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Physical review. B, Condensed matter

Approximate density matrices for spherical metal clusters

A. Rigó, M. Casas, Angelo Plastino, Llorenç Serra

Published Jul 15, 1999• 0 citations
Publisher

Abstract

On the sole basis of the knowledge of the expectation values of several physical observables, an inferred density matrix for spherical alkali-metal clusters is obtained. No explicit knowledge of any Hamiltonian model is assumed. A combination of information theory with the pseudoinverse variational formalism is employed, and densities for spherical Na clusters are obtained.

DOI
10.1103/physrevb.60.2117

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On the sole basis of the knowledge of the expectation values of several physical observables, an inferred density matrix for spherical alkali-metal clusters is obtained. No explicit knowledge of any Hamiltonian model is assumed. A combination of information theory with the pseudoinverse variational formalism is employed, and densities for spherical Na clusters are obtained.
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We present an approximate inference approach based on the Information Theory and the Pseudoinverse Formalism that allows to obtain all the accessible micro-states of a quantum system compatible with a given information. We assume that the Hamiltonian of the system is unknown and the only available information is restricted to a set of expectation values of noncommuting operators. With this information the density matrix is inferred and, exploring the Null space of the input operators, one can define the physical regions for which the density matrix is positive definite. The method is applied for the inference of entangled quantum states.
The van der Waals coefficients, C6,C8,{C}_{6},{C}_{8},C6​,C8​, and C10{C}_{10}C10​ for the alkali-metal (Li, Na, K, and Rb) and alkaline-earth-metal (Be, Mg, Ca, and Sr) atoms are estimated by a combination of ab initio and semiempirical methods. Polarizabilities and atom-wall coefficients are given as a diagnostic check, and the lowest order nonadiabatic dispersion coefficient, D8{D}_{8}D8​ and the three-body coefficient, C9{C}_{9}C9​ are also presented. The dispersion coefficients are in agreement with the available relativistic many-body perturbation theory calculations. The contribution from the core was included by using constrained sum rules involving the core polarizability and Hartree-Fock expectation values to estimate the f-value distribution.
Accurate knowledge of interaction potentials among the alkali atoms and alkaline earth ions is very useful in the studies of cold atom physics. Here we carry out theoretical studies of the long-range interactions among the Li, Na, K, and Rb alkali atoms with the Ca+^++, Ba+^++, Sr+^++, and Ra+^++ alkaline earth ions systematically which are largely motivated by their importance in a number of applications. These interactions are expressed as a power series in the inverse of the internuclear separation RRR. Both the dispersion and induction components of these interactions are determined accurately from the algebraic coefficients corresponding to each power combination in the series. Ultimately, these coefficients are expressed in terms of the electric multipole polarizabilities of the above mentioned systems which are calculated using the matrix elements obtained from a relativistic coupled-cluster method and core contributions to these quantities from the random phase approximation. We also compare our estimated polarizabilities with the other available theoretical and experimental results to verify accuracies in our calculations. In addition, we also evaluate the lifetimes of the first two low-lying states of the ions using the above matrix elements. Graphical representation of the interaction potentials versus RRR are given among all the considered atoms and ions.
Abstract We select a couple of density functional formalisms suitable for the computation of the highest spin clusters composed of a small number of heavy alkali-metal atoms such as Rb and Cs. Using B3P86 and PW91PW91 density functional methods with Lanl2dz basis set, we analyze the geometry, the binding energy, and the bond length of Rbn and Csn with n = 2–14 in the highest spin state. The exchange energy of the highest spin clusters increases the binding energy with the number of the constituent atoms.