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Development Of New Quantum Optimal Control Algorithms And Exact Optimized Effective Potential In Time Dependent Density Functional Theory
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Book Synopsis Development of New Quantum Optimal Control Algorithms and Exact Optimized Effective Potential in Time-dependent Density Functional Theory by : 廖聖侖
Download or read book Development of New Quantum Optimal Control Algorithms and Exact Optimized Effective Potential in Time-dependent Density Functional Theory written by 廖聖侖 and published by . This book was released on 2018 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Formulation and Numerical Solution of Quantum Control Problems by : Alfio Borzi
Download or read book Formulation and Numerical Solution of Quantum Control Problems written by Alfio Borzi and published by SIAM. This book was released on 2017-07-06 with total page 396 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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. ??
Book Synopsis Application of the Optimized Effective Potential Method to Quantum Chemistry by :
Download or read book Application of the Optimized Effective Potential Method to Quantum Chemistry written by and published by . This book was released on 2002 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: The difficulties in conventional density functional theory (DFT) are discussed. An alternative exact procedure, the Optimized Effective Potential (OEP) method, is discussed and its analytic properties that are significant in DFT are presented. The difficulties in solving the integral equation for the OEP are eliminated by the introduction of the Krieger-Li-Iafrate (KLI) approximation which leads to important analytic properties that are identical to those of the OEP. Detailed self-consistent calculations on atoms and negative ions demonstrate that the KLI yields results that are nearly identical to those of the OEP and are a significant improvement over those given by the local spin density approximation and its gradient corrected versions. Calculations have been extended to molecules in the exchange-only approximation and are close to Hartree-Fock results. An accurate self-interaction-free correlation energy functional has been constructed from considerations of a homogeneous electron gas with an energy gap. Calculations on atoms, molecules and surfaces demonstrate that this functional is at least as accurate as any alternative generalized gradient approximation. The contributions from low lying virtual states is being studied.
Book Synopsis Quantal Density Functional Theory by : Viraht Sahni
Download or read book Quantal Density Functional Theory written by Viraht Sahni and published by Springer. This book was released on 2016-08-12 with total page 417 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is on quantal density functional theory (QDFT) which is a time-dependent local effective potential theory of the electronic structure of matter. The time-independent QDFT constitutes a special case. The 2nd edition describes the further development of the theory, and extends it to include the presence of an external magnetostatic field. The theory is based on the ‘quantal Newtonian’ second and first laws for the individual electron. These laws are in terms of ‘classical’ fields that pervade all space, and their quantal sources. The fields are separately representative of the electron correlations that must be accounted for in local potential theory. Recent developments show that irrespective of the type of external field the electrons are subject to, the only correlations beyond those due to the Pauli exclusion principle and Coulomb repulsion that need be considered are solely of the correlation-kinetic effects. Foundational to QDFT, the book describes Schrödinger theory from the new perspective of the single electron in terms of the ‘quantal Newtonian’ laws. Hohenberg-Kohn density functional theory (DFT), new understandings of the theory and its extension to the presence of an external uniform magnetostatic field are described. The physical interpretation via QDFT, in terms of electron correlations, of Kohn-Sham DFT, approximations to it and Slater theory are provided.
Book Synopsis Time-Dependent Density Functional Theory by : Chaoyuan Zhu
Download or read book Time-Dependent Density Functional Theory written by Chaoyuan Zhu and published by CRC Press. This book was released on 2022-12-29 with total page 520 pages. Available in PDF, EPUB and Kindle. Book excerpt: In recent decades, time-dependent density functional theory has been developed for computing excited-state properties of large-scale systems to high accuracy in biomolecules and nanomaterials, especially for ab initio nonadiabatic molecular dynamic simulations. It is therefore regarded as a most unique efficient method to do accurate simulation for large complex systems. This book compiles and details cutting-edge research in quantum chemistry and chemical physics from interdisciplinary groups from Japan, China, South Korea, the United States, Hong Kong, and Taiwan. These groups are developing excited-state dynamics methods involving conical intersections and intersystem crossings for large complex systems. Edited by Chaoyuan Zhu, a prominent chemical physics researcher, this book will appeal to anyone involved in molecular dynamics and spectroscopy, photochemistry, biochemistry, and materials chemistry research.
