI":"10.1038\/35017505","article-title":"Quantum superposition of distinct macroscopic states","volume":"406","author":"Friedman","year":"2000","journal-title":"Nature"},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"589","DOI":"10.1038\/nature10122","article-title":"Atomic physics and quantum optics using superconducting circuits","volume":"474","author":"You","year":"2011","journal-title":"Nature"},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"1169","DOI":"10.1126\/science.1231930","article-title":"Superconducting circuits for quantum information: An outlook","volume":"339","author":"Devoret","year":"2013","journal-title":"Science"},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"388","DOI":"10.1103\/PhysRevLett.46.388","article-title":"Quantum-Statistical Metastability","volume":"46","author":"Affleck","year":"1981","journal-title":"Phys. Rev. Lett."},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"4450","DOI":"10.1103\/PhysRevB.32.4450","article-title":"Dissipative quantum tunneling at finite temperatures","volume":"32","author":"Waxman","year":"1985","journal-title":"Phys. Rev. B"},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"1931","DOI":"10.1103\/PhysRevB.36.1931","article-title":"Quantum decay rates for dissipative systems at finite temperatures","volume":"36","author":"Grabert","year":"1987","journal-title":"Phys. Rev. B"},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"062115","DOI":"10.1103\/PhysRevA.75.062115","article-title":"Coordinate-dependent diffusion coefficients: Decay rate in open quantum systems","volume":"75","author":"Sargsyan","year":"2007","journal-title":"Phys. Rev. A"},{"key":"ref_43","doi-asserted-by":"crossref","first-page":"012102","DOI":"10.1103\/PhysRevA.71.012102","article-title":"Stabilizing quantum metastable states in a time-periodic potential","volume":"71","author":"Ho","year":"2005","journal-title":"Phys. Rev. A"},{"key":"ref_44","doi-asserted-by":"crossref","first-page":"8576","DOI":"10.1021\/jp402565y","article-title":"Quantum stochastic dynamics in the presence of a time-periodic rapidly oscillating potential: Nonadiabatic escape rate","volume":"117","author":"Shit","year":"2013","journal-title":"J. Phys. Chem. A"},{"key":"ref_45","doi-asserted-by":"crossref","first-page":"26","DOI":"10.1016\/j.chemphys.2014.01.008","article-title":"Taming the escape dynamics of nonadiabatic time-periodically driven quantum dissipative system within the frame of Wigner formalism","volume":"431\u2013432","author":"Shit","year":"2014","journal-title":"Chem. Phys."},{"key":"ref_46","doi-asserted-by":"crossref","first-page":"273","DOI":"10.1140\/epjb\/e2004-00268-8","article-title":"Enhancement of stability in randomly switching potential with metastable state","volume":"40","author":"Spagnolo","year":"2004","journal-title":"Eur. Phys. J. B"},{"key":"ref_47","doi-asserted-by":"crossref","first-page":"6421","DOI":"10.1103\/PhysRevE.60.6421","article-title":"Mobility and stochastic resonance in spatially inhomogeneous systems","volume":"60","author":"Dan","year":"1999","journal-title":"Phys. Rev. E"},{"key":"ref_48","doi-asserted-by":"crossref","first-page":"144","DOI":"10.1016\/S0378-4371(03)00193-6","article-title":"Escape from a metastable state with fluctuating barrier","volume":"325","author":"Agudov","year":"2003","journal-title":"Physica A"},{"key":"ref_49","doi-asserted-by":"crossref","first-page":"2872","DOI":"10.1103\/PhysRevE.59.2872","article-title":"When noise decreases deterministic diffusion","volume":"59","author":"Wackerbauer","year":"1999","journal-title":"Phys. Rev. E"},{"key":"ref_50","doi-asserted-by":"crossref","first-page":"136","DOI":"10.1016\/S0378-4371(03)00192-4","article-title":"Role