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Classical Nonintegrability, Quantum Chaos

Classical Nonintegrability, Quantum Chaos
Author: Andreas Knauf
Publisher: Birkhäuser
Total Pages: 104
Release: 2012-12-06
Genre: Science
ISBN: 3034889321

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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.


Quantum Non-integrability

Quantum Non-integrability
Author: Da Hsuan Feng
Publisher:
Total Pages: 0
Release: 1992
Genre: Chaotic behavior in systems
ISBN:

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Quantum Non-integrability

Quantum Non-integrability
Author: Da-hsuan Feng
Publisher: World Scientific
Total Pages: 562
Release: 1992-09-30
Genre:
ISBN: 9814635685

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Recent developments in nonlinear dynamics has significantly altered our basic understanding of the foundations of classical physics. However, it is quantum mechanics, not classical mechanics, which describes the motion of the nucleons, atoms, and molecules in the microscopic world. What are then the quantum signatures of the ubiquitous chaotic behavior observed in classical physics? In answering this question one cannot avoid probing the deepest foundations connecting classical and quantum mechanics. This monograph reviews some of the most current thinkings and developments in this exciting field of physics.


Integrability and Nonintegrability in Geometry and Mechanics

Integrability and Nonintegrability in Geometry and Mechanics
Author: A.T. Fomenko
Publisher: Springer Science & Business Media
Total Pages: 358
Release: 2012-12-06
Genre: Mathematics
ISBN: 9400930690

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Approach your problems from the right end It isn't that they can't see the solution. It is and begin with the answers. 1hen one day, that they can't see the problem. perhaps you will find the final question. G. K. Chesterton. The Scandal of Father 'The Hermit Oad in Crane Feathers' in R. Brown 'The point of a Pin' . • 1111 Oulik'. n. . Chi" •. • ~ Mm~ Mu,d. ", Growing specialization and diversification have brought a host of monographs and textbooks on increasingly specialized topics. However, the "tree" of knowledge of mathematics and related fields does not grow only by putting forth new branches. It also happens, quite often in fact, that branches which were thought to be completely disparate are suddenly seen to be related. Further, the kind and level of sophistication of mathematics applied in various sciences has changed drastically in recent years: measure theory is used (non-trivially) in regional and theoretical economics; algebraic geometry interacts with physics; the Minkowsky lemma, coding theory and the structure of water meet one another in packing and covering theory; quantum fields, crystal defects and mathematical programming profit from homotopy theory; Lie algebras are relevant to filtering; and prediction and electrical engineering can use Stein spaces. And in addition to this there are such new emerging subdisciplines as "experimental mathematics", "CFD", "completely integrable systems", "chaos, synergetics and large-scale order", which are almost impossible to fit into the existing classification schemes. They draw upon widely different sections of mathematics.


What Is Integrability?

What Is Integrability?
Author: Vladimir E. Zakharov
Publisher: Springer Science & Business Media
Total Pages: 339
Release: 2012-12-06
Genre: Science
ISBN: 3642887031

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The idea of devoting a complete book to this topic was born at one of the Workshops on Nonlinear and Turbulent Processes in Physics taking place reg ularly in Kiev. With the exception of E. D. Siggia and N. Ercolani, all authors of this volume were participants at the third of these workshops. All of them were acquainted with each other and with each other's work. Yet it seemed to be somewhat of a discovery that all of them were and are trying to understand the same problem - the problem of integrability of dynamical systems, primarily Hamiltonian ones with an infinite number of degrees of freedom. No doubt that they (or to be more exact, we) were led to this by the logical process of scientific evolution which often leads to independent, almost simultaneous discoveries. Integrable, or, more accurately, exactly solvable equations are essential to theoretical and mathematical physics. One could say that they constitute the "mathematical nucleus" of theoretical physics whose goal is to describe real clas sical or quantum systems. For example, the kinetic gas theory may be considered to be a theory of a system which is trivially integrable: the system of classical noninteracting particles. One of the main tasks of quantum electrodynamics is the development of a theory of an integrable perturbed quantum system, namely, noninteracting electromagnetic and electron-positron fields.


