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The dynamical behavior of open quantum systems plays a key role in many applications of quantum mechanics, examples ranging from fundamental problems, such as the environment-induced decay of quantum coherence and relaxation in many-body systems, to applications in condensed matter theory, quantum transport, quantum chemistry, and quantum information. In close analogy to a classical Markovian stochastic process, the interaction of an open quantum system with a noisy environment is often modeled phenomenologically by means of a dynamical semigroup with a corresponding time-independent generator in Lindblad form, which describes a memoryless dynamics of the open system typically leading to an irreversible loss of characteristic quantum features. However, in many applications open systems exhibit pronounced memory effects and a revival of genuine quantum properties such as quantum coherence, correlations, and entanglement. Here recent theoretical results on the rich non-Markovian quantum dynamics of open systems are discussed, paying particular attention to the rigorous mathematical definition, to the physical interpretation and classification, as well as to the quantification of quantum memory effects. The general theory is illustrated by a series of physical examples. The analysis reveals that memory effects of the open system dynamics reflect characteristic features of the environment which opens a new perspective for applications, namely, to exploit a small open system as a quantum probe signifying nontrivial features of the environment it is interacting with. This Colloquium further explores the various physical sources of non-Markovian quantum dynamics, such as structured environmental spectral densities, nonlocal correlations between environmental degrees of freedom, and correlations in the initial system-environment state, in addition to developing schemes for their local detection. Recent experiments addressing the detection, quantification, and control of non-Markovian quantum dynamics are also briefly discussed.

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Abstract: The energy increasing rate (EIR) of a condensed droplet was analyzed during its growth in three different modes. The lowest EIR corresponding to one of the three ways was used as the criterion to determine the mode in which a condensed drop will increase its volume. The results show that the EIR according to the mode of increasing contact angle (CA) is much smaller than that according to the two other modes during the first period of growth of a condensate spot formed within a nanostructure. This means that the drop will grow, with CA increasing but the base area remaining constant, until a certain CA. After this, the EIR according to the mode of CA increasing becomes much higher than that according to the two other modes. The three-phase contact line of the drop starts to shift and the base area begins to increase while the CA remains constant. During this second period, the state of increased base area can be wetted; i.e., a Wenzel-state droplet forms with an apparent CA less than 160. In contrast, the expanded base area can be in a composite state; i.e., a partially wetted droplet forms with a CA greater than 160 . The growth mode and its wetted state of a condensed droplet are strongly related to nanostructure. Partially wetted condensed drops can appear only on surfaces with nanopillars of a certain height and small pitch. The calculated results were consistent with experimental observations reported in the literature for the wetting states of condensed drops on nanotextured surfaces, with an accuracy of 91.9%, which is obviously higher than those calculated with reported formulas.

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