Book Synopsis Quantal Density Functional Theory II by : Viraht Sahni
Download or read book Quantal Density Functional Theory II written by Viraht Sahni and published by Springer Science & Business Media. This book was released on 2009-10-16 with total page 426 pages. Available in PDF, EPUB and Kindle. Book excerpt: In my original proposal to Springer for a book on Quantal Density Functional Theory, I had envisaged one that was as complete in its presentation as possible, describing the basic theory as well as the approximation methods and a host of applications. However,after workingon the bookforabout ?ve years, I realizedthat the goal was too ambitious, and that I would be writing for another ?ve years for it to be achieved. Fortunately,there was a natural breakin the material, and I proposed to my editor, Dr. Claus Ascheron, that we split the book into two components: the ?rst on the basic theoretical framework, and the second on approximation methods and applications. Dr. Ascheron consented, and I am thankful to him for agreeing to do so. Hence, we published Quantal Density Functional Theory in 2004, and are now publishing Quantal Density Functional Theory II: Approximation Methods and Applications. One signi?cant advantage of this, as it turns out, is that I have been able to incorporate in each volume the most recent understandings available. This volume, like the earlier one, is aimed at advanced undergraduates in physics and chemistry, graduate students and researchers in the ?eld. It is written in the same pedagogical style with details of all proofs and numerous ?gures provided to explain the physics. The book is independent of the ?rst volume and stands on its own. However, proofs given in the ?rst volume are not repeated here.
Book Synopsis Control of Quantum Systems by : Shuang Cong
Download or read book Control of Quantum Systems written by Shuang Cong and published by John Wiley & Sons. This book was released on 2014-02-27 with total page 430 pages. Available in PDF, EPUB and Kindle. Book excerpt: Advanced research reference examining the closed and open quantum systems Control of Quantum Systems: Theory and Methods provides an insight into the modern approaches to control of quantum systems evolution, with a focus on both closed and open (dissipative) quantum systems. The topic is timely covering the newest research in the field, and presents and summarizes practical methods and addresses the more theoretical aspects of control, which are of high current interest, but which are not covered at this level in other text books. The quantum control theory and methods written in the book are the results of combination of macro-control theory and microscopic quantum system features. As the development of the nanotechnology progresses, the quantum control theory and methods proposed today are expected to be useful in real quantum systems within five years. The progress of the quantum control theory and methods will promote the progress and development of quantum information, quantum computing, and quantum communication. Equips readers with the potential theories and advanced methods to solve existing problems in quantum optics/information/computing, mesoscopic systems, spin systems, superconducting devices, nano-mechanical devices, precision metrology. Ideal for researchers, academics and engineers in quantum engineering, quantum computing, quantum information, quantum communication, quantum physics, and quantum chemistry, whose research interests are quantum systems control.
Book Synopsis Fundamentals of Time-Dependent Density Functional Theory by : Miguel A.L. Marques
Download or read book Fundamentals of Time-Dependent Density Functional Theory written by Miguel A.L. Marques and published by Springer Science & Business Media. This book was released on 2012-01-21 with total page 573 pages. Available in PDF, EPUB and Kindle. Book excerpt: There have been many significant advances in time-dependent density functional theory over recent years, both in enlightening the fundamental theoretical basis of the theory, as well as in computational algorithms and applications. This book, as successor to the highly successful volume Time-Dependent Density Functional Theory (Lect. Notes Phys. 706, 2006) brings together for the first time all recent developments in a systematic and coherent way. First, a thorough pedagogical presentation of the fundamental theory is given, clarifying aspects of the original proofs and theorems, as well as presenting fresh developments that extend the theory into new realms—such as alternative proofs of the original Runge-Gross theorem, open quantum systems, and dispersion forces to name but a few. Next, all of the basic concepts are introduced sequentially and building in complexity, eventually reaching the level of open problems of interest. Contemporary applications of the theory are discussed, from real-time coupled-electron-ion dynamics, to excited-state dynamics and molecular transport. Last but not least, the authors introduce and review recent advances in computational implementation, including massively parallel architectures and graphical processing units. Special care has been taken in editing this volume as a multi-author textbook, following a coherent line of thought, and making all the relevant connections between chapters and concepts consistent throughout. As such it will prove to be the text of reference in this field, both for beginners as well as expert researchers and lecturers teaching advanced quantum mechanical methods to model complex physical systems, from molecules to nanostructures, from biocomplexes to surfaces, solids and liquids. From the reviews of LNP 706: “This is a well structured text, with a common set of notations and a single comprehensive and up-to-date list of references, rather than just a compilation of research articles. Because of its clear organization, the book can be used by novices (basic knowledge of ground-state DFT is assumed) and experienced users of TD-DFT, as well as developers in the field.” (Anna I. Krylov, Journal of the American Chemical Society, Vol. 129 (21), 2007) “This book is a treasure of knowledge and I highly recommend it. Although it is a compilation of chapters written by many different leading researchers involved in development and application of TDDFT, the contributors have taken great care to make sure the book is pedagogically sound and the chapters complement each other [...]