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Physical Review A

Calculation of traces ofp-order replacement operators overN-electron spin-adapted spaces

Alicia Torre, Luis Laín, Judith Millán

Published Feb 1, 1993• 18 citations
Publisher

Abstract

We present here a simple method for the direct evaluation of traces of p-order replacement operators (p-RO's) calculated in a finite-dimensional, antisymmetric, and spin-adapted N-electron space. The procedure is based on the reduction of the operator order together with a performance of the summations through Slater determinants. Very useful and general formulas, which can be applied to RO's of any order p\ensuremath{\le}N, are then derived.

DOI
10.1103/physreva.47.923

Related papers

Direct computation of traces ofp-order replacement operators overN-electron spin-adapted spaces

Luis Laín, Alicia Torre

In our previous studies with the evaluation of traces of p-order replacement operators calculated in finite-dimensional, antisymmetric, and spin-adapted N-electron spaces (p\ensuremath{\le}N), we described a technique for the calculation of those expressions based on the reduction of the opertor order [A. Torre, L. Lain, and J. Millan, Phys. Rev. A 47, 923 (1993)]. Now, we report a general formula which, condensing all the reduction steps, leads to the direct evaluation of those traces. Some examples for illuminating the usefulness of that formula are reported.

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This paper reports a calculation of moments of spectral density distributions which are used in statistical theory of spectra of many-electron systems. The procedure lead to formulae which are fit for computer evaluations. The method is based on the determination of spin-adapted traces of powers of the Hamiltonian operator, represented in a finite-dimensional antisymmetric and spin-adapted Hilbert space. A whole study of the traces which appear in this problem is described.

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Traces of the reduced density operators revisited: closed-form formulae

Josep Planelles, Jacek Karwowski

Closed-form expressions for traces of the qth-order reduced density operators, q-RDOs, and symmetry-adapted q-RDOs calculated in an N-electron and spin-adapted subspace of a K-orbital Fock space are derived. The asymptotic form of the expression for traces of the q-RDOs, corresponding to and limits, is discussed in detail. Several identities fulfilled by some quantities related to the traces are derived.

Journal of Physics A Mathematical and General•May 7, 1997•2 citations
We present here a simple method for the direct evaluation of traces of p-order replacement operators (p-RO's) calculated in a finite-dimensional, antisymmetric, and spin-adapted N-electron space. The procedure is based on the reduction of the operator order together with a performance of the summations through Slater determinants. Very useful and general formulas, which can be applied to RO's of any order p\ensuremath{\le}N, are then derived.
In our previous studies with the evaluation of traces of p-order replacement operators calculated in finite-dimensional, antisymmetric, and spin-adapted N-electron spaces (p\ensuremath{\le}N), we described a technique for the calculation of those expressions based on the reduction of the opertor order [A. Torre, L. Lain, and J. Millan, Phys. Rev. A 47, 923 (1993)]. Now, we report a general formula which, condensing all the reduction steps, leads to the direct evaluation of those traces. Some examples for illuminating the usefulness of that formula are reported.