Reduced density matrices mechanics

Reduced-Density-Matrix Mechanics. With Application to Many-Electron Atoms and Molecules,... 

T. Yanai and G. K. L. Chan, Canonical transformation theory for dynamic correlations in multireference problems, in Reduced-Density-Matrix Mechanics With Application to Many-Electron Atoms and Molecules, A Special Volume of Advances in Chemical Physics, Volume 134 (D.A. Mazziotti, ed.), Wiley, Hoboken, NJ, 2007. 

REDUCED-DENSITY-MATRIX MECHANICS WITH APPLICATION TO MANY-ELECTRON ATOMS AND MOLECULES... 

This volume in Advances in Chemical Physics provides a broad yet detailed survey of the recent advances and applications of reduced-density-matrix mechanics in chemistry and physics. With advances in theory and optimization, Coulson s challenge for the direct calculation of the 2-RDM has been answered. While significant progress has been made, as evident from the many contributions to this book, there remain many open questions and exciting opportunities for further development of 2-RDM methods and applications. It is the hope of the editor and the contributors that this book will serve as a guide for many further advenmres and advancements in RDM mechanics. 

Mazziotti DA (2005) Phys Rev A 72 032510 Mazziotti DA (2006) Phys Rev A 74 032501 Mazziotti DA (ed) (2007) Reduced-density-matrix mechanics with application to many-electron atoms and molecules. Advances in Chemical Physics, vol 134. Wiley, New York Mazziotti DA (2011) Phys Rev Lett 106 083001 Mazziotti DA (2012) Chem Rev 112 244... 

D. A. Mazziotti, in Reduced-Density-Matrix Mechanics, with Applications to Many-Electron... 

Jeszenszki P, Nagy PR, Zoboki T, Szabados A, Suijan PR (2014) Int J Quantum Chem 114 1048-1052 Coleman AJ (1963) Rev Mod Phys 35 668-687 Rassolov VA (2002) J Chem Phys 117 5978 Rassolov VA, Xu F (2007) J Chem Phys 127 044104 Piris M (2007) In Mazziotti DA (ed) Reduced-density-matrix mechanics with applications to many-electron atoms and molecules. Wiley, Hoboken, pp 387-427 chapter 14 Piris M, Ugalde JM (2009) J Comput Chem 30 2078-2086 Suarez E, Diaz N, Suarez D (2009) J Chem Theory Comput 1667-1679... 

Husimi, K., Proc. Phys.-Math. Soc. Japan 22, 264, "Some formal properties of the density matrix." Introduction of the concept of reduced density matrix. Statistical-mechanical treatment of the Hartree-Fock approximation at an arbitrary temperature and an alternative method of obtaining the reduced density matrices are discussed. 

These new trajectories are the so-called reduced quantum trajectories [30], which are only explicitly related to the system reduced density matrix. The dynamics described by Equation 8.42 leads to the correct intensity (time evolution of which is described by Equation 8.40) when the statistics of a large number of particles are considered. Moreover, Equation 8.42 reduces to the well-known expression for the velocity held in Bohmian mechanics, when there is no interaction with the environment. 

In Bohmian mechanics, the way the full problem is tackled in order to obtain operational formulas can determine dramatically the final solution due to the context-dependence of this theory. More specifically, developing a Bohmian description within the many-body framework and then focusing on a particle is not equivalent to directly starting from the reduced density matrix or from the one-particle TD-DFT equation. Being well aware of the severe computational problems coming from the first and second approaches, we are still tempted to claim that those are the most natural ways to deal with a many-body problem in a Bohmian context. 

The quantum mechanical equation of motion for an ensemble of nuclei may be written in terms of the reduced density matrix, o-,37 which is defined as, where V>k(0) is a possible wave function for the ensemble of nuclear spins and py is the probability of the nuclei being in that state. The equation of motion is,... 

The wide ranging experimental results on the conductivity of DNA have motivated theoretical efforts in this direction in order to come out with a clearer picture about the remarkable behaviour of the "molecule of life". The common theoretical approaches include ab initio studies and model calculations. The quantum master equations of the reduced density matrix [153] and the single step transfer theory of Marcus [154-157] govern the model calculations. According to Marcus, quantum-mechanical tunneling can occur when vibrational fluctuations bring the donor and acceptor states of the molecule into resonance. 

The probability density of electrons p x) in a quantum-mechanical system is given by the diagonal element of the first-order reduced-density matrix, (the superscript s indicates... 

The term decoherence describes the process by which the off-diagonal elements of the reduced density matrix tend to zero when evolving with time. Our objective is to reach an understanding of the molecular mechanisms governing decoherence with an atomic resolution. In addition we wish to be in a position to treat systems consisting of tens to thousands of atoms since the brute force simulation of the time evolution of p t) by the Liouville-von Neuman equation (p (i) = ih [H, p ]), the equivalent of the TDSE in the density matrix formalism, is out of question for such molecular systems. 

Keywords Atoms in molecules - Chemical bonding - Force fields - Intermolecular potential - Multipole moments - Quantum chemical topology - Electrostatic potential Coulomb interaction - Reduced density matrix - Polarisation - Quantum mechanics Convergence... 

Quantum mechanical observables for the system of interest can be obtained from the reduced density matrix. 

From a quantum mechanical perspective, the transient vibrational relaxation dynamics is often studied within a reduced density matrix formalism. The dissipative dynamics of the so-called open system is described by a Liouville von Neumann equation that includes implicitly the effects of the surroundings on the dynamics... 

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