Journal ArticleDOI
On quantum statistical mechanics of non-Hamiltonian systems
TLDR
In this paper, a dynamical semi-group is defined as a one-parametersemi-group of linear endomorphisms of the set of all density operators corresponding to the physical system in question.About:
This article is published in Reports on Mathematical Physics.The article was published on 1972-12-01. It has received 554 citations till now. The article focuses on the topics: Hamiltonian system & Dynamical systems theory.read more
Citations
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Journal ArticleDOI
On the Generators of Quantum Dynamical Semigroups
TL;DR: In this paper, the notion of a quantum dynamical semigroup is defined using the concept of a completely positive map and an explicit form of a bounded generator of such a semigroup onB(ℋ) is derived.
Journal ArticleDOI
General properties of entropy
TL;DR: This paper discusses properties of entropy, as well as related concepts such as relative entropy, skew entropy, dynamical entropy, etc, in detail with reference to their implications in statistical mechanics, to get a glimpse of systems with infinitely many degrees of freedom.
Journal ArticleDOI
Kinetic equations from Hamiltonian dynamics: Markovian limits
TL;DR: In this paper, a variety of classical as well as quantum-mechanical models for which kinetic equations can be derived rigorously are discussed and the probabilistic nature of the problem is emphasized: the approximation of the microscopic dynamics by either a kinetic or a hydrodynamic equation can be understood as the approximate approximation of a non-Markovian stochastic process by a Markovian process.
Journal ArticleDOI
Colloquium: Non-Markovian dynamics in open quantum systems
TL;DR: In this paper, a suite of developing theoretical tools is reviewed, with which recent progress on this problem has been based, and a more refined, non-Markovian, treatment is necessary.
Journal ArticleDOI
Dynamics of non-Markovian open quantum systems
Inés de Vega,Daniel Alonso +1 more
TL;DR: In this paper, an overview is given of some of the most important techniques available to tackle the dynamics of an OQS beyond the Markov approximation, which requires a large separation of system and environment time scales.
References
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Book
Functional Analysis And Semi-Groups
Einar Hille,R. S. Phillips +1 more
TL;DR: The theory of semi-groups has been studied extensively in the literature, see as discussed by the authors for a survey of some of the main applications of semi groups in the context of functional analysis.
Book
Probability measures on metric spaces
TL;DR: The Borel subsets of a metric space Probability measures in the metric space and probability measures in a metric group Probability measure in locally compact abelian groups The Kolmogorov consistency theorem and conditional probability probabilistic probability measures on $C[0, 1]$ and $D[0-1]$ Bibliographical notes Bibliography List of symbols Author index Subject index as mentioned in this paper
Journal ArticleDOI
Exponential Operators and Parameter Differentiation in Quantum Physics
TL;DR: In this article, a wide variety of operator identities, expansions, and solutions to differential equations of interest to quantum physics are systematically derived, based on a general closed formula for the derivative of an exponential operator with respect to a parameter.