Download or read book Stochasticity and Quantum Chaos written by Z. Haba and published by Springer Science & Business Media. This book was released on 2013-03-07 with total page 222 pages. Available in PDF, EPUB and Kindle. Book excerpt: These are the proceedings of the Third Max Born Symposium which took place at SobOtka Castle in September 1993. The Symposium is organized annually by the Institute of Theoretical Physics of the University of Wroclaw. Max Born was a student and later on an assistant at the University of Wroclaw (Wroclaw belonged to Germany at this time and was called Breslau). The topic of the Max Born Sympo sium varies each year reflecting the developement of theoretical physics. The subject of this Symposium "Stochasticity and quantum chaos" may well be considered as a continuation of the research interest of Max Born. Recall that Born treats his "Lectures on the mechanics of the atom" (published in 1925) as a nrst volume of a complete monograph (supposedly to be written by another person). His lectures concern the quantum mechanics of integrable systems. The quantum mechanics of non-integrable systems was the subject of the Third Max Born Symposium. It is known that classical non-integrable Hamiltonian systems show a chaotic behaviour. On the other hand quantum systems bounded in space are quasiperi odic. We believe that quantum systems have a reasonable classical limit. It is not clear how to reconcile the seemingly regular behaviour of quantum systems with the possible chaotic properties of their classical counterparts. The quantum proper ties of classically chaotic systems constitute the main subject of these Proceedings. Other topics discussed are: the quantum mechanics of dissipative systems, quantum measurement theory, the role of noise in classical and quantum systems.
Download or read book Quantum Techniques In Stochastic Mechanics written by Baez John C and published by World Scientific. This book was released on 2018-02-14 with total page 276 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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. Contents: Stochastic Petri Nets The Rate Equation The Master Equation Probabilities vs Amplitudes Annihilation and Creation Operators An Example from Population Biology Feynman Diagrams The Anderson–Craciun–Kurtz Theorem An Example of the Anderson–Craciun–Kurtz Theorem A Stochastic Version of Noether's Theorem Quantum Mechanics vs Stochastic Mechanics Noether's Theorem: Quantum vs Stochastic Chemistry and the Desargues Graph Graph Laplacians Dirichlet Operators and Electrical Circuits Perron–Frobenius Theory The Deficiency Zero Theorem Example of the Deficiency Zero Theorem Example of the Anderson–Craciun–Kurtz Theorem The Deficiency of a Reaction Network Rewriting the Rate Equation The Rate Equation and Markov Processes Proof of the Deficiency Zero Theorem Noether's Theorem for Dirichlet Operators Computation and Petri Nets Summary Table Readership: Graduate students and researchers in the field of quantum and mathematical physics. Keywords: Stochastic;Quantum;Markov Process;Chemical Reaction Network;Petri NetReview: Key Features: It's a light-hearted introduction to a deep analogy between probability theory and quantum theory It explains how stochastic Petri nets can be used in modeling in biology, chemistry, and many other fields It gives new proofs of some fundamental theorems about chemical reaction networks
Download or read book On Quantum Chaos Stochastic Webs and Localization in a Quantum Mechanical Kick System written by Ulf Martin Engel and published by . This book was released on 2003 with total page 311 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Quantum Chaos Quantum Measurement written by P. Cvitanovic and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 325 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the proceedings of the NATO Advanced Research Workshop on `Quantum Chaos -- Theory and Experiment', held at the Niels Bohr Institute, University of Copenhagen, from 28 May to 1 June 1991. The work brings together leading quantum chaos theorists and experimentalists and greatly improves our understanding of the physics of quantum systems whose classical limit is chaotic. Quantum chaos is a subject of considerable current interest in a variety of fields, in particular nuclear physics, chemistry, statistical mechanics, atomic physics, condensed matter physics and nonlinear dynamics. The volume contains lectures about the currently most active fronts of quantum chaos, such as scars, semiclassical methods, quantum diffusion, random matrix spectra, quantum chaos in atomic and nuclear physics, and possible implications of quantum chaos for the problem of quantum measurement. Part of the book -- The Physics of Quantum Measurements -- is dedicated to the memory of John Bell.
Download or read book Chaos in Classical and Quantum Mechanics written by Martin C. Gutzwiller and published by Springer Science & Business Media. This book was released on 2013-11-27 with total page 445 pages. Available in PDF, EPUB and Kindle. Book excerpt: Describes the chaos apparent in simple mechanical systems with the goal of elucidating the connections between classical and quantum mechanics. It develops the relevant ideas of the last two decades via geometric intuition rather than algebraic manipulation. The historical and cultural background against which these scientific developments have occurred is depicted, and realistic examples are discussed in detail. This book enables entry-level graduate students to tackle fresh problems in this rich field.