. It is highly accessible to any graduate student of chemistry or physics with a solid grounding in many-particle quantum mechanics, wishing to understand both the fundamental theory as well as the exponentially growing number of applications. [...] In any case, no matter what your background is, it is a must-read and an excellent reference to have on your shelf.” Amazon.com, October 15, 2008, David Tempel (Cambridge, MA)
Book Synopsis Molecular Electronic-Structure Theory by : Trygve Helgaker
Download or read book Molecular Electronic-Structure Theory written by Trygve Helgaker and published by John Wiley & Sons. This book was released on 2014-08-11 with total page 949 pages. Available in PDF, EPUB and Kindle. Book excerpt: Ab initio quantum chemistry has emerged as an important tool in chemical research and is appliced to a wide variety of problems in chemistry and molecular physics. Recent developments of computational methods have enabled previously intractable chemical problems to be solved using rigorous quantum-mechanical methods. This is the first comprehensive, up-to-date and technical work to cover all the important aspects of modern molecular electronic-structure theory. Topics covered in the book include: * Second quantization with spin adaptation * Gaussian basis sets and molecular-integral evaluation * Hartree-Fock theory * Configuration-interaction and multi-configurational self-consistent theory * Coupled-cluster theory for ground and excited states * Perturbation theory for single- and multi-configurational states * Linear-scaling techniques and the fast multipole method * Explicity correlated wave functions * Basis-set convergence and extrapolation * Calibration and benchmarking of computational methods, with applications to moelcular equilibrium structure, atomization energies and reaction enthalpies. Molecular Electronic-Structure Theory makes extensive use of numerical examples, designed to illustrate the strengths and weaknesses of each method treated. In addition, statements about the usefulness and deficiencies of the various methods are supported by actual examples, not just model calculations. Problems and exercises are provided at the end of each chapter, complete with hints and solutions. This book is a must for researchers in the field of quantum chemistry as well as for nonspecialists who wish to acquire a thorough understanding of ab initio molecular electronic-structure theory and its applications to problems in chemistry and physics. It is also highly recommended for the teaching of graduates and advanced undergraduates.
Book Synopsis Self-healing Diffusion Quantum Monte Carlo Algorithms by :
Download or read book Self-healing Diffusion Quantum Monte Carlo Algorithms written by and published by . This book was released on 2009 with total page 16 pages. Available in PDF, EPUB and Kindle. Book excerpt: We develop a formalism and present an algorithm for optimization of the trial wave-function used in fixed-node diffusion quantum Monte Carlo (DMC) methods. The formalism is based on the DMC mixed estimator of the ground state probability density. We take advantage of a basic property of the walker configuration distribution generated in a DMC calculation, to (i) project-out a multi-determinant expansion of the fixed node ground state wave function and (ii) to define a cost function that relates the interacting-ground-state-fixed-node and the non-interacting trial wave functions. We show that (a) locally smoothing out the kink of the fixed-node ground-state wave function at the node generates a new trial wave function with better nodal structure and (b) we argue that the noise in the fixed-node wave function resulting from finite sampling plays a beneficial role, allowing the nodes to adjust towards the ones of the exact many-body ground state in a simulated annealing-like process. Based on these principles, we propose a method to improve both single determinant and multi-determinant expansions of the trial wave function. The method can be generalized to other wave function forms such as pfaffians. We test the method in a model system where benchmark configuration interaction calculations can be performed and most components of the Hamiltonian are evaluated analytically. Comparing the DMC calculations with the exact solutions, we find that the trial wave function is systematically improved. The overlap of the optimized trial wave function and the exact ground state converges to 100% even starting from wave functions orthogonal to the exact ground state. Similarly, the DMC total energy and density converges to the exact solutions for the model. In the optimization process we find an optimal non-interacting nodal potential of density-functional-like form whose existence was predicted in a previous publication [Phys. Rev. B 77 245110 (2008)]. Tests of the method are extended to a model system with a conventional Coulomb interaction where we show we can obtain the exact Kohn-Sham effective potential from the DMC data.
