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Author: Dieter Schuch
Publisher: Springer
ISBN: 3319655949
Category : Science
Languages : en
Pages : 261
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Book Description
This book provides a unique survey displaying the power of Riccati equations to describe reversible and irreversible processes in physics and, in particular, quantum physics. Quantum mechanics is supposedly linear, invariant under time-reversal, conserving energy and, in contrast to classical theories, essentially based on the use of complex quantities. However, on a macroscopic level, processes apparently obey nonlinear irreversible evolution equations and dissipate energy. The Riccati equation, a nonlinear equation that can be linearized, has the potential to link these two worlds when applied to complex quantities. The nonlinearity can provide information about the phase-amplitude correlations of the complex quantities that cannot be obtained from the linearized form. As revealed in this wide ranging treatment, Riccati equations can also be found in many diverse fields of physics from Bose-Einstein-condensates to cosmology. The book will appeal to graduate students and theoretical physicists interested in a consistent mathematical description of physical laws.
Author: Dieter Schuch
Publisher: Springer
ISBN: 3319655949
Category : Science
Languages : en
Pages : 261
Get Book Here
Book Description
This book provides a unique survey displaying the power of Riccati equations to describe reversible and irreversible processes in physics and, in particular, quantum physics. Quantum mechanics is supposedly linear, invariant under time-reversal, conserving energy and, in contrast to classical theories, essentially based on the use of complex quantities. However, on a macroscopic level, processes apparently obey nonlinear irreversible evolution equations and dissipate energy. The Riccati equation, a nonlinear equation that can be linearized, has the potential to link these two worlds when applied to complex quantities. The nonlinearity can provide information about the phase-amplitude correlations of the complex quantities that cannot be obtained from the linearized form. As revealed in this wide ranging treatment, Riccati equations can also be found in many diverse fields of physics from Bose-Einstein-condensates to cosmology. The book will appeal to graduate students and theoretical physicists interested in a consistent mathematical description of physical laws.
Author: Alexander G. Kyriakos
Publisher: AKVY PRESS
ISBN: 0980966744
Category : Quantum field theory
Languages : en
Pages : 164
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Book Description
The author proposes a special nonlinear quantum field theory. In a linear approximation, this theory can be presented in the form of the Standard Model (SM) theory. The richer physical structure of this nonlinear theory makes it possible to exceed the limits of SM and remove its known incompleteness. We show that nonlinearity of the field is critical for the appearance of charges and masses of elementary particles, for confinement of quarks, and many other effects, whose description within the framework of SM causes difficulties. In this case, the mechanism of generation of masses is mathematically similar to Higgs's mechanism, but it is considerably simpler and does not include the additional particles. The proposed theory does not examine the theory of gravity, but reveals the mathematical similarity of the nonlinear field equations of both theories. The book is intended for undergraduate and graduate students studying the theory of elementary particles, as well as for specialists working in this field.
Author: Philip Barnes Burt
Publisher: CRC Press
ISBN: 9783718600724
Category : Science
Languages : en
Pages : 352
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Book Description
Author: J R Croca
Publisher: World Scientific
ISBN: 9814487147
Category : Science
Languages : en
Pages : 228
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Book Description
The author of this book presents conceptual and experimental evidence showing that Heisenberg's uncertainty relations are not valid in all cases. Furthermore, he derives a more general set of uncertainty relations. The new relations result from the replacement of the Fourier nonlocal and nontemporal paradigm by wavelet local analysis. These results lead to a coherent and beautiful causal synthesis unifying quantum and classical physics.
Author: Xiao-feng Pang
Publisher: World Scientific
ISBN: 9814481238
Category : Science
Languages : en
Pages : 644
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Book Description
In the history of physics and science, quantum mechanics has served as the foundation of modern science. This book discusses the properties of microscopic particles in nonlinear systems, principles of the nonlinear quantum mechanical theory, and its applications in condensed matter, polymers and biological systems.The book is essentially composed of three parts. The first part presents a review of linear quantum mechanics, as well as theoretical and experimental fundamentals that establish the nonlinear quantum mechanical theory. The theory itself and its essential features are covered in the second part. In the final part, extensive applications of this theory in physics, biology and polymer are introduced. The whole volume forms a complete system of nonlinear quantum mechanics.The book is intended for researchers, graduate students as well as upper-level undergraduates.
Author: Peter Henri Bortoft
Publisher:
ISBN:
Category :
Languages : en
Pages :
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Book Description
Author: Cini
Publisher: Routledge
ISBN: 1351420348
Category : Science
Languages : en
Pages : 188
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Book Description
Quantum theory offers a strange, and perhaps unique, case in the history of science. Although research into its roots has provided important results in recent years, the debate goes on. Some theorists argue that quantum theory is weakened by the inclusion of the so called "reduction of the state vector" in its foundations. Quantum Theory without Reduction presents arguments in favor of quantum theory as a consistent and complete theory without this reduction and as a theory capable of explaining all known features of the measurement problem. This collection of invited contributions defines and explores different aspects of this issue, bringing an old debate into a new perspective and leading to a more satisfying consensus about quantum theory. The book will be of interest to researchers in theoretical physics and mathematical physics involved in the foundations of quantum theory. Scientists, engineers, and philosophers interested in the conceptual problems of quantum theory will also find this work stimulating.
Author: A Kundu
Publisher: CRC Press
ISBN: 1420034618
Category : Science
Languages : en
Pages : 310
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Book Description
Covering both classical and quantum models, nonlinear integrable systems are of considerable theoretical and practical interest, with applications over a wide range of topics, including water waves, pin models, nonlinear optics, correlated electron systems, plasma physics, and reaction-diffusion processes. Comprising one part on classical theories
Author: Andrey Anatoljevich Grib
Publisher: Springer Science & Business Media
ISBN: 1461546877
Category : Science
Languages : en
Pages : 223
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Book Description
The nonlocality phenomena exhibited by entangled quantum systems are certainly one of the most extraordinary aspects of quantum theory. This book discusses this phe nomenon according to several points of view, i.e., according to different interpretations of the mathematics of the quantum formalism. The several interpretations of the Copenhagen interpretation, the many worlds, the de Broglie-Bohm, quantum logics, the decohering by the environment approach and the histories approach interpretations are scrutinized and criticized in detail. Recent results on cryptography, quantum bit commitment, quantum erasers and teleportation are also presented and discussed. In preparing the book we benefited from discussions with many people, but we would like, in particular, to express our gratitude to Professor B. d'Espagnat for his useful comments and suggestions. We are grateful also to Ms. L. Gentry EI-Dash for the English revision, to Dr. 1. E. Maiorino for the production of the figures and a careful reading of the manuscript, and for the statI of Plenum for advice and for having produced a nice book. Finally, the authors thank FAPESP (contract no. I 99612657-0) for a grant making this book possible. A. A. ORIB AND W. A. RODRIGUES, JR.
Author: Heinz-dietrich Doebner
Publisher: World Scientific
ISBN: 981454924X
Category :
Languages : en
Pages : 494
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Book Description
In recent years nonlinear and irreversible quantum mechanics is becoming increasingly important because of the availability of precision experiments. There are new and successful attempts to understand quantum irreversibility. The development of generalized symmetries has to led to new families of evolution equations for pure and mixed states. On the one hand, this timely symposium covers nonlinear and irreversible quantum mechanics, the theory of quantization methods, causality and various problems important in this context. On the other hand, it reports the development of quantum group symmetries, and of methods to construct deformed quantum mechanical evolution equations like the q-deformed Schrödinger equations.
