In the present Thesis we study the behavior of multitime correlation functions and of thermodynamical quantities such as heat in open quantum systems undergoing an evolution generally affected by the presence of memory effects, i.e. nonMarkovian. In the last decade, a large part of the scientific community in this field has dedicated its efforts to the understanding, precise definition and quantification of nonMarkovianity in the quantum realm and now we have at our disposal several benchmark results and a plethora of different estimators that allow to determine the degree of nonMarkovianity of a given dynamics. It comes therefore natural to investigate how other different dynamical quantities relate to such estimators also in order to understand the physical implications of memory effects on the statistics of observable quantities. In the first part of this work, a quantitative test of the violation of the socalled quantum regression theorem in presence of a nonMarkovian dynamical regime is investigated. The quantum regression theorem represents a procedure that, whenever valid, allows to reconstruct twotime correlation functions of system's operators from the sole knowledge of the dynamics of mean values. It is worth stressing that twotime correlation functions are necessary in order to fully characterize the statistical properties of a quantum system, since they are able to catch aspects of the dynamics, such as fluorescence spectrum, in general not accessible looking at mean values. Despite their relevance however, obtaining twotime correlation functions often represents a formidable task, since the knowledge of the full "system+environment" dynamics is required, a generally too demanding request in the context of open quantum systems theory. The quantum regression theorem represents in this regard the easiest route to determine twotime correlation functions, this highlighting its importance. In this work we show that, in a puredephasing spinboson model, the quantum regression theorem represents a stronger condition than nonMarkovianity, in the sense that any presence of memory effects in the reduced dynamics inevitably results in violations to the former. These results have been published in [G.Guarnieri, A. Smirne, B. Vacchini, Phys. Rev. A 90, 022110 (2014)]. The second part of the Thesis is devoted to the characterization of heat ow at the microscopic level in open quantum systems, both finite and infinite dimensional. In particular we begin by studying the time behavior of its mean value in a nonMarkovian dynamical regime, showing that, at variance with what happens in the BornMarkov semigroup limiting case, heat can backflow from the environment to the system. After providing a condition for the occurrence of such phenomenon and a measure for its amount for a given dynamics, the relationship with suitable nonMarkovianity estimators is sought in two paradigmatic models, namely the spinboson and the quantum brownian motion. The results, collected in [ G. Guarnieri, C. Uchiyama, B. Vacchini, Phys. Rev. A 93, 012118 (2016); G. Guarnieri, J. Nokkala, R. Schmidt, S. Maniscalco, B. Vacchini, Phys. Rev. A 94, 062101 (2016)], on the one hand allow for the identification of parameterregions where the heat backflow is absent or maximum. On the other hand they show that the occurrence of heat backflow represents a stricter condition than nonMarkovianity, in the sense that nonMarkovianity allows for the observation of heat flowing back from the environment to the system and, vice versa, a Markovian dynamics prevents its occurrence. This Thesis concludes with the formulation of a new family of lower bounds to the mean dissipated heat in an environmentalassisted erasureprotocol scenario where Landauer's principle applies. As originally conceived for classical systems, this principle states that every irreversible erasure of information stored in a system inevitably carries along an amount of heat dissipated into the environment which is expended to perform the action. Within the framework recently put forward in [D. Reeb, M. M. Wolf, New J. Phys. 16, 103011 (2014)], which guarantees the validity of Landauer's principle in an open quantum systems scenario, we provide an asymptotically tight family of lower bounds to the dissipated heat which are also valid in the nonequilibrium setting. This construction is applied to an open system consisting of a threelevel Vsystem, in which one transition is externally pumped by a laser field while the other is coupled through an XXinteraction to an environment consisting of a spin chain. Beside calculating all these quantities, an exact solution for the dynamics of such system is also provided. These results are collected in [G. Guarnieri, S. Campbell, J. Goold, S. Pigeon, M. Paternostro, B. Vacchini, in preparation].
Characterizzation of dynamical properties of nonMarkovian open quantum systems / G. Guarnieri ; supervisore: B. Vacchini ; coordinator: F. Ragusa.  : . DIPARTIMENTO DI FISICA, 2017 Jan 19. ((29. ciclo, Anno Accademico 2016. [10.13130/guarnierigiacomo_phd20170119].
