Stochastic Aspects of Classical and Quantum Systems
| Author | : S. Albeverio |
| Publisher | : Springer |
| Total Pages | : 239 |
| Release | : 2007-01-05 |
| Genre | : Mathematics |
| ISBN | : 354039138X |
Stochastic Aspects Of Classical And Quantum Systems
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Stochastic Behavior in Classical and Quantum Hamiltonian Systems
| Author | : Giulio Casati |
| Publisher | : |
| Total Pages | : 388 |
| Release | : 2014-01-15 |
| Genre | : |
| ISBN | : 9783662183656 |
Quantum Techniques In Stochastic Mechanics
| Author | : John C Baez |
| Publisher | : World Scientific |
| Total Pages | : 276 |
| Release | : 2018-02-14 |
| Genre | : Science |
| ISBN | : 981322696X |
We 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 | : Springer Science & Business Media |
| Total Pages | : 299 |
| Release | : 2012-12-13 |
| Genre | : Mathematics |
| ISBN | : 3034805667 |
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 commutation relations or, equivalently, the uncertainty principle. Quantum stochastic integration enables the possibility of seeing new relationships between fermion and boson fields. Many quantum dynamical semigroups as well as classical Markov semigroups are realised 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. - - - This is an excellent volume which will be a valuable companion both to 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) This monograph gives a systematic and self-contained introduction to the Fock space quantum stochastic calculus in its basic form (...) by making emphasis on the mathematical aspects of quantum formalism and its connections with classical probability and by extensive presentation of carefully selected functional analytic material. This makes the book very convenient for a reader with the probability-theoretic orientation, wishing to make acquaintance with wonders of the noncommutative probability, and, more specifcally, for a mathematics student studying this field. (Zentralblatt MATH) 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)
Stochastic Quantum Mechanics and Quantum Spacetime
| Author | : Eduard Prugovečki |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 334 |
| Release | : 1984-01-31 |
| Genre | : Gardening |
| ISBN | : 9789027716170 |
The 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.
Stochastic Quantization
| Author | : Poul Henrik Damgaard |
| Publisher | : World Scientific |
| Total Pages | : 512 |
| Release | : 1988 |
| Genre | : Science |
| ISBN | : 9789971502546 |
This collection of selected reprints presents as broad a selection as possible, emphasizing formal and numerical aspects of Stochastic Quantization. It reviews and explains the most important concepts placing selected reprints and crucial papers into perspective and compact form.
Quantum Stochastic Thermodynamics
| Author | : Philipp Strasberg |
| Publisher | : Oxford University Press |
| Total Pages | : 337 |
| Release | : 2022 |
| Genre | : Science |
| ISBN | : 0192895583 |
The theory of thermodynamics has been one of the bedrocks of 19th-century physics, and thermodynamic problems have inspired Planck's quantum hypothesis. One hundred years later, in an era where we design increasingly sophisticated nanotechnologies, researchers in quantum physics have been 'returning to their roots', attempting to reconcile modern nanoscale devices with the theory of thermodynamics. This textbook explains how it is possible to unify the two opposite pictures of microscopic quantum physics and macroscopic thermodynamics in one consistent framework, proving that the ancient theory of thermodynamics still offers many remarkable insights into present-day problems. This textbook focuses on the microscopic derivation and understanding of key principles and concepts and their interrelation. The topics covered in this book include (quantum) stochastic processes, (quantum) master equations, local detailed balance, classical stochastic thermodynamics, (quantum) fluctuation theorems, strong coupling and non-Markovian effects, thermodynamic uncertainty relations, operational approaches, Maxwell's demon, and time-reversal symmetry, among other topics. The textbook also explores several practical applications of the theory in more detail, including single-molecule pulling experiments, quantum transport and thermoelectric effects in quantum dots, the micromaser, and related setups in quantum optics. The aim of this book is to inspire readers to investigate a plethora of modern nanoscale devices from a thermodynamic point of view, allowing them to address their dissipation, efficiency, reliability, and power based on a conceptually clear understanding about the microscopic origin of heat, entropy, and the second law. The book is accessible to graduate students, post-docs, and lecturers, but will also be of interest to all researchers striving for a deeper understanding of the laws of thermodynamics beyond their traditional realm of applicability.
Probabilistic and Statistical Aspects of Quantum Theory
| Author | : Alexander S. Holevo |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 336 |
| Release | : 2011-05-05 |
| Genre | : Mathematics |
| ISBN | : 8876423788 |
This 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 Stochastics
| Author | : Mou-Hsiung Chang |
| Publisher | : Cambridge University Press |
| Total Pages | : 425 |
| Release | : 2015-02-19 |
| Genre | : Language Arts & Disciplines |
| ISBN | : 110706919X |
This 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.
Quantum Fluctuations
| Author | : Edward Nelson |
| Publisher | : Princeton University Press |
| Total Pages | : 155 |
| Release | : 1985-05-21 |
| Genre | : Science |
| ISBN | : 0691083797 |
Stochastic 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.
