effective evolution equations from quantum dynamics springerbriefs in mathematical physics

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Effective Evolution Equations From Quantum Dynamics

Author : Niels Benedikter
ISBN : 9783319248981
Genre : Science
File Size : 83. 86 MB
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These notes investigate the time evolution of quantum systems, and in particular the rigorous derivation of effective equations approximating the many-body Schrödinger dynamics in certain physically interesting regimes. The focus is primarily on the derivation of time-dependent effective theories (non-equilibrium question) approximating many-body quantum dynamics. The book is divided into seven sections, the first of which briefly reviews the main properties of many-body quantum systems and their time evolution. Section 2 introduces the mean-field regime for bosonic systems and explains how the many-body dynamics can be approximated in this limit using the Hartree equation. Section 3 presents a method, based on the use of coherent states, for rigorously proving the convergence towards the Hartree dynamics, while the fluctuations around the Hartree equation are considered in Section 4. Section 5 focuses on a discussion of a more subtle regime, in which the many-body evolution can be approximated by means of the nonlinear Gross-Pitaevskii equation. Section 6 addresses fermionic systems (characterized by antisymmetric wave functions); here, the fermionic mean-field regime is naturally linked with a semiclassical regime, and it is proven that the evolution of approximate Slater determinants can be approximated using the nonlinear Hartree-Fock equation. In closing, Section 7 reexamines the same fermionic mean-field regime, but with a focus on mixed quasi-free initial data approximating thermal states at positive temperature.

Advances In Quantum Mechanics

Author : Alessandro Michelangeli
ISBN : 9783319589046
Genre : Mathematics
File Size : 34. 30 MB
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This volume collects recent contributions on the contemporary trends in the mathematics of quantum mechanics, and more specifically in mathematical problems arising in quantum many-body dynamics, quantum graph theory, cold atoms, unitary gases, with particular emphasis on the developments of the specific mathematical tools needed, including: linear and non-linear Schrödinger equations, topological invariants, non-commutative geometry, resonances and operator extension theory, among others. Most of contributors are international leading experts or respected young researchers in mathematical physics, PDE, and operator theory. All their material is the fruit of recent studies that have already become a reference in the community. Offering a unified perspective of the mathematics of quantum mechanics, it is a valuable resource for researchers in the field.

Lieb Robinson Bounds For Multi Commutators And Applications To Response Theory

Author : Jean-Bernard Bru
ISBN : 9783319457840
Genre : Science
File Size : 40. 44 MB
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Lieb-Robinson bounds for multi-commutators are effective mathematical tools to handle analytic aspects of infinite volume dynamics of non-relativistic quantum particles with short-range, possibly time-dependent interactions.In particular, the existence of fundamental solutions is shown for those (non-autonomous) C*-dynamical systems for which the usual conditions found in standard theories of (parabolic or hyperbolic) non-autonomous evolution equations are not given. In mathematical physics, bounds on multi-commutators of an order higher than two can be used to study linear and non-linear responses of interacting particles to external perturbations. These bounds are derived for lattice fermions, in view of applications to microscopic quantum theory of electrical conduction discussed in this book. All results also apply to quantum spin systems, with obvious modifications. In order to make the results accessible to a wide audience, in particular to students in mathematics with little Physics background, basics of Quantum Mechanics are presented, keeping in mind its algebraic formulation. The C*-algebraic setting for lattice fermions, as well as the celebrated Lieb-Robinson bounds for commutators, are explained in detail, for completeness.

Quantum Physics Fuzzy Sets And Logic

Author : Jarosław Pykacz
ISBN : 9783319193847
Genre : Science
File Size : 27. 26 MB
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This Brief presents steps towards elaborating a new interpretation of quantum mechanics based on a specific version of Łukasiewicz infinite-valued logic. It begins with a short survey of main interpretations of quantum mechanics already proposed, as well as various models of many-valued logics and previous attempts to apply them for the description of quantum phenomena. The prospective many-valued interpretation of quantum mechanics is soundly based on a theorem concerning the isomorphic representation of Birkhoff-von Neumann quantum logic in the form of a special Łukasiewicz infinite-valued logic endowed with partially defined conjunctions and disjunctions.

Open Quantum Systems

Author : Ángel Rivas
ISBN : 3642233546
Genre : Science
File Size : 30. 85 MB
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In this volume the fundamental theory of open quantum systems is revised in the light of modern developments in the field. A unified approach to the quantum evolution of open systems is presented by merging concepts and methods traditionally employed by different communities, such as quantum optics, condensed matter, chemical physics and mathematical physics. The mathematical structure and the general properties of the dynamical maps underlying open system dynamics are explained in detail. The microscopic derivation of dynamical equations, including both Markovian and non-Markovian evolutions, is also discussed. Because of the step-by-step explanations, this work is a useful reference to novices in this field. However, experienced researches can also benefit from the presentation of recent results.