Download or read book Stochastic Processes in Quantum Physics written by Masao Nagasawa and published by Birkhäuser. This book was released on 2012-12-06 with total page 609 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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
Download or read book The Transition to Chaos written by Linda Reichl and published by Springer Science & Business Media. This book was released on 2013-11-11 with total page 692 pages. Available in PDF, EPUB and Kindle. Book excerpt: Based on courses given at the universities of Texas and California, this book treats an active field of research that touches upon the foundations of physics and chemistry. It presents, in as simple a manner as possible, the basic mechanisms that determine the dynamical evolution of both classical and quantum systems in sufficient generality to include quantum phenomena. The book begins with a discussion of Noether's theorem, integrability, KAM theory, and a definition of chaotic behavior; continues with a detailed discussion of area-preserving maps, integrable quantum systems, spectral properties, path integrals, and periodically driven systems; and concludes by showing how to apply the ideas to stochastic systems. The presentation is complete and self-contained; appendices provide much of the needed mathematical background, and there are extensive references to the current literature; while problems at the ends of chapters help students clarify their understanding. This new edition has an updated presentation throughout, and a new chapter on open quantum systems.
Download or read book Chaos Noise and Fractals written by E. Roy Pike and published by CRC Press. This book was released on 2020-08-26 with total page 264 pages. Available in PDF, EPUB and Kindle. Book excerpt: The study of nonlinear dynamical systems has been gathering momentum since the late 1950s. It now constitutes one of the major research areas of modern theoretical physics. The twin themes of fractals and chaos, which are linked by attracting sets in chaotic systems that are fractal in structure, are currently generating a great deal of excitement. The degree of structure robustness in the presence of stochastic and quantum noise is thus a topic of interest. Chaos, Noise and Fractals discusses the role of fractals in quantum mechanics, the influence of phase noise in chaos and driven optical systems, and the arithmetic of chaos. The book represents a balanced overview of the field and is a worthy addition to the reading lists of researchers and students interested in any of the varied, and sometimes bizarre, aspects of this intriguing subject.
Download or read book Stochastic Quantum Mechanics and Quantum Spacetime written by Margaret Prugovecki and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 319 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Quantum Chaos written by Katsuhiro Nakamura and published by CUP Archive. This book was released on 1994-06-02 with total page 228 pages. Available in PDF, EPUB and Kindle. Book excerpt: Past studies on chaos have been concerned with classical systems but this book is one of the first to deal with quantum chaos.
Download or read book The Transition to Chaos written by Linda Reichl and published by Springer Nature. This book was released on 2021-04-12 with total page 555 pages. Available in PDF, EPUB and Kindle. Book excerpt: Based on courses given at the universities of Texas and California, this book treats an active field of research that touches upon the foundations of physics and chemistry. It presents, in as simple a manner as possible, the basic mechanisms that determine the dynamical evolution of both classical and quantum systems in sufficient generality to include quantum phenomena. The book begins with a discussion of Noether's theorem, integrability, KAM theory, and a definition of chaotic behavior; continues with a detailed discussion of area-preserving maps, integrable quantum systems, spectral properties, path integrals, and periodically driven systems; and concludes by showing how to apply the ideas to stochastic systems. The presentation is complete and self-contained; appendices provide much of the needed mathematical background, and there are extensive references to the current literature; while problems at the ends of chapters help students clarify their understanding. This new edition has an updated presentation throughout, and a new chapter on open quantum systems.
Download or read book Quantum Chaos and Mesoscopic Systems written by N.E. Hurt and published by Springer Science & Business Media. This book was released on 1997-02-28 with total page 362 pages. Available in PDF, EPUB and Kindle. Book excerpt: 4. 2 Variance of Quantum Matrix Elements. 125 4. 3 Berry's Trick and the Hyperbolic Case 126 4. 4 Nonhyperbolic Case . . . . . . . 128 4. 5 Random Matrix Theory . . . . . 128 4. 6 Baker's Map and Other Systems 129 4. 7 Appendix: Baker's Map . . . . . 129 5 Error Terms 133 5. 1 Introduction. . . . . . . . . . . . . . . . . . . . . . . 133 5. 2 The Riemann Zeta Function in Periodic Orbit Theory 135 5. 3 Form Factor for Primes . . . . . . . . . . . . . . . . . 137 5. 4 Error Terms in Periodic Orbit Theory: Co-compact Case. 138 5. 5 Binary Quadratic Forms as a Model . . . . . . . . . . . . 139 6 Co-Finite Model for Quantum Chaology 141 6. 1 Introduction. . . . . . . . 141 6. 2 Co-finite Models . . . . . 141 6. 3 Geodesic Triangle Spaces 144 6. 4 L-Functions. . . . . . . . 145 6. 5 Zelditch's Prime Geodesic Theorem. 146 6. 6 Zelditch's Pseudo Differential Operators 147 6. 7 Weyl's Law Generalized 148 6. 8 Equidistribution Theory . . . . . . . . . 150 7 Landau Levels and L-Functions 153 7. 1 Introduction. . . . . . . . . . . . . . . . . . . . . . . 153 7. 2 Landau Model: Mechanics on the Plane and Sphere. 153 7. 3 Landau Model: Mechanics on the Half-Plane 155 7. 4 Selberg's Spectral Theorem . . . . . . . . . . . 157 7. 5 Pseudo Billiards . . . . . . . . . . . . . . . . . 158 7. 6 Landau Levels on a Compact Riemann Surface 159 7. 7 Automorphic Forms . . . . . 160 7. 8 Maass-Selberg Trace Formula 162 7. 9 Degeneracy by Selberg. . . . 163 7. 10 Hecke Operators . . . . . . . 163 7. 11 Selberg Trace Formula for Hecke Operators 167 7. 12 Eigenvalue Statistics on X . . . . 169 7. 13 Mesoscopic Devices. . . . . . . . 170 7. 14 Hall Conductance on Leaky Tori 170 7.
