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Books on the topic 'Real-time time-dependent density functional theory'

Author: Grafiati

Published: 4 June 2021

Last updated: 11 February 2022

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1

Marques, Miguel A. L., Carsten A. Ullrich, Fernando Nogueira, Angel Rubio, Kieron Burke, and Eberhard K. U. Gross, eds. Time-Dependent Density Functional Theory. Berlin, Heidelberg: Springer Berlin Heidelberg, 2006. http://dx.doi.org/10.1007/b11767107.

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2

T, Maitra Neepa, Nogueira Fernando M. S, Gross E. K. U, Rubio Angel, and SpringerLink (Online service), eds. Fundamentals of Time-Dependent Density Functional Theory. Berlin, Heidelberg: Springer Berlin Heidelberg, 2012.

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3

Marques, Miguel A. L., Neepa T. Maitra, Fernando M. S. Nogueira, E. K. U. Gross, and Angel Rubio, eds. Fundamentals of Time-Dependent Density Functional Theory. Berlin, Heidelberg: Springer Berlin Heidelberg, 2012. http://dx.doi.org/10.1007/978-3-642-23518-4.

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4

Time-dependent density-functional theory: Concepts and applications. Oxford: Oxford University Press, 2012.

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5

Rubio, Angel, Fernando Nogueira, Eberhard K. U. Gross, Miguel A. L. Marques, Carsten A. Ullrich, and Kieron Burke. Time-Dependent Density Functional Theory. Springer, 2010.

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6

Maitra, Neepa T., Miguel A. L. Marques, and Fernando M. S. Nogueira. Fundamentals of Time-Dependent Density Functional Theory. Springer, 2012.

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7

Ullrich, Carsten A. Time-Dependent Density-Functional Theory: Concepts and Applications. Oxford University Press, 2019.

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8

Miguel A.L. Marques (Editor), Carsten A. Ullrich (Editor), Fernando Nogueira (Editor), Angel Rubio (Editor), Kieron Burke (Editor), and Eberhard K.U. Gross (Editor), eds. Time-Dependent Density Functional Theory (Lecture Notes in Physics). Springer, 2006.

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9

Nalewajski, R. F. Density Functional Theory Ii: Relativistic And Time Dependent Extensions. Springer, 2010.

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10

Excited States of Silicon Carbide Clusters by Time Dependent Density Functional Theory. Storming Media, 2004.

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11

Density Functional Theory II: Relativistic and Time Dependent Extensions (Topics in Current Chemistry). Springer, 1996.

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12

Nalewajski, R. F. Density Functional Theory IV: Relativistic and Time Dependent Extensions (Topics in Current Chemistry, Vol 183). Springer Verlag, 1996.

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13

Nalewajski, R. F. Density Functional Theory II: Relativistic and Time Dependent Extensions (Topics in Current Chemistry, Vol 181). Springer Verlag, 1996.

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14

Mann, Peter. Lagrangian Field Theory. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198822370.003.0025.

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In this chapter, Hamiltonian field theory is derived classically via a Hamiltonian density, using the zeroth component of a 4-momentum density. In field theory, space and time are considered to be on equal footing but, in the canonical formalism, time is treated as being special and therefore, by definition, it is not covariant. Consequently, most field theoretic models are built on Lagrangian formulations. A covariant canonical formalism is the subject of the de Donder–Weyl formalism, which is briefly discussed as a covariant Hamiltonian field theory. In addition, the chapter examines the case of a generalised Poisson bracket in the continuous form for two local smooth functionals of phase space.

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15

Morawetz, Klaus. Transient Time Period. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198797241.003.0019.

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The formation of correlations at short- time scales is considered. A universal response function is found which allows describing the formation of collective modes in plasmas created by femto-second lasers as well as the formation of occupations in cold atomic optical lattices. Quantum quench and sudden switching of interactions are possible to describe by such Levinson-type kinetic equations on the transient time regime. On larger time scales it is shown that non-Markovian–Levnson equations double count correlations and the extended quasiparticle picture to distinguish between the reduced density matrix and quasiparticle distribution solve this shortcoming. The problem of initial correlations and how they can be incorporated into the Green’s function technique to result into modified kinetic equations is solved and a systematic expansion is suggested.

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16

Horing, Norman J. Morgenstern. Retarded Green’s Functions. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198791942.003.0005.

