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Books on the topic 'Density matrices'

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Published: 4 June 2021

Last updated: 20 February 2023

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1

Erdahl, Robert, and Vadene H. Smith, eds. Density Matrices and Density Functionals. Dordrecht: Springer Netherlands, 1987. http://dx.doi.org/10.1007/978-94-009-3855-7.

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2

Danos, Michael. Irreducible density matrices. Gaithersburg, MD: U.S. Dept. of Commerce, National Bureau of Standards, 1985.

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3

Danos, Michael. Irreducible density matrices. Gaithersburg, MD: U.S. Dept. of Commerce, National Bureau of Standards, 1985.

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4

Coleman, A. John, and Vyacheslav I. Yukalov. Reduced Density Matrices. Berlin, Heidelberg: Springer Berlin Heidelberg, 2000. http://dx.doi.org/10.1007/978-3-642-58304-9.

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5

Blum, Karl. Density matrix theory and applications. 2nd ed. New York: Plenum Press, 1996.

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6

Cioslowski, Jerzy, ed. Many-Electron Densities and Reduced Density Matrices. Boston, MA: Springer US, 2000. http://dx.doi.org/10.1007/978-1-4615-4211-7.

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7

Jerzy, Cioslowski, ed. Many-electron densities and reduced density matrices. New York: Kluwer Academic/Plenum Publishers, 2000.

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8

Blum, Karl. Density matrix theory and applications. 3rd ed. Heidelberg: Springer, 2012.

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9

Raynal, Ph. Unambiguous state discrimination of two density matrices in quantum information theory. Erlangen: Lehrstuhl für Mikrocharakterisierung, Friedrich-Alexander-Universität Erlangen-Nürnberg, 2008.

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10

1942-, Peschel Ingo, ed. Density-matrix renormalization: A new numerical method in physics : lectures of a seminar and workshop held at the Max-Planck-Institut für Physik komplexer Systeme, Dresden, Germany, August 24th to September 18th, 1998. Berlin: Springer, 1999.

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11

Wong, Herbert. Density operator and superoperator methods in multiple pulse NMR: Fundamentals of the Hilbert and Liouville space approach. Petone, N.Z: DSIR, 1990.

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12

V, Kudrin Alexander, and Zaboronkova Tatyana M, eds. Electrodynamics of density ducts in magnetized plasmas. Amsterdam: Gordon & Breach, 1999.

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13

D, Mateescu Gh. 2D NMR: Density matrix and product operator treatment. Englewood Cliffs, N.J: PTR Prentice Hall, 1993.

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14

Rand, Stephen Colby. Lectures on light: Nonlinear and quantum optics using the density matrix. Oxford [England]: Oxford University Press, 2010.

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15

Principles of nonlinear optical spectroscopy. New York: Oxford University Press, 1995.

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16

Understanding Density Matrices. Nova Science Publishers, Incorporated, 2019.

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17

Danielsen, Nadia V. Understanding Density Matrices. Nova Science Publishers, Incorporated, 2019.

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18

Davidson, Ernest. Reduced Density Matrices in Quantum Chemistry. Elsevier Science & Technology Books, 2012.

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19

Keller, L., C. Amador, and M. P. Das. Density Functional Theory. Springer, 2014.

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20

Many-Electron Densities and Reduced Density Matrices. Springer, 2011.

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21

Cioslowski, Jerzy. Many-Electron Densities and Reduced Density Matrices. Springer London, Limited, 2012.

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22

Cioslowski, Jerzy. Many-Electron Densities and Reduced Density Matrices. Springer, 2012.

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23

1918-, Coleman A. John, Erdahl Robert, and Smith Vedene H, eds. Density matrices and density functionals: Proceedings of the A. John Coleman symposium. Dordrecht: D. Reidel Pub. Co., 1987.

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24

Erdahl, R. M., and Vedene H. Smith Jr. Density Matrices and Density Functionals: Proceedings of the A. John Coleman Symposium. Springer London, Limited, 2012.

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25

Erdahl, R., and Smith V. H. Jr. Density Matrices and Density Functionals: Proceedings of the A. John Coleman Symposium. Springer Netherlands, 2011.

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26

1937-, Lin S. H., ed. Density matrix method and femtosecond processes. Singapore: World Scientific, 1991.

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27

I, Gidopoulos N., and Wilson S. 1950-, eds. The fundamentals of electron density, density matrix, and density functional theory in atoms, molecules, and the solid state. Dordrecht: Kluwer Academic Publishers, 2003.

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28

Coleman, A. J., and V. I. Yukalov. Reduced Density Matrices: Coulson's Challenge (Lecture Notes in Chemistry). Springer, 2000.