Book Synopsis Density Functional Theory by : David S. Sholl
Download or read book Density Functional Theory written by David S. Sholl and published by John Wiley & Sons. This book was released on 2011-09-20 with total page 252 pages. Available in PDF, EPUB and Kindle. Book excerpt: Demonstrates how anyone in math, science, and engineering can master DFT calculations Density functional theory (DFT) is one of the most frequently used computational tools for studying and predicting the properties of isolated molecules, bulk solids, and material interfaces, including surfaces. Although the theoretical underpinnings of DFT are quite complicated, this book demonstrates that the basic concepts underlying the calculations are simple enough to be understood by anyone with a background in chemistry, physics, engineering, or mathematics. The authors show how the widespread availability of powerful DFT codes makes it possible for students and researchers to apply this important computational technique to a broad range of fundamental and applied problems. Density Functional Theory: A Practical Introduction offers a concise, easy-to-follow introduction to the key concepts and practical applications of DFT, focusing on plane-wave DFT. The authors have many years of experience introducing DFT to students from a variety of backgrounds. The book therefore offers several features that have proven to be helpful in enabling students to master the subject, including: Problem sets in each chapter that give readers the opportunity to test their knowledge by performing their own calculations Worked examples that demonstrate how DFT calculations are used to solve real-world problems Further readings listed in each chapter enabling readers to investigate specific topics in greater depth This text is written at a level suitable for individuals from a variety of scientific, mathematical, and engineering backgrounds. No previous experience working with DFT calculations is needed.
Book Synopsis Density Functional Methods In Physics by : Reiner M. Dreizler
Download or read book Density Functional Methods In Physics written by Reiner M. Dreizler and published by Springer Science & Business Media. This book was released on 2013-11-11 with total page 530 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Molecular Quantum Dynamics by : Fabien Gatti
Download or read book Molecular Quantum Dynamics written by Fabien Gatti and published by Springer Science & Business Media. This book was released on 2014-04-09 with total page 281 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book focuses on current applications of molecular quantum dynamics. Examples from all main subjects in the field, presented by the internationally renowned experts, illustrate the importance of the domain. Recent success in helping to understand experimental observations in fields like heterogeneous catalysis, photochemistry, reactive scattering, optical spectroscopy, or femto- and attosecond chemistry and spectroscopy underline that nuclear quantum mechanical effects affect many areas of chemical and physical research. In contrast to standard quantum chemistry calculations, where the nuclei are treated classically, molecular quantum dynamics can cover quantum mechanical effects in their motion. Many examples, ranging from fundamental to applied problems, are known today that are impacted by nuclear quantum mechanical effects, including phenomena like tunneling, zero point energy effects, or non-adiabatic transitions. Being important to correctly understand many observations in chemical, organic and biological systems, or for the understanding of molecular spectroscopy, the range of applications covered in this book comprises broad areas of science: from astrophysics and the physics and chemistry of the atmosphere, over elementary processes in chemistry, to biological processes (such as the first steps of photosynthesis or vision). Nevertheless, many researchers refrain from entering this domain. The book "Molecular Quantum Dynamics" offers them an accessible introduction. Although the calculation of large systems still presents a challenge - despite the considerable power of modern computers - new strategies have been developed to extend the studies to systems of increasing size. Such strategies are presented after a brief overview of the historical background. Strong emphasis is put on an educational presentation of the fundamental concepts, so that the reader can inform himself about the most important concepts, like eigenstates, wave packets, quantum mechanical resonances, entanglement, etc. The chosen examples highlight that high-level experiments and theory need to work closely together. This book thus is a must-read both for researchers working experimentally or theoretically in the concerned fields, and generally for anyone interested in the exciting world of molecular quantum dynamics.
