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Journal articles on the topic 'Density matrices'

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Author: Grafiati

Published: 4 June 2021

Last updated: 20 February 2023

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1

Soirat, A., M. Flocco, and L. Massa. "ApproximatelyN-representable density functional density matrices." International Journal of Quantum Chemistry 49, no. 3 (January 20, 1994): 291–98. http://dx.doi.org/10.1002/qua.560490317.

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2

March, N. H. "Density functional theory via density matrices." International Journal of Quantum Chemistry 56, S29 (February 25, 1995): 137–44. http://dx.doi.org/10.1002/qua.560560814.

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3

Życzkowski, Karol, Karol A. Penson, Ion Nechita, and Benoît Collins. "Generating random density matrices." Journal of Mathematical Physics 52, no. 6 (June 2011): 062201. http://dx.doi.org/10.1063/1.3595693.

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4

Brüning, E., H. Mäkelä, A. Messina, and F. Petruccione. "Parametrizations of density matrices." Journal of Modern Optics 59, no. 1 (January 10, 2012): 1–20. http://dx.doi.org/10.1080/09500340.2011.632097.

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5

Schwarz, W. H. E., and B. Müller. "Density matrices from densities." Chemical Physics Letters 166, no. 5-6 (March 1990): 621–26. http://dx.doi.org/10.1016/0009-2614(90)87161-j.

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6

Peres, Asher. "Separability Criterion for Density Matrices." Physical Review Letters 77, no. 8 (August 19, 1996): 1413–15. http://dx.doi.org/10.1103/physrevlett.77.1413.

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7

Henderson, Thomas M., Carlos A. Jiménez-Hoyos, and Gustavo E. Scuseria. "Magnetic Structure of Density Matrices." Journal of Chemical Theory and Computation 14, no. 2 (December 29, 2017): 649–59. http://dx.doi.org/10.1021/acs.jctc.7b01016.

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8

Kim, Sejong, Sungwoon Kim, and Hosoo Lee. "Factorizations of invertible density matrices." Linear Algebra and its Applications 463 (December 2014): 190–204. http://dx.doi.org/10.1016/j.laa.2014.09.014.

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9

Asorey, M., A. Kossakowski, G. Marmo, and E. C. G. Sudarshan. "Dynamical maps and density matrices." Journal of Physics: Conference Series 196 (November 1, 2009): 012023. http://dx.doi.org/10.1088/1742-6596/196/1/012023.

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10

Brüning, E., and S. Nagamachi. "Parametrizations of degenerate density matrices." Reviews in Mathematical Physics 29, no. 08 (August 20, 2017): 1750026. http://dx.doi.org/10.1142/s0129055x1750026x.

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It turns out that a parametrization of degenerate density matrices requires a parametrization of [Formula: see text], [Formula: see text] where [Formula: see text] denotes the set of all unitary [Formula: see text]-matrices with complex entries. Unfortunately, the parametrization of this quotient space is quite involved. Our solution does not rely on Lie algebra methods directly, but succeeds through the construction of suitable sections for natural projections, by using techniques from the theory of homogeneous spaces. We mention the relation to the Lie algebra background and conclude with two concrete examples.

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11

Akhtarshenas, S. J. "Coset parameterization of density matrices." Optics and Spectroscopy 103, no. 3 (September 2007): 411–15. http://dx.doi.org/10.1134/s0030400x0709010x.

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12

Jenčová, Anna. "Geodesic distances on density matrices." Journal of Mathematical Physics 45, no. 5 (May 2004): 1787–94. http://dx.doi.org/10.1063/1.1689000.

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13

Nechita, Ion. "Asymptotics of Random Density Matrices." Annales Henri Poincaré 8, no. 8 (November 22, 2007): 1521–38. http://dx.doi.org/10.1007/s00023-007-0345-5.

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14

Gibbons, G. W. "Typical states and density matrices." Journal of Geometry and Physics 8, no. 1-4 (March 1992): 147–62. http://dx.doi.org/10.1016/0393-0440(92)90046-4.

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15

Fano, Ugo. "Density matrices as polarization vectors." Rendiconti Lincei 6, no. 2 (June 1995): 123–30. http://dx.doi.org/10.1007/bf03001661.

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16

MENDAŠ, ISTOK. "CLASSIFICATION OF DENSITY MATRICES FOR A FOUR-STATE SYSTEM." International Journal of Quantum Information 07, no. 01 (February 2009): 323–48. http://dx.doi.org/10.1142/s0219749909004682.