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29

Farrar, Thomas C. Density Matrix Theory and Its Applications in Nmr Spectroscopy. Farragut Press, 1992.

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30

(Editor), N. I. Gidopoulos, and S. Wilson (Editor), eds. The Fundamentals of Electron Density, Density Matrix and Density Functional Theory in Atoms, Molecules and the Solid State (Progress in Theoretical Chemistry and Physics). Springer, 2003.

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31

Density-Matrix Renormalization - A New Numerical Method in Physics: Lectures of a Seminar and Workshop held at the Max-Planck-Institut für Physik komplexer ... 18th, 1998 (Lecture Notes in Physics). Springer, 1999.

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32

Cioslowski, Jerzy. Many-Electron Densities and Reduced Density Matrices (Mathematical and Computational Chemistry). Springer, 2000.

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33

Mateescu, Gheorghe D., and Adrian Valeriu. 2D Nmr: Density Matrix and Product Operator Treatment. Prentice Hall, 1993.

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34

Nakahara, Mikio. Frontiers in Quantum Information Research - Proceedings of the Summer School on Decoherence, Entanglement and Entropy and Proceedings of the Workshop on Mps and Dmrg. World Scientific Publishing Co Pte Ltd, 2012.

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35

Speicher, Roland. Random banded and sparse matrices. Edited by Gernot Akemann, Jinho Baik, and Philippe Di Francesco. Oxford University Press, 2018. http://dx.doi.org/10.1093/oxfordhb/9780198744191.013.23.

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This article discusses some mathematical results and conjectures about random band matrix ensembles (RBM) and sparse matrix ensembles. Spectral problems of RBM and sparse matrices can be expressed in terms of supersymmetric (SUSY) statistical mechanics that provides a dual representation for disordered quantum systems. This representation offers important insights into nonperturbative aspects of the spectrum and eigenfunctions of RBM. The article first presents the definition of RBM ensembles before considering the density of states, the behaviour of eigenvectors, and eigenvalue statistics for RBM and sparse random matrices. In particular, it highlights the relations with random Schrödinger (RS) and the role of the dimension of the lattice. It also describes the connection between RBM and statistical mechanics, the spectral theory of large random sparse matrices, conjectures and theorems about eigenvectors and local spacing statistics, and the RS operator on the Cayley tree or Bethe lattice.

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36

Rand, Stephen C. Lectures on Light: Nonlinear and Quantum Optics Using the Density Matrix. Oxford University Press, 2019.

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37

Rand, Stephen C. Lectures on Light: Nonlinear and Quantum Optics Using the Density Matrix. Oxford University Press, 2014.

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38

Rand, Stephen C. Lectures on Light: Nonlinear and Quantum Optics using the Density Matrix. Oxford University Press, 2016.

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39

Rand, Stephen C. Lectures on Light: Nonlinear and Quantum Optics Using the Density Matrix. Oxford University Press, 2010.

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40

Mateescu, Gheorghe D., and Adrian Valeriu. 2D Nmr: Density Matrix and Product Operator Treatment. Prentice Hall, 1993.

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41

A Method of Calculating Ground-state Properties of Many Particle Systems Using Reduced Density Matrices. Franklin Classics, 2018.

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42

Garrod, Claude, and Jerome K. Percus. A Method of Calculating Ground-State Properties of Many Particle Systems Using Reduced Density Matrices. Franklin Classics Trade Press, 2018.

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43

Beenakker, Carlo W. J. Extreme eigenvalues of Wishart matrices: application to entangled bipartite system. Edited by Gernot Akemann, Jinho Baik, and Philippe Di Francesco. Oxford University Press, 2018. http://dx.doi.org/10.1093/oxfordhb/9780198744191.013.37.

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This article describes the application of random matrix theory (RMT) to the estimation of the bipartite entanglement of a quantum system, with particular emphasis on the extreme eigenvalues of Wishart matrices. It first provides an overview of some spectral properties of unconstrained Wishart matrices before introducing the problem of the random pure state of an entangled quantum bipartite system consisting of two subsystems whose Hilbert spaces have dimensions M and N respectively with N ≤ M. The focus is on the smallest eigenvalue which serves as an important measure of entanglement between the two subsystems. The minimum eigenvalue distribution for quadratic matrices is also considered. The article shows that the N eigenvalues of the reduced density matrix of the smaller subsystem are distributed exactly as the eigenvalues of a Wishart matrix, except that the eigenvalues satisfy a global constraint: the trace is fixed to be unity.

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44

Zabrodin, Anton. Financial applications of random matrix theory: a short review. Edited by Gernot Akemann, Jinho Baik, and Philippe Di Francesco. Oxford University Press, 2018. http://dx.doi.org/10.1093/oxfordhb/9780198744191.013.40.

