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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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In this paper, we have extended the corrected propagator method to finite-temperature simulations and calculated a quantum reaction rate in a condensed-phase environment. Quantum rate processes in a condensed phase has been studied extensively by a variety of methods.28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38 We apply the corrected propagator to the study of a model system, consisting of a symmetric double-well potential, bilinearly coupled to a bath of harmonic oscillators. The thermal rate constant for this model system has been calculated using a number of approximate methods. Numerically exact quantum-mechanical calculations, including the path integral technique39 and the multilayer multiconfigurational time-dependent Hartree approach,25 have been used as benchmark results to evaluate the accuracy of different methods.
However, for a system in the condensed-phase environment the Boltzmannized flux operator is no longer a low rank operator. Therefore, the calculation of thermal observables will require finding a large number of eigenstates followed by their real-time propagation. To overcome the first obstacle, we employ a Monte Carlo importance sampling to the bath states while performing a direct summation of the eigenstates of the system Boltzmannized flux operator. This technique has been successfully applied for condensed-phase reactive systems by Wang et al.36, 47 using a multilayer multiconfigurational time-dependent Hartree method.48 In our application, the dynamics of the bath and the primary system is governed by the corrected propagator.
The project investigated the behaviour of periodically driven Floquet and MBL systems in the presence of dissipation. Dr Pal brought expertise in MBL, Floquet systems, and quantum information with a focus on numerical methods including Exact Diagonalization (ED) and methods based on tensor networks. Dr Pal also brought expertise on the implementation of quantum information processing in solid states systems, with a view towards quantum technological applications. Dr Bhaseen gave expertise in nonequilibrium quantum many-body systems and field theory techniques, with applications to condensed matter systems and cold atomic gases. 2ff7e9595c
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