Given an open quantum mechanical process, whether the decoherence followed by a physical system is non-Markovian (and to what extent) is of the utmost importance since it defines the predictions that can be made for the physical observables. Furthermore, non-local correlations in time are the quintessential effect of Non-Markovian dynamics. Since in quantum mechanics, time and energy are canonical conjugate variables, it is natural to expect that those correlations in time can also be observed in the energy domain. In this paper, we resort to the principle of composition or divisibility to observe memory effects in the Wigner propagation function in complex phase spaces. In this sense, we show that the sudden coupling of the system to the bath contributes to non-Markovian effects, and we show the constraints for experimental accessibility. Furthermore, we incorporate sufficient and necessary criteria in the energy domain to compose it in the time domain. Finally, we indicate that the results are applicable to radiative quenching, ionization of atoms, intramolecular relaxation, and photon bath coupling based on the Weiskopf model. • We establish the conditions under which the Wigner function along damped classical trajectories with unitary dynamics results in experimentally accessible Markovian behavior, or conversely, when non-unitary quantum dynamics inherit memory effects. • We apply the divisibility principle to derive necessary and sufficient criteria in the energy domain of an open quantum system interacting with a discrete or continuous manifold, thereby enabling composition in the time domain. • Our results are directly applicable to radiative damping, intramolecular relaxation, and photon–bath coupling within the framework of the Weisskopf model.
Given an open quantum mechanical process, whether the decoherence followed by a physical system is non-Markovian (and to what extent) is of the utmost importance since it defines the predictions that can be made for the physical observables. Furthermore, non-local correlations in time are the quintessential effect of Non-Markovian dynamics. Since in quantum mechanics, time and energy are canonical conjugate variables, it is natural to expect that those correlations in time can also be observed in the energy domain. In this paper, we resort to the principle of composition or divisibility to observe memory effects in the Wigner propagation function in complex phase spaces. In this sense, we show that the sudden coupling of the system to the bath contributes to non-Markovian effects, and we show the constraints for experimental accessibility. Furthermore, we incorporate sufficient and necessary criteria in the energy domain to compose it in the time domain. Finally, we indicate that the results are applicable to radiative quenching, ionization of atoms, intramolecular relaxation, and photon bath coupling based on the Weiskopf model. • We establish the conditions under which the Wigner function along damped classical trajectories with unitary dynamics results in experimentally accessible Markovian behavior, or conversely, when non-unitary quantum dynamics inherit memory effects. • We apply the divisibility principle to derive necessary and sufficient criteria in the energy domain of an open quantum system interacting with a discrete or continuous manifold, thereby enabling composition in the time domain. • Our results are directly applicable to radiative damping, intramolecular relaxation, and photon–bath coupling within the framework of the Weisskopf model.
ABSTRACT: We use the divisibility approach to describe non-Markovian dynamics (memory effects) in open quantum systems coupled to an environment (reservoir). Specifically, sufficient and necessary criteria were incorporated in the energy domain that play a relevant role in dynamics of the system. In this case, we adopt the Feshbach partition in the space of (Hilbert-Liouville). On the other hand, to investigate both Markovianity and non-Markovianity, we study the divisibility of the Wigner function propagator. For this, within the framework of path integrals, we carry out an analysis of non-classical paths in phase space. Furthermore, we have used tools of topology to propose theorems intimately related to measures of non-Markovianity that are experementally accessible.
In the present Thesis we study the behavior of multi-time 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. non-Markovian. 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 non-Markovianity 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 non-Markovianity 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 so-called quantum regression theorem in presence of a non-Markovian dynamical regime is investigated. The quantum regression theorem represents a procedure that, whenever valid, allows to reconstruct two-time correlation functions of system's operators from the sole knowledge of the dynamics of mean values. It is worth stressing that two-time 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 two-time 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 two-time correlation functions, this highlighting its importance. In this work we show that, in a pure-dephasing spin-boson model, the quantum regression theorem represents a stronger condition than non-Markovianity, 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 non-Markovian dynamical regime, showing that, at variance with what happens in the Born-Markov 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 non-Markovianity estimators is sought in two paradigmatic models, namely the spin-boson 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 parameter-regions 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 non-Markovianity, in the sense that non-Markovianity 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 environmental-assisted erasure-protocol 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 non-equilibrium setting. This construction is applied to an open system consisting of a three-level V-system, in which one transition is externally pumped by a laser field while the other is coupled through an XX-interaction 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].