The Geometry Of Special Relativity A Concise Course

Author : Norbert Dragon
ISBN : 9783642283291
Genre : Science
File Size : 37. 19 MB
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In this concise primer it is shown that, with simple diagrams, the phenomena of time dilatation, length contraction and Lorentz transformations can be deduced from the fact that in a vacuum one cannot distinguish physically straight and uniform motion from rest, and that the speed of light does not depend on the speed of either the source or the observer. The text proceeds to derive the important results of relativistic physics and to resolve its apparent paradoxes. A short introduction into the covariant formulation of electrodynamics is also given. This publication addresses, in particular, students of physics and mathematics in their final undergraduate year.

Automatic Trend Estimation

Author : C ̆alin Vamos ̧
ISBN : 9789400748248
Genre : Science
File Size : 23. 6 MB
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Our book introduces a method to evaluate the accuracy of trend estimation algorithms under conditions similar to those encountered in real time series processing. This method is based on Monte Carlo experiments with artificial time series numerically generated by an original algorithm. The second part of the book contains several automatic algorithms for trend estimation and time series partitioning. The source codes of the computer programs implementing these original automatic algorithms are given in the appendix and will be freely available on the web. The book contains clear statement of the conditions and the approximations under which the algorithms work, as well as the proper interpretation of their results. We illustrate the functioning of the analyzed algorithms by processing time series from astrophysics, finance, biophysics, and paleoclimatology. The numerical experiment method extensively used in our book is already in common use in computational and statistical physics.

From Stars To States

Author : Thierry J.-L. Courvoisier
ISBN : 9783319592329
Genre : Science
File Size : 50. 91 MB
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The aim of this essay is to understand the relationship between knowledge and society and to reflect on the links between science and political decision making. The text evolved from a number of reflections the author made while president of the European Astronomical Society, president of the Swiss Academy of Sciences and vice-president of the European Academies Science Advisory Council (EASAC). The book starts by using astronomy as a showcase for what science brings to society in terms of intellectual enrichment, of practical tools and of societal inputs. It then turns to looking generally at science as a human endeavour for which pleasure is a prime motivation and it describes the efforts made by researchers to rationalise their findings, thus making them universally acceptable. The author also describes the role of science in shaping our environment and discusses resulting responsibility of the scientists with respect to the evolution of the world. As part of an analysis of the relationship between science and policy the author describes the way in which scientists can (and must) bring knowledge in the political decision making process. The argument is closed with considerations on global governance, while the conclusion puts evidence based decision making processes in relation with the more emotional aspects of our behaviour. The readership of the book is intended to be all scientists involved in “science for policy” activities, as well as those who should become more active in this domain. This includes, but is not limited to, all members of science academies. Astronomers will find specific elements to help them think about their science. The intended readers of the book also include civil servants and policy makers who develop legislation and societal action in domains in which a solid knowledge base is important. The book should furthermore be of interest to citizens following public life and all those worried by the “post evidence” trends in policy.

Fractional Order Devices

Author : Karabi Biswas
ISBN : 9783319544601
Genre : Technology & Engineering
File Size : 77. 75 MB
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This book focuses on two specific areas related to fractional order systems – the realization of physical devices characterized by non-integer order impedance, usually called fractional-order elements (FOEs); and the characterization of vegetable tissues via electrical impedance spectroscopy (EIS) – and provides readers with new tools for designing new types of integrated circuits. The majority of the book addresses FOEs. The interest in these topics is related to the need to produce “analogue” electronic devices characterized by non-integer order impedance, and to the characterization of natural phenomena, which are systems with memory or aftereffects and for which the fractional-order calculus tool is the ideal choice for analysis. FOEs represent the building blocks for designing and realizing analogue integrated electronic circuits, which the authors believe hold the potential for a wealth of mass-market applications. The freedom to choose either an integer- or non-integer-order analogue integrator/derivator is a new one for electronic circuit designers. The book shows how specific non-integer-order impedance elements can be created using materials with specific structural properties. EIS measures the electrical impedance of a specimen across a given range of frequencies, producing a spectrum that represents the variation of the impedance versus frequency – a technique that has the advantage of avoiding aggressive examinations. Biological tissues are complex systems characterized by dynamic processes that occur at different lengths and time scales; this book proposes a model for vegetable tissues that describes the behavior of such materials by considering the interactions among various relaxing phenomena and memory effects.

Fundamentals Of Plasma Physics

Author : J. A. Bittencourt
ISBN : 9781483293196
Genre : Science
File Size : 42. 59 MB
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A general introduction designed to present a comprehensive, logical and unified treatment of the fundamentals of plasma physics based on statistical kinetic theory. Its clarity and completeness make it suitable for self-learning and self-paced courses. Problems are included.

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