of the initial conditions on the enhancement of the escape time in static and fluctuating potentials","volume":"325","author":"Fiasconaro","year":"2003","journal-title":"Physica A"},{"key":"ref_51","doi-asserted-by":"crossref","first-page":"10819","DOI":"10.1073\/pnas.0502884102","article-title":"Noise-induced stability in dryland plant ecosystems","volume":"102","author":"Laio","year":"2005","journal-title":"Proc. Natl. Acad. Sci. USA"},{"key":"ref_52","doi-asserted-by":"crossref","first-page":"061110","DOI":"10.1103\/PhysRevE.72.061110","article-title":"Signatures of noise-enhanced stability in metastable states","volume":"72","author":"Fiasconaro","year":"2005","journal-title":"Phys. Rev. E"},{"key":"ref_53","doi-asserted-by":"crossref","first-page":"405","DOI":"10.1140\/epjb\/e2006-00388-1","article-title":"Role of Noise in a Market Model with Stochastic Volatility","volume":"53","author":"Bonanno","year":"2006","journal-title":"Eur. Phys. J. B"},{"key":"ref_54","doi-asserted-by":"crossref","first-page":"050101","DOI":"10.1103\/PhysRevE.74.050101","article-title":"Metastability, nucleation, and noise-enhanced stabilization out of equilibrium","volume":"74","author":"Hurtado","year":"2006","journal-title":"Phys. Rev. E"},{"key":"ref_55","doi-asserted-by":"crossref","first-page":"041110","DOI":"10.1103\/PhysRevE.80.041110","article-title":"Stability measures in metastable states with Gaussian colored noise","volume":"80","author":"Fiasconaro","year":"2009","journal-title":"Phys. Rev. E"},{"key":"ref_56","doi-asserted-by":"crossref","first-page":"041104","DOI":"10.1103\/PhysRevE.82.041104","article-title":"Thermal-inertial ratchet effects: Negative mobility, resonant activation, noise-enhanced stability, and noise-weakened stability","volume":"82","author":"Li","year":"2010","journal-title":"Phys. Rev. E"},{"key":"ref_57","doi-asserted-by":"crossref","first-page":"225","DOI":"10.1140\/epjb\/e2010-10106-1","article-title":"Non-Gaussian noise effects in the dynamics of a short overdamped Josephson junction","volume":"78","author":"Augello","year":"2010","journal-title":"Eur. Phys. J. B"},{"key":"ref_58","doi-asserted-by":"crossref","first-page":"132405","DOI":"10.1103\/PhysRevB.82.132405","article-title":"Influence of the size of uniaxial magnetic nanoparticle on the reliability of high-speed switching","volume":"82","author":"Smirnov","year":"2010","journal-title":"Phys. Rev. B"},{"key":"ref_59","doi-asserted-by":"crossref","first-page":"041120","DOI":"10.1103\/PhysRevE.82.041120","article-title":"Noise-induced enhancement of stability in a metastable system with damping","volume":"82","author":"Fiasconaro","year":"2010","journal-title":"Phys. Rev. E"},{"key":"ref_60","doi-asserted-by":"crossref","unstructured":"Jia, Z.-L., and Mei, D.-C. (2011). Effects of linear and nonlinear time-delayed feedback on the noise-enhanced stability phenomenon in a periodically driven bistable system. J. Stat. Mech. Theory Exp., 2011.","DOI":"10.1088\/1742-5468\/2011\/10\/P10010"},{"key":"ref_61","doi-asserted-by":"crossref","first-page":"180603","DOI":"10.1103\/PhysRevLett.107.180603","article-title":"Noise-induced stabilization in population dynamics","volume":"107","author":"Parker","year":"2011","journal-title":"Phys. Rev. Lett."