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Properties and structure of the 15-dimensional parameter space of four-state density matrices are examined using the SU(4) generator expansion. Appropriate classification of one-, two- and three-parameter density matrices is obtained, based on the sameness of the characteristic polynomial of density matrices belonging to a given type. It is found that in the one parameter case of 15 different density matrices only three distinct types exist, while in the two parameter case 105 different density matrices group into 11 distinct types. In the three parameter case appropriate classification of 455 different density matrices into 44 types is determined. Two- and three-dimensional cross sections of the space of generalized Bloch vectors are illustrated by randomly drawing matrices for several types of density matrices, providing some insight into the intricate and complex structure of the space of density matrices for a four-state system. Positions of the representative points corresponding to the pure states are found for all types. Global properties of observables are determined by generating, by the Monte Carlo sampling method, and averaging over nearly all density matrices pertaining to a given type.

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17

Brüning, E., and F. Petruccione. "Density Matrices and Their Time Evolution." Open Systems & Information Dynamics 15, no. 02 (June 2008): 109–21. http://dx.doi.org/10.1142/s1230161208000109.

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Already in the case of finite dimensional Hilbert spaces [Formula: see text] the general form of density matrices ρ is not known. The main reason for this lack of knowledge is the nonlinear constraint for these matrices. We propose a representation of density matrices on finite dimensional Hilbert spaces in terms of finitely many independent parameters. For dimensions 2, 3, and 4 we write down this representation explicitly. As a further application of this representation we study the time dependence of density matrices ρ(t) which in our case is implemented through time dependence of the independent parameters. Under obvious differentiability assumptions the explicit form of [Formula: see text] is determined. As a special case we recover, for instance, the Lindblad form.

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18

Holas, A., and N. H. March. "Density matrices and density functionals in strong magnetic fields." Physical Review A 56, no. 6 (December 1, 1997): 4595–605. http://dx.doi.org/10.1103/physreva.56.4595.

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19

Janesko, Benjamin G., and Austin Aguero. "Nonspherical model density matrices for Rung 3.5 density functionals." Journal of Chemical Physics 136, no. 2 (January 14, 2012): 024111. http://dx.doi.org/10.1063/1.3675681.

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20

Wu, Chai Wah. "Conditions for separability in generalized Laplacian matrices and diagonally dominant matrices as density matrices." Physics Letters A 351, no. 1-2 (February 2006): 18–22. http://dx.doi.org/10.1016/j.physleta.2005.10.049.

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21

Linden, N., S. Popescu, and A. Sudbery. "Nonlocal Parameters for Multiparticle Density Matrices." Physical Review Letters 83, no. 2 (July 12, 1999): 243–47. http://dx.doi.org/10.1103/physrevlett.83.243.

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22

Harriman, John E. "Distance and entropy for density matrices." Journal of Chemical Physics 115, no. 20 (November 22, 2001): 9223–32. http://dx.doi.org/10.1063/1.1412877.

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23

Fiolhais, Miguel C. N. "The Cabibbo-Kobayashi-Maskawa density matrices." EPL (Europhysics Letters) 98, no. 5 (June 1, 2012): 51001. http://dx.doi.org/10.1209/0295-5075/98/51001.

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24

Bachmann, Michael, Hagen Kleinert, and Axel Pelster. "Variational perturbation theory for density matrices." Physical Review A 60, no. 5 (November 1, 1999): 3429–43. http://dx.doi.org/10.1103/physreva.60.3429.

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25

March, N. H. "Exchange, idempotent density matrices and beyond." Journal of Molecular Structure: THEOCHEM 501-502 (April 2000): 17–27. http://dx.doi.org/10.1016/s0166-1280(99)00409-1.

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26

Brüning, Erwin, and Francesco Petruccione. "‘Nonlinear’ positive mappings for density matrices." Physica E: Low-dimensional Systems and Nanostructures 42, no. 3 (January 2010): 436–38. http://dx.doi.org/10.1016/j.physe.2009.06.017.

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27

Frantsuzov, Pavel, Arnold Neumaier, and Vladimir A. Mandelshtam. "Gaussian resolutions for equilibrium density matrices." Chemical Physics Letters 381, no. 1-2 (November 2003): 117–22. http://dx.doi.org/10.1016/j.cplett.2003.09.104.

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28

Belov, Dmitri, and Anatoly Konechny. "On spectral density of Neumann matrices." Physics Letters B 558, no. 1-2 (April 2003): 111–18. http://dx.doi.org/10.1016/s0370-2693(03)00242-9.