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Chapter 5 introduces single-particle retarded Green’s functions, which provide the probability amplitude that a particle created at (x, t) is later annihilated at (x′,t′). Partial Green’s functions, which represent the time development of one (or a few) state(s) that may be understood as localized but are in interaction with a continuum of states, are discussed and applied to chemisorption. Introductions are also made to the Dyson integral equation, T-matrix and the Dirac delta-function potential, with the latter applied to random impurity scattering. The retarded Green’s function in the presence of random impurity scattering is exhibited in the Born and self-consistent Born approximations, with application to Ando’s semi-elliptic density of states for the 2D Landau-quantized electron-impurity system. Important retarded Green’s functions and their methods of derivation are discussed. These include Green’s functions for electrons in magnetic fields in both three dimensions and two dimensions, also a Hamilton equation-of-motion method for the determination of Green’s functions with application to a 2D saddle potential in a time-dependent electric field. Moreover, separable Hamiltonians and their product Green’s functions are discussed with application to a one-dimensional superlattice in axial electric and magnetic fields. Green’s function matching/joining techniques are introduced and applied to spatially varying mass (heterostructures) and non-local electrostatics (surface plasmons).

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17

Deruelle, Nathalie, and Jean-Philippe Uzan. Kinetic theory. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198786399.003.0010.

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This chapter covers the equations governing the evolution of particle distribution and relates the macroscopic thermodynamical quantities to the distribution function. The motion of N particles is governed by 6N equations of motion of first order in time, written in either Hamiltonian form or in terms of Poisson brackets. Thus, as this chapter shows, as the number of particles grows it becomes necessary to resort to a statistical description. The chapter first introduces the Liouville equation, which states the conservation of the probability density, before turning to the Boltzmann–Vlasov equation. Finally, it discusses the Jeans equations, which are the equations obtained by taking various averages over velocities.

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18

Horing, Norman J. Morgenstern. Q. M. Pictures; Heisenberg Equation; Linear Response; Superoperators and Non-Markovian Equations. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198791942.003.0003.

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Three fundamental and equivalent mathematical frameworks (“pictures”) in which quantum theory can be lodged are exhibited and their relations and relative advantages/disadvantages are discussed: (1) The Schrödinger picture considers the dynamical development of the overall system state vector as a function of time relative to a fixed complete set of time-independent basis eigenstates; (2) The Heisenberg picture (convenient for the use of Green’s functions) embeds the dynamical development of the system in a time-dependent counter-rotation of the complete set of basis eigenstates relative to the fixed, time-independent overall system state, so that the relation of the latter fixed system state to the counter-rotating basis eigenstates is identically the same in the Heisenberg picture as it is in the Schrödinger picture; (3) the Interaction Picture addresses the situation in which a Hamiltonian, H=H0+H1, involves a part H0 whose equations are relatively easy to solve and a more complicated part, H1, treated perturbatively. The Heisenberg equation of motion for operators is discussed, and is applied to annihilation and creation operators. The S-matrix, density matrix and von Neumann equation, along with superoperators and non-Markovian kinetic equations are also addressed (e.g. the intracollisional field effect).

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19

Berber, Stevan. Discrete Communication Systems. Oxford University Press, 2021. http://dx.doi.org/10.1093/oso/9780198860792.001.0001.

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The book present essential theory and practice of the discrete communication systems design, based on the theory of discrete time stochastic processes, and their relation to the existing theory of digital communication systems. Using the notion of stochastic linear time invariant systems, in addition to the orhogonality principles, a general structure of the discrete communication system is constructed in terms of mathematical operators. Based on this structure, the MPSK, MFSK, QAM, OFDM and CDMA systems, using discrete modulation methods, are deduced as special cases. The signals are processed in the time and frequency domain, which requires precise derivatives of their amplitude spectral density functions, correlation functions and related energy and pover spectral densities. The book is self-sufficient, because it uses the unified notation both in the main ten chapters explaining communications systems theory and nine supplementary chapters dealing with the continuous and discrete time signal processing for both the deterministic and stochastic signals. In this context, the indexing of vital signals and finctions makes obvious distinction beteween them. Having in mind the controversial nature of the continuous time white Gaussian noise process, a separate chapter is dedicated to the noise discretisation by introducing notions of noise entropy and trauncated Gaussian density function to avoid limitations in applying the Nyquist criterion. The text of the book is acompained by the solutions of problems for all chapters and a set of deign projects with the defined projects’ topics and tasks and offered solutions.

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20

Akemann, Gernot. Random matrix theory and quantum chromodynamics. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198797319.003.0005.