},{"key":"ref_62","doi-asserted-by":"crossref","first-page":"214510","DOI":"10.1103\/PhysRevB.89.214510","article-title":"Switching times in long-overlap Josephson junctions subject to thermal fluctuations and non-Gaussian noise sources","volume":"89","author":"Valenti","year":"2014","journal-title":"Phys. Rev. B"},{"key":"ref_63","doi-asserted-by":"crossref","first-page":"052119","DOI":"10.1103\/PhysRevE.92.052119","article-title":"Modulated escape from a metastable state driven by colored noise","volume":"92","author":"Schuecker","year":"2015","journal-title":"Phys. Rev. E"},{"key":"ref_64","doi-asserted-by":"crossref","first-page":"284","DOI":"10.1016\/S0031-8914(40)90098-2","article-title":"Brownian Motion in a Field of Force and the Diffusion Model of Chemical Reactions","volume":"7","author":"Kramers","year":"1940","journal-title":"Physica"},{"key":"ref_65","doi-asserted-by":"crossref","first-page":"251","DOI":"10.1103\/RevModPhys.62.251","article-title":"Reaction Rate Theory: Fifty Years After Kramers","volume":"62","author":"Talkner","year":"1990","journal-title":"Rev. Mod. Phys."},{"key":"ref_66","doi-asserted-by":"crossref","first-page":"374","DOI":"10.1016\/0003-4916(83)90202-6","article-title":"Quantum tunnelling in a dissipative system","volume":"149","author":"Caldeira","year":"1983","journal-title":"Ann. Phys."},{"key":"ref_67","doi-asserted-by":"crossref","first-page":"1515","DOI":"10.1063\/1.1696963","article-title":"Calculation of Matrix Elements for One-Dimensional Quantum-Mechanical Problems and the Application to Anharmonic Oscillators","volume":"43","author":"Harris","year":"1965","journal-title":"J. Chem. Phys."},{"key":"ref_68","doi-asserted-by":"crossref","first-page":"118","DOI":"10.1016\/0003-4916(63)90068-X","article-title":"The theory of a general quantum system interacting with a linear dissipative system","volume":"24","author":"Feynman","year":"1963","journal-title":"Ann. Phys."},{"key":"ref_69","unstructured":"Magazz\u00f9, L. (2015). Dissipative Dynamics of Multi-State Bistable Quantum Systems. [Ph.D. Thesis, Palermo University]."},{"key":"ref_70","unstructured":"Light, J.C., and Carrington, T. (2007). Discrete-Variable Representations and their Utilization, Advances in Chemical Physics; Wiley."},{"key":"ref_71","doi-asserted-by":"crossref","first-page":"054016","DOI":"10.1088\/1742-5468\/2016\/05\/054016","article-title":"Quantum dissipative dynamics of a bistable system in the sub-Ohmic to super-Ohmic regime","volume":"2016","author":"Carollo","year":"2016","journal-title":"J. Stat. Mech. Theory Exp."},{"key":"ref_72","doi-asserted-by":"crossref","first-page":"15","DOI":"10.1006\/aphy.2001.6174","article-title":"Strong Coupling Theory for Tunneling and Vibrational Relaxation in Driven Bistable Systems","volume":"293","author":"Thorwart","year":"2001","journal-title":"Ann. Phys."},{"key":"ref_73","doi-asserted-by":"crossref","first-page":"032123","DOI":"10.1103\/PhysRevE.92.032123","article-title":"Dissipative dynamics in a quantum bistable system: Crossover from weak to strong damping","volume":"92","author":"Valenti","year":"2015","journal-title":"Phys. Rev. E"},{"key":"ref_74","doi-asserted-by":"crossref","first-page":"R2033","DOI":"10.1103\/PhysRevE.53.R2033","article-title":"Exact master equations for driven dissipative tight-binding models","volume":"53","author":"Grifoni","year":"1996","journal-title":"Phys. Rev. E"},{"key":"ref_75","doi-asserted-by":"crossref","first-page":"023031","DOI":"10.1088\/1367-2630\/14\/2\/023031","article-title":"Superconducting qubit manipulated by fast pulses: Experimental observation of distinct decoherence regimes","volume":"14","author":"Chiarello","year":"2012","journal-title":"New J. Phys."},{"key":"ref_76","doi-asserted-by":"crossref","first-page":"685","DOI":"10.1016\/j.crhy.2013.09.004","article-title":"Out-of-equilibrium dynamics of classical and quantum complex systems","volume":"14","author":"Cugliandolo","year":"2013","journal-title":"C. R. Phys."