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This article reviews some applications of random matrix theory (RMT) in the context of financial markets and econometric models, with emphasis on various theoretical results (for example, the Marčenko-Pastur spectrum and its various generalizations, random singular value decomposition, free matrices, largest eigenvalue statistics) as well as some concrete applications to portfolio optimization and out-of-sample risk estimation. The discussion begins with an overview of principal component analysis (PCA) of the correlation matrix, followed by an analysis of return statistics and portfolio theory. In particular, the article considers single asset returns, multivariate distribution of returns, risk and portfolio theory, and nonequal time correlations and more general rectangular correlation matrices. It also presents several RMT results on the bulk density of states that can be obtained using the concept of matrix freeness before concluding with a description of empirical correlation matrices of stock returns.

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45

Kondratiev, I. G., A. V. Kudrin, and T. M. Zaboronkova. Electrodynamics of Density Ducts in Magnetized Plasmas: The Mathematical Theory of Excitation and Propagation of Electromagnetic Waves in Plasma Waveguides. CRC, 1999.

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46

Steinberg, Aephraim M. Quantum measurements: a modern view for quantum optics experimentalists. Oxford University Press, 2017. http://dx.doi.org/10.1093/oso/9780198768609.003.0007.

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This chapter introduces the theory and practice of various approaches to measuring quantum systems, focusing on quantum-optical settings, including monitored spontaneous emission, the quantum eraser, and unambiguous state discrimination. Beginning with a review of classical probability and update rules, it explains the motivation for the consideration of density matrices and generalized quantum measurements, treats the connection with decoherence, and goes on to introduce and discuss retrodiction, including ‘interaction-free measurement’, Hardy’s paradox, and ‘weak measurement’.

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47

Bouchaud, Jean-Philippe. Random matrix theory and (big) data analysis. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198797319.003.0006.

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This chapter reviews methods from random matrix theory to extract information about a large signal matrix C (for example, a correlation matrix arising in big data problems), from its noisy observation matrix M. The chapter shows that the replica method can be used to obtain both the spectral density and the overlaps between noise-corrupted eigenvectors and the true ones, for both additive and multiplicative noise. This allows one to construct optimal rotationally invariant estimators of C based on the observation of M alone. This chapter also discusses the case of rectangular correlation matrices and the problem of random singular value decomposition.

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48

Morawetz, Klaus. Systems with Condensates and Pairing. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198797241.003.0012.

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The Bose–Einstein condensation and appearance of superfluidity and superconductivity are introduced from basic phenomena. A systematic theory based on the asymmetric expansion of chapter 11 is shown to correct the T-matrix from unphysical multiple-scattering events. The resulting generalised Soven scheme provides the Beliaev equations for Boson’s and the Nambu–Gorkov equations for fermions without the usage of anomalous and non-conserving propagators. This systematic theory allows calculating the fluctuations above and below the critical parameters. Gap equations and Bogoliubov–DeGennes equations are derived from this theory. Interacting Bose systems with finite temperatures are discussed with successively better approximations ranging from Bogoliubov and Popov up to corrected T-matrices. For superconductivity, the asymmetric theory leading to the corrected T-matrix allows for establishing the stability of the condensate and decides correctly about the pair-breaking mechanisms in contrast to conventional approaches. The relation between the correlated density from nonlocal kinetic theory and the density of Cooper pairs is shown.

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49

Botsford, Louis W., J. Wilson White, and Alan Hastings. Population Dynamics for Conservation. Oxford University Press, 2019. http://dx.doi.org/10.1093/oso/9780198758365.001.0001.

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This book is a quantitative exposition of our current understanding of the dynamics of plant and animal populations, with the goal that readers will be able to understand, and participate in the management of populations in the wild. The book uses mathematical models to establish the basic principles of population behaviour. It begins with a philosophical approach to mathematical models of populations. It then progresses from a description of models with a single variable, abundance, to models that describe changes in the abundance of individuals at each age, then similar models that describe populations in terms of the abundance over size, life stage, and space. The book assumes a knowledge of basic calculus, but explains more advanced mathematical concepts such as partial derivatives, matrices, and random signals, as it makes use of them. The book explains the basis of the principles underlying important population processes, such as the mechanism that allow populations to persist, rather than go extinct, the way in which populations respond to variable environments, and the origin of population cycles.The next two chapters focus on application of the principles of population dynamics to manage for the prevention of extinction, as well as the management of fisheries for sustainable, high yields. The final chapter recapitulates how different population behaviors arise in situations with different levels of density dependence and replacement (the potential lifetime reproduction per individual), and how variability arises at different time scales set by a species’ life history.

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50

Vermeul, Vincent R. A method for quantifying macroporosity. 1990.

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