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This chapter was originally presented to a mixed audience of physicists and mathematicians with some basic working knowledge of random matrix theory. The first part is devoted to the solution of the chiral Gaussian unitary ensemble in the presence of characteristic polynomials, using orthogonal polynomial techniques. This includes all eigenvalue density correlation functions, smallest eigenvalue distributions, and their microscopic limit at the origin. These quantities are relevant for the description of the Dirac operator spectrum in quantum chromodynamics with three colors in four Euclidean space-time dimensions. In the second part these two theories are related based on symmetries, and the random matrix approximation is explained. In the last part recent developments are covered, including the effect of finite chemical potential and finite space-time lattice spacing, and their corresponding orthogonal polynomials. This chapter also provides some open random matrix problems.

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21

Morawetz, Klaus. Nonequilibrium Quantum Hydrodynamics. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198797241.003.0015.

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The balance equations resulting from the nonlocal kinetic equation are derived. They show besides the Landau-like quasiparticle contributions explicit two-particle correlated parts which can be interpreted as molecular contributions. It looks like as if two particles form a short-living molecule. All observables like density, momentum and energy are found as a conserving system of balance equations where the correlated parts are in agreement with the forms obtained when calculating the reduced density matrix with the extended quasiparticle functional. Therefore the nonlocal kinetic equation for the quasiparticle distribution forms a consistent theory. The entropy is shown to consist also of a quasiparticle part and a correlated part. The explicit entropy gain is proved to complete the H-theorem even for nonlocal collision events. The limit of Landau theory is explored when neglecting the delay time. The rearrangement energy is found to mediate between the spectral quasiparticle energy and the Landau variational quasiparticle energy.

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22

Coen, David, Alexander Katsaitis, and Matia Vannoni. Business Lobbying in the European Union. Oxford University Press, 2021. http://dx.doi.org/10.1093/oso/9780199589753.001.0001.

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At a time when Europe and business stand at crossroads, this study provides a perspective into how business representation in the EU has evolved and valuable insights into how to organize lobbying strategies and influence policy-making. Uniquely, the study analyses business lobbying in Brussels by drawing on insights from political science, public management, and business studies. At the macro-level, we explore over thirty years of increasing business lobbying and explore the emergence of a distinct European business-government relations style. At the meso-level, we assess how the role of EU institutions, policy types, and the policy cycle shape the density and diversity of business activity. Finally, at the micro-level we seek to explore how firms organize their political affairs functions and mobilized strategic political responses. The study utilizes a variety of methods to analyse business-government relations drawing on unique company and policy-maker surveys; in-depth case studies and elite interviews; large statistical analysis of lobbying registers to examine business the density and diversity; and managerial career path and organizational analyses to assess corporate political capabilities. In doing so, this study contributes to discussions on corporate political strategy and interest groups activity. This monograph should be of interest to public policy scholars, policy-makers, and businesses managers seeking to understand EU government affair and political representation.

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23

Sapse, Anne-Marie, ed. Molecular Orbital Calculations for Biological Systems. Oxford University Press, 1998. http://dx.doi.org/10.1093/oso/9780195098730.001.0001.

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Molecular Orbital Calculations for Biological Systems is a hands-on guide to computational quantum chemistry and its applications in organic chemistry, biochemistry, and molecular biology. With improvements in software, molecular modeling techniques are now becoming widely available; they are increasingly used to complement experimental results, saving significant amounts of lab time. Common applications include pharmaceutical research and development; for example, ab initio and semi-empirical methods are playing important roles in peptide investigations and in drug design. The opening chapters provide an introduction for the non-quantum chemist to the basic quantum chemistry methods, ab initio, semi-empirical, and density functionals, as well as to one of the main families of computer programs, the Gaussian series. The second part then describes current research which applies quantum chemistry methods to such biological systems as amino acids, peptides, and anti-cancer drugs. Throughout the authors seek to encourage biochemists to discover aspects of their own research which might benefit from computational work. They also show that the methods are accessible to researchers from a wide range of mathematical backgrounds. Combining concise introductions with practical advice, this volume will be an invaluable tool for research on biological systems.

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24

Dyall, Kenneth G., and Knut Faegri. Introduction to Relativistic Quantum Chemistry. Oxford University Press, 2007. http://dx.doi.org/10.1093/oso/9780195140866.001.0001.