},{"key":"ref_77","doi-asserted-by":"crossref","first-page":"124","DOI":"10.1038\/nphys3215","article-title":"Quantum many-body systems out of equilibrium","volume":"11","author":"Eisert","year":"2015","journal-title":"Nat. Phys."},{"key":"ref_78","doi-asserted-by":"crossref","first-page":"51","DOI":"10.1038\/nature00968","article-title":"Collapse and revival of the matter wave field of a Bose\u2013Einstein condensate","volume":"419","author":"Greiner","year":"2002","journal-title":"Nature"},{"key":"ref_79","doi-asserted-by":"crossref","first-page":"136801","DOI":"10.1103\/PhysRevLett.96.136801","article-title":"Time dependence of correlation functions following a quantum quench","volume":"96","author":"Calabrese","year":"2006","journal-title":"Phys. Rev. Lett."},{"key":"ref_80","doi-asserted-by":"crossref","first-page":"180601","DOI":"10.1103\/PhysRevLett.98.180601","article-title":"Quench dynamics and non equilibrium phase diagram of the Bose\u2013Hubbard model","volume":"98","author":"Kollath","year":"2007","journal-title":"Phys. Rev. Lett."},{"key":"ref_81","doi-asserted-by":"crossref","first-page":"863","DOI":"10.1103\/RevModPhys.83.863","article-title":"Non-equilibrium dynamics of closed interacting quantum systems","volume":"83","author":"Polkovnikov","year":"2011","journal-title":"Rev. Mod. Phys."},{"key":"ref_82","doi-asserted-by":"crossref","first-page":"485","DOI":"10.1002\/lapl.201110002","article-title":"Equilibration and thermalization in finite quantum systems","volume":"8","author":"Yukalov","year":"2011","journal-title":"Laser Phys. Lett."},{"key":"ref_83","doi-asserted-by":"crossref","first-page":"325","DOI":"10.1038\/nphys2232","article-title":"Probing the relaxation towards equilibrium in an isolated strongly correlated one-dimensional Bose gas","volume":"8","author":"Trotzky","year":"2012","journal-title":"Nat. Phys."},{"key":"ref_84","doi-asserted-by":"crossref","first-page":"329","DOI":"10.1016\/S0375-9601(97)00599-9","article-title":"On certain time characteristics of dynamical systems driven by noise","volume":"234","author":"Pankratov","year":"1997","journal-title":"Phys. Lett. A"},{"key":"ref_85","doi-asserted-by":"crossref","first-page":"235412","DOI":"10.1103\/PhysRevB.91.235412","article-title":"Stabilization of quantum metastable states by dissipation","volume":"91","author":"Valenti","year":"2015","journal-title":"Phys. Rev. B"},{"key":"ref_86","doi-asserted-by":"crossref","first-page":"237","DOI":"10.1006\/aphy.1997.5699","article-title":"A Conceptual Analysis of Quantum Zeno; Paradox, Measurement, and Experiment","volume":"258","author":"Home","year":"1997","journal-title":"Ann. Phys."},{"key":"ref_87","doi-asserted-by":"crossref","first-page":"139","DOI":"10.1016\/S0375-9601(98)00144-3","article-title":"Temporal behavior and quantum Zeno time of an excited state of the hydrogen atom","volume":"241","author":"Facchi","year":"1998","journal-title":"Phys. Lett. A"},{"key":"ref_88","doi-asserted-by":"crossref","first-page":"546","DOI":"10.1038\/35014537","article-title":"Acceleration of quantum decay processes by frequent observations","volume":"405","author":"Kofman","year":"2000","journal-title":"Nature"},{"key":"ref_89","doi-asserted-by":"crossref","first-page":"2699","DOI":"10.1103\/PhysRevLett.86.2699","article-title":"From the Quantum Zeno to the Inverse Quantum Zeno Effect","volume":"86","author":"Facchi","year":"2001","journal-title":"Phys. Rev. Lett."},{"key":"ref_90","doi-asserted-by":"crossref","first-page":"022302","DOI":"10.1103\/PhysRevA.71.022302","article-title":"Control of decoherence: Analysis and comparison of three different strategies","volume":"71","author":"Facchi","year":"2005","journal-title":"Phys. Rev. A"},{"key":"ref_91","doi-asserted-by":"crossref","first-page":"119","DOI":"10.1142\/S0219749911007137","article-title":"Dynamics of a Quantum Particle in Asymmetric Bistable Potential with Environmental Noise","volume":"9","author":"Caldara","year":"2011","journal-title":"Int. J. Quantum Inf."