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29

Abramson, Michael P., Alfred W. Hales, and Richard A. Stong. "Minimal density conjugation of binary matrices." Advances in Applied Mathematics 47, no. 1 (July 2011): 23–48. http://dx.doi.org/10.1016/j.aam.2010.04.002.

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30

Coleman, A. J., and V. I. Yukalov. "Order indices for boson density matrices." Il Nuovo Cimento B Series 11 107, no. 5 (May 1992): 535–52. http://dx.doi.org/10.1007/bf02723631.

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31

Christandl, Matthias, Brent Doran, Stavros Kousidis, and Michael Walter. "Eigenvalue Distributions of Reduced Density Matrices." Communications in Mathematical Physics 332, no. 1 (August 19, 2014): 1–52. http://dx.doi.org/10.1007/s00220-014-2144-4.

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32

Mazziotti, David A. "Complete reconstruction of reduced density matrices." Chemical Physics Letters 326, no. 3-4 (August 2000): 212–18. http://dx.doi.org/10.1016/s0009-2614(00)00773-9.

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33

Gori, F., V. Ramírez-Sánchez, M. Santarsiero, and T. Shirai. "On genuine cross-spectral density matrices." Journal of Optics A: Pure and Applied Optics 11, no. 8 (May 28, 2009): 085706. http://dx.doi.org/10.1088/1464-4258/11/8/085706.

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34

Sommers, Hans-Jürgen, and Karol yczkowski. "Statistical properties of random density matrices." Journal of Physics A: Mathematical and General 37, no. 35 (August 18, 2004): 8457–66. http://dx.doi.org/10.1088/0305-4470/37/35/004.

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35

Purwanto, Agus, Heru Sukamto, and Lila Yuwana. "Quantum Entanglement and Reduced Density Matrices." International Journal of Theoretical Physics 57, no. 8 (May 8, 2018): 2426–36. http://dx.doi.org/10.1007/s10773-018-3764-9.

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36

Davidson, Ernest R. "Linear inequalities for density matrices: III." International Journal of Quantum Chemistry 91, no. 1 (November 21, 2002): 1–4. http://dx.doi.org/10.1002/qua.10340.

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37

Coleman, A. John. "Reduced density matrices?Then and now." International Journal of Quantum Chemistry 85, no. 4-5 (2001): 196–203. http://dx.doi.org/10.1002/qua.1537.

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38

Zapol, Boris P. "Integral-geometrical consideration of density matrices." International Journal of Quantum Chemistry 56, no. 5 (December 5, 1995): 535–45. http://dx.doi.org/10.1002/qua.560560511.

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39

Song, Yuan-Feng, Li-Zhu Ge, Yao-Kun Wang, Hui Tang, and Yan Tian. "Relative entropies of coherence of X states in three-dimensional mutually unbiased bases." Laser Physics Letters 19, no. 8 (June 13, 2022): 085201. http://dx.doi.org/10.1088/1612-202x/ac7572.

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Abstract In this paper, we calculate the density matrices of one class of X states in the three-dimensional mutually unbiased bases and find that the density matrices are equal to their corresponding conjugate transpose matrices. After obtaining the relations of these density matrices, we calculate the relative entropies of coherence for the density matrices of X states in these nontrivial mutually unbiased bases and obtain that their relative entropies of coherence are equal. At last, the density matrices of other two classes of X states in these mutually unbiased bases are discussed. We also investigate their relative entropies of coherence and clarify their relationships.

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40

Soirat, A., M. Flocco, and L. Massa. "ApproximatelyN-representable density functional density matrices: The case of largeN." Proceedings / Indian Academy of Sciences 106, no. 2 (April 1994): 209–16. http://dx.doi.org/10.1007/bf02840744.

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41

Zhang, Lin, Jiamei Wang, and Zhihua Chen. "Spectral density of mixtures of random density matrices for qubits." Physics Letters A 382, no. 23 (June 2018): 1516–23. http://dx.doi.org/10.1016/j.physleta.2018.04.018.

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42

Kribs, David, Jeremy Levick, and Rajesh Pereira. "Totally Positive Density Matrices and Linear Preservers." Electronic Journal of Linear Algebra 31 (February 5, 2016): 313–20. http://dx.doi.org/10.13001/1081-3810.3129.

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The intersection between the set of totally nonnegative matrices, which are of interest in many areas of matrix theory and its applications, and the set of density matrices, which provide the mathematical description of quantum states, are investigated. The single qubit case is characterized, and several equivalent conditions for a quantum channel to preserve the set in that case are given. Higher dimensional cases are also discussed.

