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22nd International Workshop on software and Compilers for Embedded Systems, SCOPES 2019

作者： El Hakim, Viktorio S. Bekooij, Marco J. G. Computer Architectures for Embedded Systems University of Twente Enschede Netherlands Algorithms and Software Innovation NXP Semiconductors Eindhoven Netherlands

ISBN: (纸本)9781450367622

Disributed control systems often exhibit aperiodic sampling behavior due to varying communication delays and execution times. In such cases traditional analysis methods fall short because the functional and temporal behaviors need to be analyzed simultaneously. Therefore such systems are often modeled by Hybrid Automata (HA) with clock and non-clock variables, and verified using reachability analysis. However, modern reachability tools introduce a large overapproximation error because non-clock variables, as well as clock variables, are equally treated by the algorithm. In this paper we present a reachability algorithm which exploits the explicit separation of clock and non-clock variables in the Hybrid Automata with Clocked Linear Dynamics (HA-CLD) subclass, as well as restricting that guard and invariant constraints can only be specified in the HA-CLD model for clock variables. These properties of HA-CLD allow independent computation of tight reachable set over-approximations, in the form of flow-pipes, of clock and non-clock variables. A computationaly efficient and tight intersection operation is obtained by relating segments of the clock flow-pipe with segments of the non-clock flow-pipe. We demonstrate the effectiveness of our approach using two benchmarks, in the context of verifying stability. From the results it can be concluded that our reachability approach obtains significantly tighter results with an up-to 65 times smaller run-time compared to the start-of-the-art model checker SpaceEx. © 2019 ACM.

关键词： Clocks

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A many-body approach to transport in quantum systems: From the transient regime to the stationary state

arXiv

引用

arXiv 2022年

作者： Ridley, M. Talarico, N.W. Karlsson, D. Lo Gullo, N. Tuovinen, Riku School of Physics and Astronomy Tel-Aviv University Tel-Aviv69978 Israel Quantum Research Centre Technology Innovation Institute Abu Dhabi United Arab Emirates QTF Centre of Excellence Center for Quantum Engineering Department of Applied Physics Aalto University School of Science AaltoFIN-00076 Finland Algorithmiq Ltd. Kanavakatu 3c Helsinki00160 Finland Department of Physics Nanoscience Center University of Jyväskylä Jyväskylä40014 Finland CSC-IT Center for Science P.O. Box 405 Espoo02101 Finland Quantum Algorithms and Software VTT Technical Research Centre of Finland Ltd. Finland QTF Centre of Excellence Turku Centre for Quantum Physics Department of Physics and Astronomy University of Turku Turku20014 Finland QTF Centre of Excellence Department of Physics University of Helsinki P.O. Box 64 00014 Finland

We review one of the most versatile theoretical approaches to the study of time-dependent correlated quantum transport in nano-systems: the non-equilibrium Green’s function (NEGF) formalism. Within this formalism, one can treat, on the same footing, inter-particle interactions, external drives and/or perturbations, and coupling to baths with a (piece-wise) continuum set of degrees of freedom. After a historical overview on the theory of transport in quantum systems, we present a modern introduction of the NEGF approach to quantum transport. We discuss the inclusion of inter-particle interactions using diagrammatic techniques, and the use of the so-called embedding and inbedding techniques which take the bath couplings into account non-perturbatively. In various limits, such as the non-interacting limit and the steady-state limit, we then show how the NEGF formalism elegantly reduces to well-known formulae in quantum transport as special cases. We then discuss non-equilibrium transport in general, for both particle and energy currents. Under the presence of a time-dependent drive – encompassing pump–probe scenarios as well as driven quantum systems – we discuss the transient as well as asymptotic behavior, and also how to use NEGF to infer information on the out-of-equilibrium system. As illustrative examples, we consider model systems general enough to pave the way to realistic systems. These examples encompass one- and two-dimensional electronic systems, systems with electron–phonon couplings, topological superconductors, and optically responsive molecular junctions where electron–photon couplings are relevant. Copyright © 2022, The Authors. All rights reserved.

关键词： Quantum optics

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