},{"key":"ref_92","doi-asserted-by":"crossref","first-page":"240401","DOI":"10.1103\/PhysRevLett.118.240401","article-title":"Quantum Zeno Effects from Measurement Controlled Qubit-Bath Interactions","volume":"118","author":"Harrington","year":"2017","journal-title":"Phys. Rev. Lett."},{"key":"ref_93","doi-asserted-by":"crossref","first-page":"3830","DOI":"10.1103\/PhysRevLett.76.3830","article-title":"Macroscopic Measurement of Resonant Magnetization Tunneling in High-Spin Molecules","volume":"76","author":"Friedman","year":"1996","journal-title":"Phys. Rev. Lett."},{"key":"ref_94","doi-asserted-by":"crossref","first-page":"2341","DOI":"10.3390\/e17042341","article-title":"Multi-State Quantum Dissipative Dynamics in Sub-Ohmic Environment: The Strong Coupling Regime","volume":"17","author":"Valenti","year":"2015","journal-title":"Entropy"},{"key":"ref_95","doi-asserted-by":"crossref","first-page":"042104","DOI":"10.1103\/PhysRevE.95.042104","article-title":"Quantum resonant activation","volume":"95","author":"Spagnolo","year":"2017","journal-title":"Phys. Rev. E"},{"key":"ref_96","doi-asserted-by":"crossref","first-page":"860","DOI":"10.1103\/PhysRevLett.85.860","article-title":"Strong Coupling Theory for Driven Tunneling and Vibrational Relaxation","volume":"85","author":"Thorwart","year":"2000","journal-title":"Phys. Rev. Lett."},{"key":"ref_97","doi-asserted-by":"crossref","first-page":"195143","DOI":"10.1103\/PhysRevB.92.195143","article-title":"Sub-Ohmic to super-Ohmic crossover behavior in nonequilibrium quantum systems with electron-phonon interactions","volume":"92","author":"Wilner","year":"2015","journal-title":"Phys. Rev. B"},{"key":"ref_98","doi-asserted-by":"crossref","first-page":"128301","DOI":"10.1103\/PhysRevLett.89.128301","article-title":"Kinetically Locked-In Colloidal Transport in an Array of Optical Tweezers","volume":"89","author":"Korda","year":"2002","journal-title":"Phys. Rev. Lett."},{"key":"ref_99","doi-asserted-by":"crossref","first-page":"2787","DOI":"10.1063\/1.1785844","article-title":"Optical trapping","volume":"75","author":"Neuman","year":"2004","journal-title":"Rev. Sci. Instrum."},{"key":"ref_100","doi-asserted-by":"crossref","first-page":"183602","DOI":"10.1103\/PhysRevLett.109.183602","article-title":"Cavity-Assisted Quantum Bath Engineering","volume":"109","author":"Murch","year":"2012","journal-title":"Phys. Rev. Lett."},{"key":"ref_101","doi-asserted-by":"crossref","first-page":"633","DOI":"10.1038\/nphys1342","article-title":"Quantum computation, quantum state engineering, and quantum phase transitions driven by dissipation","volume":"5","author":"Verstraete","year":"2009","journal-title":"Nat. Phys."},{"key":"ref_102","first-page":"021028","article-title":"Open-System Quantum Annealing in Mean-Field Models with Exponential Degeneracy","volume":"6","author":"Kechedzhi","year":"2016","journal-title":"Phys. Rev. X"}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/20\/4\/226\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T14:58:35Z","timestamp":1760194715000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/20\/4\/226"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,3,26]]},"references-count":102,"journal-issue":{"issue":"4","published-online":{"date-parts":[[2018,4]]}},"alternative-id":["e20040226"],"URL":"https:\/\/doi.org\/10.3390\/e20040226","relation":{},"ISSN":["1099-4300"],"issn-type":[{"value":"1099-4300","type":"electronic"}],"subject":[],"published":{"date-parts":[[2018,3,26]]}}}