This technical note introduces clockability as an operational criterion for assessing the validity of time-local descriptions in open quantum systems. While non-Markovian dynamics are commonly characterized through information backflow or violations of CP-divisibility, the structural conditions under which a temporal description remains operationally meaningful are rarely made explicit. This work reframes non-Markovianity not as a dynamical anomaly, but as a signal of local clockability breakdown: the failure of the environment to function as a stable register of persistent and locally accessible traces. Within this framework, CP-divisibility emerges as a sufficient condition for local clockability, whereas its violation marks the loss of applicability of time-local master equations rather than a failure of quantum dynamics itself. The note clarifies the relationship between divisibility-based and information-theoretic measures of non-Markovianity and motivates a hierarchical domain-of-validity analysis for temporal descriptions. No new physical mechanisms or mathematical formalisms are introduced. Instead, the work provides a diagnostic, information-theoretic perspective on when time-local representations (e.g., GKSL forms) are structurally justified, and when dynamical descriptions should be interpreted as non-local, history-dependent responses. This contribution is intended as a conceptual and methodological clarification relevant to quantum information theory, open quantum systems, and the operational foundations of time.
A profound understanding of decoherence and dissipation in quantum dynamics is crucial for the realistic modeling of the evolution of quantum systems. In open quantum dynamics one distinguishes between a memoryless, so-called Markovian evolution and dynamics incorporating memory effects, termed non-Markovian. In this work we study how prevalent memory effects are in the set of all such dynamics. We thus investigate how often a Markovian description is applicable. This question is approached by investigating randomly generated two-step qubit dynamics with respect to different concepts and witnesses of non-Markovianity. We observe that almost all dynamics are non-Markovian, and only a small (yet finite) fraction is Markovian. Furthermore, we study how this proportion changes when considering certain subclasses such as lower rank or mixed-unitary dynamics. Importantly, our results shed light on the relative ratios of -- and interrelations between -- the sets of dynamics that are non-Markovian with respect to different criteria. Finally, we investigate the fraction of dynamics in which the memory effects are necessarily of quantum nature and establish a connection between two recently developed concepts that characterize the quantumness of memory in non-Markovian dynamics.
We introduce a systematic framework to derive the effective Hamiltonian governing the coherent dynamics of non-Markovian open quantum systems. By applying the minimal dissipation principle, we uniquely isolate the coherent contribution to the time-local generator of the reduced dynamics. We derive a general expression for the effective Hamiltonian and develop a recursive perturbative expansion that expresses it in terms of system-bath interaction terms and bath correlation functions. This expansion provides a systematic tool for analyzing energy renormalization effects across different coupling regimes. Applying our framework to paradigmatic spin systems, we reveal how environmental correlations influence energy shifts and eigenbasis rotations, offering insights into strong-coupling effects and non-Markovian quantum thermodynamics.
The problem of defining quantum non-Markovianity has proven elusive, with various inequivalent criteria put forth to address it. We consider the question: what is the weakest notion of quantum non-Markovianity of system dynamics that would account for any aspect of memory? That is, a process indicated to be non-Markovian according to any existing criterion is also non-Markovian according to this criterion, but the converse may not be true. Correspondingly, we identify true memorylessness with the idea of the quantum dynamics being temporally self-similar, whereby the form of the intermediate map that propagates the state between two arbitrary time intervals is independent of the initial time t0. This is identified with the quantum dynamical semigroup (QDS), renewing advocacy for a familiar candidate. Of practical importance is that our weaker criterion is useful for indicating the non-Markovianity of CP-divisible channels that manifest an effect of counteracting decoherence. This is illustrated with the examples of power-law noise (PLN) and Ornstein-Uhlenbeck Noise (OUN). For physically well motivated channels, we propose a geometric quantification of non-Markovianity according to our definition, which is shown to be applicable to stronger manifestations of quantum non-Markovianity, demonstrated here by application to various channels, including those that are CP-indivisible, P-indivisible and eternally non-Markovian. Finally, we indicate a few open questions that come up as natural consequences of this work.