Stochastic Aspects of Classical and Quantum Systems
Author: S. Albeverio
Publisher: Springer
Published: 2007-01-05
Total Pages: 239
ISBN-13: 354039138X
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Stochastic Behavior in Classical and Quantum Hamiltonian Systems
Author: Giulio Casati
Publisher:
Published: 2014-01-15
Total Pages: 388
ISBN-13: 9783662183656
DOWNLOAD EBOOKQuantum Techniques In Stochastic Mechanics
Author: John C Baez
Publisher: World Scientific
Published: 2018-02-14
Total Pages: 276
ISBN-13: 981322696X
DOWNLOAD EBOOKWe introduce the theory of chemical reaction networks and their relation to stochastic Petri nets — important ways of modeling population biology and many other fields. We explain how techniques from quantum mechanics can be used to study these models. This relies on a profound and still mysterious analogy between quantum theory and probability theory, which we explore in detail. We also give a tour of key results concerning chemical reaction networks and Petri nets.
An Introduction to Quantum Stochastic Calculus
Author: K.R. Parthasarathy
Publisher: Birkhäuser
Published: 2012-12-06
Total Pages: 299
ISBN-13: 3034886411
DOWNLOAD EBOOK"Elegantly written, with obvious appreciation for fine points of higher mathematics...most notable is [the] author's effort to weave classical probability theory into [a] quantum framework." – The American Mathematical Monthly "This is an excellent volume which will be a valuable companion both for those who are already active in the field and those who are new to it. Furthermore there are a large number of stimulating exercises scattered through the text which will be invaluable to students." – Mathematical Reviews An Introduction to Quantum Stochastic Calculus aims to deepen our understanding of the dynamics of systems subject to the laws of chance both from the classical and the quantum points of view and stimulate further research in their unification. This is probably the first systematic attempt to weave classical probability theory into the quantum framework and provides a wealth of interesting features: The origin of Ito's correction formulae for Brownian motion and the Poisson process can be traced to communication relations or, equivalently, the uncertainty principle. Quantum stochastic interpretation enables the possibility of seeing new relationships between fermion and boson fields. Quantum dynamical semigroups as well as classical Markov semigroups are realized through unitary operator evolutions. The text is almost self-contained and requires only an elementary knowledge of operator theory and probability theory at the graduate level.
Stochastic Quantum Mechanics and Quantum Spacetime
Author: Eduard Prugovečki
Publisher: Springer Science & Business Media
Published: 1984-01-31
Total Pages: 334
ISBN-13: 9789027716170
DOWNLOAD EBOOKThe principal intent of this monograph is to present in a systematic and self-con tained fashion the basic tenets, ideas and results of a framework for the consistent unification of relativity and quantum theory based on a quantum concept of spacetime, and incorporating the basic principles of the theory of stochastic spaces in combination with those of Born's reciprocity theory. In this context, by the physicial consistency of the present framework we mean that the advocated approach to relativistic quantum theory relies on a consistent probabilistic interpretation, which is proven to be a direct extrapolation of the conventional interpretation of nonrelativistic quantum mechanics. The central issue here is that we can derive conserved and relativistically convariant probability currents, which are shown to merge into their nonrelativistic counterparts in the nonrelativistic limit, and which at the same time explain the physical and mathe matical reasons behind the basic fact that no probability currents that consistently describe pointlike particle localizability exist in conventional relativistic quantum mechanics. Thus, it is not that we dispense with the concept oflocality, but rather the advanced central thesis is that the classical concept of locality based on point like localizability is inconsistent in the realm of relativistic quantum theory, and should be replaced by a concept of quantum locality based on stochastically formulated systems of covariance and related to the aforementioned currents.
Quantum Theory and Its Stochastic Limit
Author: Luigi Accardi
Publisher: Springer Science & Business Media
Published: 2013-03-14
Total Pages: 485
ISBN-13: 3662049295
DOWNLOAD EBOOKWell suited as a textbook in the emerging field of stochastic limit, which is a new mathematical technique developed for solving nonlinear problems in quantum theory.
Probabilistic and Statistical Aspects of Quantum Theory
Author: Alexander S. Holevo
Publisher: Springer Science & Business Media
Published: 2011-05-05
Total Pages: 336
ISBN-13: 8876423788
DOWNLOAD EBOOKThis book is devoted to aspects of the foundations of quantum mechanics in which probabilistic and statistical concepts play an essential role. The main part of the book concerns the quantitative statistical theory of quantum measurement, based on the notion of positive operator-valued measures. During the past years there has been substantial progress in this direction, stimulated to a great extent by new applications such as Quantum Optics, Quantum Communication and high-precision experiments. The questions of statistical interpretation, quantum symmetries, theory of canonical commutation relations and Gaussian states, uncertainty relations as well as new fundamental bounds concerning the accuracy of quantum measurements, are discussed in this book in an accessible yet rigorous way. Compared to the first edition, there is a new Supplement devoted to the hidden variable issue. Comments and the bibliography have also been extended and updated.
Quantum Fluctuations
Author: Edward Nelson
Publisher: Princeton University Press
Published: 1985-05-21
Total Pages: 155
ISBN-13: 0691083797
DOWNLOAD EBOOKStochastic mechanics is a description of quantum phenomena in classical probabilistic terms. This work contains a detailed account of the kinematics of diffusion processes, including diffusions on curved manifolds which are necessary for the treatment of spin in stochastic mechanics. The dynamical equations of the theory are derived from a variational principle, and interference, the asymptotics of free motion, bound states, statistics, and spin are described in classical terms. In addition to developing the formal mathematical aspects of the theory, the book contains discussion of possible physical causes of quantum fluctuations in terms of an interaction with a background field. The author gives a critical analysis of stochastic mechanics as a candidate for a realistic theory of physical processes, discussing measurement, local causality in the sense of Bell, and the failure of the theory in its present form to satisfy locality.
Quantum Stochastics
Author: Mou-Hsiung Chang
Publisher: Cambridge University Press
Published: 2015-02-19
Total Pages: 425
ISBN-13: 110706919X
DOWNLOAD EBOOKThis book provides a systematic, self-contained treatment of the theory of quantum probability and quantum Markov processes for graduate students and researchers. Building a framework that parallels the development of classical probability, it aims to help readers up the steep learning curve of the quantum theory.
Stochastic Methods in Fluid Mechanics
Author: Sergio Chibbaro
Publisher: Springer Science & Business Media
Published: 2013-09-05
Total Pages: 175
ISBN-13: 3709116228
DOWNLOAD EBOOKSince their first introduction in natural sciences through the work of Einstein on Brownian motion in 1905 and further works, in particular by Langevin, Smoluchowski and others, stochastic processes have been used in several areas of science and technology. For example, they have been applied in chemical studies, or in fluid turbulence and for combustion and reactive flows. The articles in this book provide a general and unified framework in which stochastic processes are presented as modeling tools for various issues in engineering, physics and chemistry, with particular focus on fluid mechanics and notably dispersed two-phase flows. The aim is to develop what can referred to as stochastic modeling for a whole range of applications.
