On time-local generators of quantum evolution

Abstract

We present a basic introduction to the dynamics of open quantum systems based on local-in-time master equations. We characterize the properties of time-local generators giving rise to legitimate completely positive trace preserving quantum evolutions. The analysis of Markovian and non-Markovian quantum dynamics is presented as well. The whole discussion is illustrated by the family of many instructive examples.

Lecture presented at the school "Open Quantum Systems", Torun, June 20-24, 2012 (30 pages)

References in corpus (8)

• The Magnus expansion and some of its applications
• Assessing non-Markovian dynamics
• On measures of non-Markovianity: divisibility vs. backflow of information
• Foundations and Measures of Quantum Non-Markovianity
• Markovian and non-Markovian dynamics in quantum and classical systems
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• Coherent and dissipative dynamics at quantum phase transitions
• Adding dynamical generators in quantum master equations
• Irreversible quantum evolution with quadratic generator: Review
• The interplay between local and non-local master equations: exact and approximated dynamics
• Generalized Kac's Lemma for Recurrence Time in Iterated Open Quantum Systems
• Quantum Fluctuations in Mesoscopic Systems
• Quantum renewal processes
• Characterizing the dynamical semigroups that do not decrease a quantum entropy
• Evolution equations for quantum semi-Markov dynamics
• Construction of propagators for divisible dynamical maps
• Understanding and Generalizing Unique Decompositions of Generators of Dynamical Semigroups
• Dynamic Quantum Tomography Model for Phase-Damping Channels
• Noisy effects in interferometric quantum gravity tests
• Long-lived mesoscopic entanglement between two damped infinite harmonic chains
• A possible time dependent generalization of the bipartite quantum marginal problem
• Frontiers of open quantum system dynamics
• $k$-Positive Maps: New Characterizations and a Generation Method
• Bound on dissipative effects from semileptonic neutral B-meson decays
• Stochastic unravelings for Heisenberg picture and trace-nonpreserving dynamics