Markov Processes And Quantum Theory
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| Author | : Masao Nagasawa |
| Publisher | : Springer Nature |
| Total Pages | : 339 |
| Release | : 2021-06-23 |
| Genre | : Computers |
| ISBN | : 3030626881 |
This book discusses quantum theory as the theory of random (Brownian) motion of small particles (electrons etc.) under external forces. Implying that the Schrödinger equation is a complex-valued evolution equation and the Schrödinger function is a complex-valued evolution function, important applications are given. Readers will learn about new mathematical methods (theory of stochastic processes) in solving problems of quantum phenomena. Readers will also learn how to handle stochastic processes in analyzing physical phenomena.
| Author | : Masao Nagasawa |
| Publisher | : Birkhäuser |
| Total Pages | : 609 |
| Release | : 2012-12-06 |
| Genre | : Mathematics |
| ISBN | : 3034883838 |
From the reviews: "The text is almost self-contained and requires only an elementary knowledge of probability theory at the graduate level. The book under review is recommended to mathematicians, physicists and graduate students interested in mathematical physics and stochastic processes. Furthermore, some selected chapters can be used as sub-textbooks for advanced courses on stochastic processes, quantum theory and quantum chemistry." ZAA
| 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.
| Author | : K.H. Namsrai |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 440 |
| Release | : 2012-12-06 |
| Genre | : Science |
| ISBN | : 9400945183 |
over this stochastic space-time leads to the non local fields considered by G. V. Efimov. In other words, stochasticity of space-time (after being averaged on a large scale) as a self-memory makes the theory nonlocal. This allows one to consider in a unified way the effect of stochasticity (or nonlocality) in all physical processes. Moreover, the universal character of this hypothesis of space-time at small distances enables us to re-interpret the dynamics of stochastic particles and to study some important problems of the theory of stochastic processes [such as the relativistic description of diffusion, Feynman type processes, and the problem of the origin of self-turbulence in the motion of free particles within nonlinear (stochastic) mechanics]. In this direction our approach (Part II) may be useful in recent developments of the stochastic interpretation of quantum mechanics and fields due to E. Nelson, D. Kershaw, I. Fenyes, F. Guerra, de la Pena-Auerbach, J. -P. Vigier, M. Davidson, and others. In particular, as shown by N. Cufaro Petroni and J. -P. Vigier, within the discussed approach, a causal action-at-distance interpretation of a series of experiments by A. Aspect and his co-workers indicating a possible non locality property of quantum mechanics, may also be obtained. Aspect's results have recently inspired a great interest in different nonlocal theories and models devoted to an understanding of the implications of this nonlocality. This book consists of two parts.
| Author | : Kai Lai Chung |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 443 |
| Release | : 2005-07-15 |
| Genre | : Mathematics |
| ISBN | : 0387220267 |
From the reviews of the First Edition: "This excellent book is based on several sets of lecture notes written over a decade and has its origin in a one-semester course given by the author at the ETH, Zürich, in the spring of 1970. The author's aim was to present some of the best features of Markov processes and, in particular, of Brownian motion with a minimum of prerequisites and technicalities. The reader who becomes acquainted with the volume cannot but agree with the reviewer that the author was very successful in accomplishing this goal...The volume is very useful for people who wish to learn Markov processes but it seems to the reviewer that it is also of great interest to specialists in this area who could derive much stimulus from it. One can be convinced that it will receive wide circulation." (Mathematical Reviews) This new edition contains 9 new chapters which include new exercises, references, and multiple corrections throughout the original text.
| Author | : Mingsheng Ying |
| Publisher | : Cambridge University Press |
| Total Pages | : 223 |
| Release | : 2021-02-04 |
| Genre | : Computers |
| ISBN | : 1108484301 |
The first book introducing computer aided verification techniques for quantum systems with quantum computing and communication hardware.
| 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.
| Author | : Robert M. Blumenthal |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 287 |
| Release | : 2012-12-06 |
| Genre | : Mathematics |
| ISBN | : 1468494120 |
Let {Xti t ~ O} be a Markov process in Rl, and break up the path X t into (random) component pieces consisting of the zero set ({ tlX = O}) and t the "excursions away from 0," that is pieces of path X. : T ::5 s ::5 t, with Xr- = X = 0, but X. 1= 0 for T
| Author | : Valia Allori |
| Publisher | : Springer Nature |
| Total Pages | : 430 |
| Release | : 2020-10-02 |
| Genre | : Science |
| ISBN | : 3030467775 |
This book is a tribute to the scientific legacy of GianCarlo Ghirardi, who was one of the most influential scientists in the field of modern foundations of quantum theory. In this appraisal, contributions from friends, collaborators and colleagues reflect the influence of his world of thoughts on theory, experiments and philosophy, while also offering prospects for future research in the foundations of quantum physics. The themes of the contributions revolve around the physical reality of the wave function and its notorious collapse, randomness, relativity and experiments.
| 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)