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43

Johnson, Paul A., Hubert Fortin, Samuel Cloutier, and Charles-Émile Fecteau. "Transition density matrices of Richardson–Gaudin states." Journal of Chemical Physics 154, no. 12 (March 28, 2021): 124125. http://dx.doi.org/10.1063/5.0041051.

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44

Fannes, Mark. "Using density matrices in classical dynamical systems." Banach Center Publications 43, no. 1 (1998): 175–82. http://dx.doi.org/10.4064/-43-1-175-182.

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45

Moisset, Jean-David, Charles-Émile Fecteau, and Paul A. Johnson. "Density matrices of seniority-zero geminal wavefunctions." Journal of Chemical Physics 156, no. 21 (June 7, 2022): 214110. http://dx.doi.org/10.1063/5.0088602.

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Scalar products and density matrix elements of closed-shell pair geminal wavefunctions are evaluated directly in terms of the pair amplitudes, resulting in an analog of Wick’s theorem for fermions or bosons. This expression is, in general, intractable, but it is shown how it becomes feasible in three distinct ways for Richardson–Gaudin (RG) states, the antisymmetrized geminal power, and the antisymmetrized product of strongly orthogonal geminals. Dissociation curves for hydrogen chains are computed with off-shell RG states and the antisymmetrized product of interacting geminals. Both are near exact, suggesting that the incorrect results observed with ground state RG states (a local maximum rather than smooth dissociation) may be fixable using a different RG state.

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46

Chen, Eddy Keming, and Roderich Tumulka. "Uniform probability distribution over all density matrices." Quantum Studies: Mathematics and Foundations 9, no. 2 (January 16, 2022): 225–33. http://dx.doi.org/10.1007/s40509-021-00267-5.

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AbstractLet $$\mathscr {H}$$ H be a finite-dimensional complex Hilbert space and $$\mathscr {D}$$ D the set of density matrices on $$\mathscr {H}$$ H , i.e., the positive operators with trace 1. Our goal in this note is to identify a probability measure u on $$\mathscr {D}$$ D that can be regarded as the uniform distribution over $$\mathscr {D}$$ D . We propose a measure on $$\mathscr {D}$$ D , argue that it can be so regarded, discuss its properties, and compute the joint distribution of the eigenvalues of a random density matrix distributed according to this measure.

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47

Brüning, Erwin, Dariusz Chruściński, and Francesco Petruccione. "Parametrizing Density Matrices for Composite Quantum Systems." Open Systems & Information Dynamics 15, no. 04 (December 2008): 397–408. http://dx.doi.org/10.1142/s1230161208000274.

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A parametrization of density operators for bipartite quantum systems is proposed. It is based on the particular parametrization of the unitary group found recently by Jarlskog. It is expected that this parametrization will find interesting applications in the study of quantum properties of multipartite systems.

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48

Peschel, Ingo, and Ming-Chiang Chung. "Density matrices for a chain of oscillators." Journal of Physics A: Mathematical and General 32, no. 48 (November 17, 1999): 8419–28. http://dx.doi.org/10.1088/0305-4470/32/48/305.

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49

Cicuta, Giovanni M., and Madan Lal Mehta. "Probability density of determinants of random matrices." Journal of Physics A: Mathematical and General 33, no. 45 (November 3, 2000): 8029–35. http://dx.doi.org/10.1088/0305-4470/33/45/302.

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50

Harriman, John E. "Electron Densities, Momentum Densities, and Density Matrices." Zeitschrift für Naturforschung A 48, no. 1-2 (February 1, 1993): 203–10. http://dx.doi.org/10.1515/zna-1993-1-240.

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Abstract Relationships among electron coordinate-space and momentum densities and the one-electron charge density matrix or Wigner function are examined. A knowledge of either or both densities places constraints on possible density matrices. Questions are approached in the context of a finite-basis-set model problem in which density matrices are elements in a Euclidean vector space of Hermitian operators or matrices, and densities are elements of other vector spaces. The maps (called "collapse") of the operator space to the density spaces define a decomposition of the operator space into orthogonal subspaces. The component of a density matrix in a given subspace is determined by one density, both densities, or neither. Linear dependencies among products of basis functions play a fundamental role. Algorithms are discussed for finding the subspaces and constructing an orthonormal set of functions spanning the same space as a linearly dependent set. Examples are presented and additional investigations suggested.

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