Download or read book Quantum Chaos written by Giulio Casati and published by Cambridge University Press. This book was released on 1995-04-27 with total page 703 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a comprehensive overview of our understanding of chaotic behaviour in quantum systems.
Download or read book Chaotic Behavior in Quantum Systems written by Giulio Casati and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 380 pages. Available in PDF, EPUB and Kindle. Book excerpt: Six years ago, in June 1977, the first international conference on chaos in classical dynamical systems took place here in Como. For the first time, physicists, mathematicians, biologists, chemists, economists, and others got together to discuss the relevance of the recent progress in nonlinear classical dynamics for their own research field. Immediately after, pUblication of "Nonlinear Science Abstracts" started, which, in turn, led to the Physica D Journal and to a rapid increase of the research activity in the whole area with the creation of numerous "Nonlinear Centers" around the world. During these years great progress has been made in understanding the qualitative behavior of classical dynamical systems and now we can appreciate the beautiful complexity and variety of their motion. Meanwhile, an increasing number of scientists began to wonder whether and how such beautiful structures would persist in quantum motion. Indeed, mainly integrable systems have been previously con sidered by Quantum Mechanics and therefore the problem is open how to describe the qualitative behavior of systems whose classical limit is non-integrable. The present meeting was organized in view of the fact that scientists working in different fields - mathematicians, theoretical physicists, solid state physicists, nuclear physicists, chemists and others - had common problems. Moreover, we felt that it was necessary to clarify some fundamental questions concerning the logical basis for the discussion including the very definition of chaos in Quantum Mechanics.
Download or read book Quantum Measurement and Chaos written by Edward Roy Pike and published by Plenum Publishing Corporation. This book was released on 1987 with total page 288 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Classical Nonintegrability Quantum Chaos written by Andreas Knauf and published by Birkhäuser. This book was released on 2012-12-06 with total page 104 pages. Available in PDF, EPUB and Kindle. Book excerpt: Our DMV Seminar on 'Classical Nonintegrability, Quantum Chaos' intended to introduce students and beginning researchers to the techniques applied in nonin tegrable classical and quantum dynamics. Several of these lectures are collected in this volume. The basic phenomenon of nonlinear dynamics is mixing in phase space, lead ing to a positive dynamical entropy and a loss of information about the initial state. The nonlinear motion in phase space gives rise to a linear action on phase space functions which in the case of iterated maps is given by a so-called transfer operator. Good mixing rates lead to a spectral gap for this operator. Similar to the use made of the Riemann zeta function in the investigation of the prime numbers, dynamical zeta functions are now being applied in nonlinear dynamics. In Chapter 2 V. Baladi first introduces dynamical zeta functions and transfer operators, illustrating and motivating these notions with a simple one-dimensional dynamical system. Then she presents a commented list of useful references, helping the newcomer to enter smoothly into this fast-developing field of research. Chapter 3 on irregular scattering and Chapter 4 on quantum chaos by A. Knauf deal with solutions of the Hamilton and the Schr6dinger equation. Scatter ing by a potential force tends to be irregular if three or more scattering centres are present, and a typical phenomenon is the occurrence of a Cantor set of bounded orbits. The presence of this set influences those scattering orbits which come close.
Download or read book Dissipative Quantum Chaos and Decoherence written by Daniel Braun and published by Springer Science & Business Media. This book was released on 2001-01-25 with total page 139 pages. Available in PDF, EPUB and Kindle. Book excerpt: This overview of the state of the art of research in an exciting field mainly emphasizes the development of a semiclassical formalism that allows one to incorporate the effect of dissipation and decoherence in a precise, yet tractable way into the quantum mechanics of classically chaotic systems.