Book Synopsis Time-optimal Control of Quantum Systems by : Tyler Holden
Download or read book Time-optimal Control of Quantum Systems written by Tyler Holden and published by . This book was released on 2011 with total page 143 pages. Available in PDF, EPUB and Kindle. Book excerpt: As technological advances allow us to peer into and beyond microscopic phenomena, new theoretical developments are necessary to facilitate this exploration. In particular, the potential afforded by utilizing quantum resources promises to dramatically affect scientific research, communications, computation, and material science. Control theory is the field dedicated to the manipulation of systems, and quantum control theory pertains to the manoeuvring of quantum systems. Due to the inherent sensitivity of quantum ensembles to their environment, time-optimal solutions should be found in order to minimize exposure to external sources. Furthermore, the complexity of the Schr\"odinger equation in describing the evolution of a unitary operator makes the analytical discovery of time-optimal solutions rare, motivating the development of numerical algorithms. The seminal result of classical control is the Pontryagin Maximum Principle, which implies that a restriction to bounded control amplitudes admits two classifications of trajectories: bang-bang and singular. Extensions of this result to generalized control problems yield the same classification and hence arise in the study of quantum dynamics. While singular trajectories are often avoided in both classical and quantum literature, a full optimal synthesis requires that we analyze the possibility of their existence. With this in mind, this treatise will examine the issue of time-optimal quantum control. In particular, we examine the results of existing numerical algorithms, including Gradient Ascent Pulse Engineering and the Kaya-Huneault method. We elaborate on the ideas of the Kaya-Huneault algorithm and present an alternative algorithm that we title the Real-Embedding algorithm. These methods are then compared when used to simulate unitary evolution. This is followed by a brief examination on the conditions for the existence of singular controls, as well possible ideas and developments in creating geometry based numerical algorithms.
Book Synopsis Density-potential Mapping in the Standard and Quantum Electrodynamical Time-dependent Density Functional Theory by : Mehdi Farzanehpour
Download or read book Density-potential Mapping in the Standard and Quantum Electrodynamical Time-dependent Density Functional Theory written by Mehdi Farzanehpour and published by . This book was released on 2015 with total page 129 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Development of Time-dependent Density Functional Theory in Chemical and Solid-state Physics by : Fan Zhang
Download or read book Development of Time-dependent Density Functional Theory in Chemical and Solid-state Physics written by Fan Zhang and published by . This book was released on 2005 with total page 146 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Parallel Algorithms for Time Dependent Density Functional Theory in Real-space and Real-time by : James Kestyn
Download or read book Parallel Algorithms for Time Dependent Density Functional Theory in Real-space and Real-time written by James Kestyn and published by . This book was released on 2018 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Density functional theory (DFT) and time dependent density functional theory (TDDFT) have had great success solving for ground state and excited states properties of molecules, solids and nanostructures. However, these problems are particularly hard to scale. Both the size of the discrete system and the number of needed eigenstates increase with the number of electrons. A complete parallel framework for DFT and TDDFT calculations applied to molecules and nanostructures is presented in this dissertation. This includes the development of custom numerical algorithms for eigenvalue problems and linear systems. New functionality in the FEAST eigenvalue solver presents an additional level of distributed memory parallelism and is used for the ground state DFT calculation, allowing larger molecules to be simulated. A parallel domain decomposition linear system solver has also been implemented. This approach uses a Schur complement technique and a combination of direct sparse solvers to outperform black box distributed memory solvers in both performance and scalability. All other aspects of the code have been rewritten to operate in the domain decomposition framework and have been parallelized using both MPI and OpenMP. Numerical experiments demonstrate that our all-electron code can be applied to systems containing up to a few thousand atoms.