Quantum Communication, Computing, and Measurement

Quantum Communication, Computing, and Measurement
Author: Osamu Hirota
Publisher: Springer Science & Business Media
Total Pages: 521
Release: 2012-12-06
Genre: Mathematics
ISBN: 1461559235

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This volume contains the proceedings of the Third International Conference on Quantum Communication and Measurement. The series of international conferences on quantum communication and measurement was established to encourage scientists working in the interdisciplinary research fields of quantum communication science and technology. The first such conference, organized by C. Benjaballah and O. Hirota under the title "Quantum Aspects of Optical Communication," assembled approximately 80 researchers in Paris in 1990. The second conference, held in Nottingham in 1994, was organized by V. P. Belavkin, R. L. Hudson, and O. Hirota and attracted about 130 participants from 22 countries. The present conference, organized by O. Hirota, A. S. Holevo, C. M. Caves, H. P. Yuen, and L. Accardi, was heldSeptember 25-30, 1996, in Fuji-Hakone Land, Japan, andjnvolved about 120 researchers from 15 countries. The topics at this third conference included the foundations of quantum communi cation and information theory, quantum measurement theory, quantum cryptography and quantum computation, quantum devices and high-precision measurements, gener ation of nonclassical light, and atom optics. Special emphasis was placed on bringing together research workers in experimental and engineering fields of quantum commu nication and quantum computing and theoreticians working in quantum measurement and information theory. Nineteen plenary and parallel sessions and one poster ses sion were organized, at which a total of 82 papers were presented. Interesting and stimulating scientific discussions took place between and after sessions as well as in the evenings.


Non-Hermitian Quantum Mechanics

Non-Hermitian Quantum Mechanics
Author: Nimrod Moiseyev
Publisher: Cambridge University Press
Total Pages: 409
Release: 2011-02-17
Genre: Science
ISBN: 1139496999

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Non-Hermitian quantum mechanics (NHQM) is an important alternative to the standard (Hermitian) formalism of quantum mechanics, enabling the solution of otherwise difficult problems. The first book to present this theory, it is useful to advanced graduate students and researchers in physics, chemistry and engineering. NHQM provides powerful numerical and analytical tools for the study of resonance phenomena - perhaps one of the most striking events in nature. It is especially useful for problems whose solutions cause extreme difficulties within the structure of a conventional Hermitian framework. NHQM has applications in a variety of fields, including optics, where the refractive index is complex; quantum field theory, where the parity-time (PT) symmetry properties of the Hamiltonian are investigated; and atomic and molecular physics and electrical engineering, where complex potentials are introduced to simplify numerical calculations.


Current Topics In Physics - Proceedings Of The Inauguration Conference Of The Asia-pacific Center For Theoretical Physics (In 2 Volumes)

Current Topics In Physics - Proceedings Of The Inauguration Conference Of The Asia-pacific Center For Theoretical Physics (In 2 Volumes)
Author: Yongmin Cho
Publisher: World Scientific
Total Pages: 1156
Release: 1998-04-04
Genre:
ISBN: 9814545538

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This volume is a collection of lectures on the current topics in various areas of physics which were presented at the Inauguration Conference of Asia-Pacific Center for Theoretical Physics.


A Collection of Papers on Chaos Theory and Its Applications

A Collection of Papers on Chaos Theory and Its Applications
Author: Paul Bracken
Publisher: BoD – Books on Demand
Total Pages: 265
Release: 2021-04-14
Genre: Mathematics
ISBN: 1839628588

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This current volume contains 12 new papers on the subject of chaos in the physical sciences, which was initiated with the publication of the book Research Advances in Chaos Theory. It is clear the subject continues to attract a great deal of attention among scientists in the scientific community. This volume looks at such problems as chaos in nonlinear systems, in dynamical systems, quantum chaos, biological applications, and a few new emerging areas as well.


Quantum Mechanics for Mathematicians

Quantum Mechanics for Mathematicians
Author: Leon Armenovich Takhtadzhi͡an
Publisher: American Mathematical Soc.
Total Pages: 410
Release: 2008
Genre: Mathematics
ISBN: 0821846302

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Presents a comprehensive treatment of quantum mechanics from a mathematics perspective. Including traditional topics, like classical mechanics, mathematical foundations of quantum mechanics, quantization, and the Schrodinger equation, this book gives a mathematical treatment of systems of identical particles with spin.