Quantum Control: Mathematical and Numerical Challenges PDF Download

Author: André D. Bandrauk
Publisher: American Mathematical Soc.
ISBN: 9780821833308
Category : Science
Languages : en
Pages : 228

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Book Description
It brought together mathematicians, theoretical chemists, and physicists working in the area of control and optimization of systems to address the outstanding numerical and mathematical problems."

Author: Alfio Borzi
Publisher: SIAM
ISBN: 1611974836
Category : Technology & Engineering
Languages : en
Pages : 396

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Book Description
This book provides an introduction to representative nonrelativistic quantum control problems and their theoretical analysis and solution via modern computational techniques. The quantum theory framework is based on the Schr?dinger picture, and the optimization theory, which focuses on functional spaces, is based on the Lagrange formalism. The computational techniques represent recent developments that have resulted from combining modern numerical techniques for quantum evolutionary equations with sophisticated optimization schemes. Both finite and infinite-dimensional models are discussed, including the three-level Lambda system arising in quantum optics, multispin systems in NMR, a charged particle in a well potential, Bose?Einstein condensates, multiparticle spin systems, and multiparticle models in the time-dependent density functional framework. This self-contained book covers the formulation, analysis, and numerical solution of quantum control problems and bridges scientific computing, optimal control and exact controllability, optimization with differential models, and the sciences and engineering that require quantum control methods. ??

Author: N. U. Ahmed
Publisher: Springer Nature
ISBN: 3031372603
Category : Mathematics
Languages : en
Pages : 236

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Book Description
This book offers the first comprehensive presentation of measure-valued solutions for nonlinear deterministic and stochastic evolution equations on infinite dimensional Banach spaces. Unlike traditional solutions, measure-valued solutions allow for a much broader class of abstract evolution equations to be addressed, providing a broader approach. The book presents extensive results on the existence of measure-valued solutions for differential equations that have no solutions in the usual sense. It covers a range of topics, including evolution equations with continuous/discontinuous vector fields, neutral evolution equations subject to vector measures as impulsive forces, stochastic evolution equations, and optimal control of evolution equations. The optimal control problems considered cover the existence of solutions, necessary conditions of optimality, and more, significantly complementing the existing literature. This book will be of great interest to researchers in functional analysis, partial differential equations, dynamic systems and their optimal control, and their applications, advancing previous research and providing a foundation for further exploration of the field.

Author: Jean Levine
Publisher: Springer Science & Business Media
ISBN: 3642161340
Category : Technology & Engineering
Languages : en
Pages : 374

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Book Description
In the 60's, control, signals and systems had a common linear algebraic background and, according to their evolution, their respective backgrounds have now dramatically differed. Recovering such a common background, especially in the nonlinear context, is currently a fully open question. The role played by physical models, finite or infinite dimensional, in this hypothetical convergence is extensively discussed in this book. The discussion does not only take place on a theoretical basis but also in the light of two wide classes of applications, among the most active in the current industrially oriented researches: - Electrical and Mechatronical systems; - Chemical Processes and systems appearing in Life Sciences. In this perspective, this book is a contribution to the enhancement of the dialogue between theoretical laboratories and more practically oriented ones and industries. This book is a collection of articles that have been presented by leading international experts at a series of three workshops of a Bernoulli program entitled “Advances in the Theory of Control, Signals and Systems, with Physical Modeling” hosted by the Bernoulli Centre of EPFL during the first semester of 2009. It provides researchers, engineers and graduate students with an unprecedented collection of topics and internationally acknowledged top-quality works and surveys.

Author: Ning Xi
Publisher: CRC Press
ISBN: 1466554061
Category : Mathematics
Languages : en
Pages : 175

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Book Description
Micro/nano-scale engineering—especially the design and implementation of ultra-fast and ultra-scale energy devices, sensors, and cellular and molecular systems—remains a daunting challenge. Modeling and control has played an essential role in many technological breakthroughs throughout the course of history. Therefore, the need for a practical guide to modeling and control for micro/nano-scale devices and systems has emerged. The first edited volume to address this rapidly growing field, Modeling and Control for Micro/Nano Devices and Systems gives control engineers, lab managers, high-tech researchers, and graduate students easy access to the expert contributors’ cutting-edge knowledge of micro/nanotechnology, energy, and bio-systems. The editors offer an integrated view from theory to practice, covering diverse topics ranging from micro/nano-scale sensors to energy devices and control of biology systems in cellular and molecular levels. The book also features numerous case studies for modeling of micro/nano devices and systems, and explains how the models can be used for control and optimization purposes. Readers benefit from learning the latest modeling techniques for micro/nano-scale devices and systems, and then applying those techniques to their own research and development efforts.

Author: Qi Lü
Publisher: Springer Nature
ISBN: 3030823318
Category : Science
Languages : en
Pages : 592

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Book Description
This is the first book to systematically present control theory for stochastic distributed parameter systems, a comparatively new branch of mathematical control theory. The new phenomena and difficulties arising in the study of controllability and optimal control problems for this type of system are explained in detail. Interestingly enough, one has to develop new mathematical tools to solve some problems in this field, such as the global Carleman estimate for stochastic partial differential equations and the stochastic transposition method for backward stochastic evolution equations. In a certain sense, the stochastic distributed parameter control system is the most general control system in the context of classical physics. Accordingly, studying this field may also yield valuable insights into quantum control systems. A basic grasp of functional analysis, partial differential equations, and control theory for deterministic systems is the only prerequisite for reading this book.

Author: Piergiulio Tempesta
Publisher: American Mathematical Soc.
ISBN: 0821833294
Category : Mathematics
Languages : en
Pages : 362

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Book Description
Superintegrable systems are integrable systems (classical and quantum) that have more integrals of motion than degrees of freedom. Such systems have many interesting properties. This title is based on the Workshop on Superintegrability in Classical and Quantum Systems organized by the Centre de Recherches Mathematiques in Montreal (Quebec).

Author: Pavel Winternitz
Publisher: American Mathematical Soc.
ISBN: 9780821870341
Category : Mathematics
Languages : en
Pages : 316

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Book Description
The Workshop on Group Theory and Numerical Analysis brought together scientists working in several different but related areas. The unifying theme was the application of group theory and geometrical methods to the solution of differential and difference equations. The emphasis was on the combination of analytical and numerical methods and also the use of symbolic computation. This meeting was organized under the auspices of the Centre de Recherches Mathematiques, Universite de Montreal (Canada). This volume has the character of a monograph and should represent a useful reference book for scientists working in this highly topical field.

Author: Alexander Y. Khapalov
Publisher: Springer
ISBN: 3642124135
Category : Mathematics
Languages : en
Pages : 296

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Book Description
This monograph addresses the global controllability of partial differential equations in the context of multiplicative (or bilinear) controls, which enter the model equations as coefficients. The methodology is illustrated with a variety of model equations.

Author: P. Tempesta, P. Winternitz, J. Harnad, W. Miller, Jr., G. Pogosyan, and M. Rodriguez
Publisher: American Mathematical Soc.
ISBN: 9780821870327
Category : Differential equations, Partial
Languages : en
Pages : 364

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Book Description
Superintegrable systems are integrable systems (classical and quantum) that have more integrals of motion than degrees of freedom. Such systems have many interesting properties. This title is based on the Workshop on Superintegrability in Classical and Quantum Systems organized by the Centre de Recherches Mathematiques in Montreal (Quebec).