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@PHDTHESIS{Reimer:764486,
      author       = {Reimer, Viktor},
      othercontributors = {Wegewijs, Maarten Rolf and Schoeller, Herbert},
      title        = {{Q}uantum information $\&$ open-system dynamics : periodic
                      driving within and complete positivity beyond the
                      {M}arkovian limit},
      school       = {RWTH Aachen University},
      type         = {Dissertation},
      address      = {Aachen},
      reportid     = {RWTH-2019-06830},
      pages        = {1 Online-Ressource (xi, 153 Seiten) : Illustrationen,
                      Diagramme},
      year         = {2019},
      note         = {Veröffentlicht auf dem Publikationsserver der RWTH Aachen
                      University; Dissertation, RWTH Aachen University, 2019},
      abstract     = {In this thesis, the dynamics of generic open quantum
                      systems is studied at the interface of quantum information
                      and statistical field theory. Taking advantage of their
                      synergies, we put the dynamical correlations that such
                      systems develop with their effective environment on center
                      stage: The key step to access the latter is a reformulation
                      of the open system's dynamics as derived from nontrivial
                      microscopic models in terms of Kraus operator-sums. This
                      decomposition into physical processes conditional on
                      measurements performed on the effective environment enables
                      progress on three interrelated questions. How do quantum
                      (non-)Markovian systems affect their environment? The common
                      notion of a Markovian process entails an environment that
                      loosely speaking retains no `memory' of its previous
                      interactions with the system. More precisely, the dynamics
                      is insensitive to a division at intermediate times at which
                      the environment is reinitialized. We provide some new
                      physical intuition for different divisibility criteria by
                      explicitly determining the dynamics of the effective
                      environment for a tunnel-coupled resonant level without
                      interactions. From the time-dependence of transport currents
                      and observable measures of information exchange between the
                      system and its environment, we find that the details of the
                      reinitialization matter even in this simple model. Obtaining
                      this complete picture of the open system's dynamics not only
                      requires an exact treatment of the problem, but also a
                      combination of various approaches --including the Kraus
                      operator-sum. How does periodic driving of the environment
                      modify Markovian systems? For any but the simplest models, a
                      detailed analysis such as the above is out of reach due to
                      the necessity of employing approximations. The paradigmatic
                      Born-Markov approximation is the prime example that manages
                      to maintain a consistent yet intuitive operational
                      understanding of the dynamics even in the presence of fast
                      time periodic driving. We illustrate for quantum optical
                      systems how such time-periodic driving influences the
                      dynamical system-environment correlations and leads to
                      driven-dissipative phase transitions which reflect a
                      memory-effect within this originally Markovian setup. A
                      hallmark feature of this transition is the temporary
                      suppression of effective dissipation rates that gives rise
                      to long-lived metastable states and interesting
                      time-periodic steady states. We develop a new formalism for
                      efficiently computing these periodic steady states without
                      the need to integrate over the full transient approach. How
                      can approximations beyond the Markovian limit be formulated?
                      Beyond these Markovian approximations, little is known
                      regarding the preservation of even the most fundamental
                      properties of a reduced system state, namely its positivity
                      and trace-normalization. Here, we focus on the stronger
                      notion of completely positive dynamics and reorganize the
                      real-time diagrammatic series into an operational framework
                      of a Kraus operator-sum in which each term makes this
                      property explicit and has a transparent physical meaning.
                      Based on these principles, we establish for the first time
                      the fundamental structure of the Nakajima-Zwanzig
                      memory-kernel that guarantees the solution of a
                      time-nonlocal quantum master equation to be completely
                      positive. This is a crucial step towards non-Markovian
                      approximation schemes that do not violate fundamental
                      dynamical properties.},
      cin          = {135110 / 130000},
      ddc          = {530},
      cid          = {$I:(DE-82)135110_20140620$ / $I:(DE-82)130000_20140620$},
      typ          = {PUB:(DE-HGF)11},
      doi          = {10.18154/RWTH-2019-06830},
      url          = {https://publications.rwth-aachen.de/record/764486},
}