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This book provides an introduction to the essentials of relativistic effects in quantum chemistry, and a reference work that collects all the major developments in this field. It is designed for the graduate student and the computational chemist with a good background in nonrelativistic theory. In addition to explaining the necessary theory in detail, at a level that the non-expert and the student should readily be able to follow, the book discusses the implementation of the theory and practicalities of its use in calculations. After a brief introduction to classical relativity and electromagnetism, the Dirac equation is presented, and its symmetry, atomic solutions, and interpretation are explored. Four-component molecular methods are then developed: self-consistent field theory and the use of basis sets, double-group and time-reversal symmetry, correlation methods, molecular properties, and an overview of relativistic density functional theory. The emphases in this section are on the basics of relativistic theory and how relativistic theory differs from nonrelativistic theory. Approximate methods are treated next, starting with spin separation in the Dirac equation, and proceeding to the Foldy-Wouthuysen, Douglas-Kroll, and related transformations, Breit-Pauli and direct perturbation theory, regular approximations, matrix approximations, and pseudopotential and model potential methods. For each of these approximations, one-electron operators and many-electron methods are developed, spin-free and spin-orbit operators are presented, and the calculation of electric and magnetic properties is discussed. The treatment of spin-orbit effects with correlation rounds off the presentation of approximate methods. The book concludes with a discussion of the qualitative changes in the picture of structure and bonding that arise from the inclusion of relativity.

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25

Lattman, Eaton E., Thomas D. Grant, and Edward H. Snell. Biological Small Angle Scattering. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780199670871.001.0001.

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The technique of small angle solution scattering has been revolutionized in the last two decades. Exponential increases in computing power, parallel algorithm development, and the development of synchrotron, free-electron X-ray sources, and neutron sources, have combined to allow new classes of studies for biological specimens. These include time-resolved experiments in which functional motions of proteins are monitored on a picosecond timescale, and the first steps towards determining actual electron density fluctuations within particles. In addition, more traditional experiments involving the determination of size and shape, and contrast matching that isolate substructures such as nucleic acid, have become much more straightforward to carry out, and simultaneously require much less material. These new capabilities have sparked an upsurge of interest in solution scattering on the part of investigators in related disciplines. Thus, this book seeks to guide structural biologists to understand the basics of small angle solution scattering in both the X-ray and neutron case, to appreciate its strengths, and to be cognizant of its limitations. It is also directed at those who have a general interest in its potential. The book focuses on three areas: theory, practical aspects and applications, and the potential of developing areas. It is an introduction and guide to the field but not a comprehensive treatment of all the potential applications.

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26

Nitzan, Abraham. Chemical Dynamics in Condensed Phases. Oxford University Press, 2006. http://dx.doi.org/10.1093/oso/9780198529798.001.0001.

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This text provides a uniform and consistent approach to diversified problems encountered in the study of dynamical processes in condensed phase molecular systems. Given the broad interdisciplinary aspect of this subject, the book focuses on three themes: coverage of needed background material, in-depth introduction of methodologies, and analysis of several key applications. The uniform approach and common language used in all discussions help to develop general understanding and insight on condensed phases chemical dynamics. The applications discussed are among the most fundamental processes that underlie physical, chemical and biological phenomena in complex systems. The first part of the book starts with a general review of basic mathematical and physical methods (Chapter 1) and a few introductory chapters on quantum dynamics (Chapter 2), interaction of radiation and matter (Chapter 3) and basic properties of solids (chapter 4) and liquids (Chapter 5). In the second part the text embarks on a broad coverage of the main methodological approaches. The central role of classical and quantum time correlation functions is emphasized in Chapter 6. The presentation of dynamical phenomena in complex systems as stochastic processes is discussed in Chapters 7 and 8. The basic theory of quantum relaxation phenomena is developed in Chapter 9, and carried on in Chapter 10 which introduces the density operator, its quantum evolution in Liouville space, and the concept of reduced equation of motions. The methodological part concludes with a discussion of linear response theory in Chapter 11, and of the spin-boson model in chapter 12. The third part of the book applies the methodologies introduced earlier to several fundamental processes that underlie much of the dynamical behaviour of condensed phase molecular systems. Vibrational relaxation and vibrational energy transfer (Chapter 13), Barrier crossing and diffusion controlled reactions (Chapter 14), solvation dynamics (Chapter 15), electron transfer in bulk solvents (Chapter 16) and at electrodes/electrolyte and metal/molecule/metal junctions (Chapter 17), and several processes pertaining to molecular spectroscopy in condensed phases (Chapter 18) are the main subjects discussed in this part.

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