Characterizzation of dynamical properties of nonMarkovian open quantum systems
G. Guarnieri
20170119
Abstract
In the present Thesis we study the behavior of multitime correlation functions and of thermodynamical quantities such as heat in open quantum systems undergoing an evolution generally affected by the presence of memory effects, i.e. nonMarkovian. In the last decade, a large part of the scientific community in this field has dedicated its efforts to the understanding, precise definition and quantification of nonMarkovianity in the quantum realm and now we have at our disposal several benchmark results and a plethora of different estimators that allow to determine the degree of nonMarkovianity of a given dynamics. It comes therefore natural to investigate how other different dynamical quantities relate to such estimators also in order to understand the physical implications of memory effects on the statistics of observable quantities. In the first part of this work, a quantitative test of the violation of the socalled quantum regression theorem in presence of a nonMarkovian dynamical regime is investigated. The quantum regression theorem represents a procedure that, whenever valid, allows to reconstruct twotime correlation functions of system's operators from the sole knowledge of the dynamics of mean values. It is worth stressing that twotime correlation functions are necessary in order to fully characterize the statistical properties of a quantum system, since they are able to catch aspects of the dynamics, such as fluorescence spectrum, in general not accessible looking at mean values. Despite their relevance however, obtaining twotime correlation functions often represents a formidable task, since the knowledge of the full "system+environment" dynamics is required, a generally too demanding request in the context of open quantum systems theory. The quantum regression theorem represents in this regard the easiest route to determine twotime correlation functions, this highlighting its importance. In this work we show that, in a puredephasing spinboson model, the quantum regression theorem represents a stronger condition than nonMarkovianity, in the sense that any presence of memory effects in the reduced dynamics inevitably results in violations to the former. These results have been published in [G.Guarnieri, A. Smirne, B. Vacchini, Phys. Rev. A 90, 022110 (2014)]. The second part of the Thesis is devoted to the characterization of heat ow at the microscopic level in open quantum systems, both finite and infinite dimensional. In particular we begin by studying the time behavior of its mean value in a nonMarkovian dynamical regime, showing that, at variance with what happens in the BornMarkov semigroup limiting case, heat can backflow from the environment to the system. After providing a condition for the occurrence of such phenomenon and a measure for its amount for a given dynamics, the relationship with suitable nonMarkovianity estimators is sought in two paradigmatic models, namely the spinboson and the quantum brownian motion. The results, collected in [ G. Guarnieri, C. Uchiyama, B. Vacchini, Phys. Rev. A 93, 012118 (2016); G. Guarnieri, J. Nokkala, R. Schmidt, S. Maniscalco, B. Vacchini, Phys. Rev. A 94, 062101 (2016)], on the one hand allow for the identification of parameterregions where the heat backflow is absent or maximum. On the other hand they show that the occurrence of heat backflow represents a stricter condition than nonMarkovianity, in the sense that nonMarkovianity allows for the observation of heat flowing back from the environment to the system and, vice versa, a Markovian dynamics prevents its occurrence. This Thesis concludes with the formulation of a new family of lower bounds to the mean dissipated heat in an environmentalassisted erasureprotocol scenario where Landauer's principle applies. As originally conceived for classical systems, this principle states that every irreversible erasure of information stored in a system inevitably carries along an amount of heat dissipated into the environment which is expended to perform the action. Within the framework recently put forward in [D. Reeb, M. M. Wolf, New J. Phys. 16, 103011 (2014)], which guarantees the validity of Landauer's principle in an open quantum systems scenario, we provide an asymptotically tight family of lower bounds to the dissipated heat which are also valid in the nonequilibrium setting. This construction is applied to an open system consisting of a threelevel Vsystem, in which one transition is externally pumped by a laser field while the other is coupled through an XXinteraction to an environment consisting of a spin chain. Beside calculating all these quantities, an exact solution for the dynamics of such system is also provided. These results are collected in [G. Guarnieri, S. Campbell, J. Goold, S. Pigeon, M. Paternostro, B. Vacchini, in preparation].File  Dimensione  Formato  

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