1983
DOI: 10.1002/prop.2190311202
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Localized-Particles Approach for Classical and Quantum Crystals

Abstract: This paper is the first review devoted to the localized-particles approach for strongly anharmonic crystals . We present mathematical basises of such an approach for classical and quantum cases and we discuss its different applications .

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Cited by 44 publications
(42 citation statements)
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“…This approach was motivated by and applied to many-particle systems with strong interactions [11][12][13][14][15][16][17][18][19][20][21]. Technically, the approach is based on the methods of perturbation and iteration theories combined with optimal control theory.…”
Section: Optimized Perturbation Theorymentioning
confidence: 99%
“…This approach was motivated by and applied to many-particle systems with strong interactions [11][12][13][14][15][16][17][18][19][20][21]. Technically, the approach is based on the methods of perturbation and iteration theories combined with optimal control theory.…”
Section: Optimized Perturbation Theorymentioning
confidence: 99%
“…For instance, it has been argued that anharmonicity is fundamental for the stability of graphene and it cannot be taken into account by means of perturbative methods starting from harmonic or quasiharmonic approximations. In order to properly deal with those anharmonic effects in structural, dynamical, and thermodynamic properties of a 2D graphene crystal, we use the unsymmetrized self-consistent field method (USF) [16][17][18][19][20][21][22][23][24] for anharmonic crystals, which we extend for the first time to layered non-Bravais crystals. In this approach it is possible to construct several zeroth-order approximations to any order of anharmonicity.…”
mentioning
confidence: 99%
“…The temperature dependence of the molar volume along the melting curve is approximated by [55] In summary, a method is given for the calculation of interatomic correlations in anharmonic crystals. We have given here a classical approach, although it enables also the calculation of quantum correction [31]. When there is no permutation symmetry, even in the zeroth mean-field approximation, the long-range static and the short-range dynamic correlations are taken into account preventing the unlimited approaching of atoms to each other.…”
Section: Fulleritementioning
confidence: 99%
“…More than that, it is just because of the core that the one-particle probability densities vanish except inside the corresponding lattice cell thus leading to a convergence of the statistical averages. It is based on the assumption that the classical phase probability density [55] or the quantum density matrix [31,36,56] is not symmetric with respect to the interchange of coordinates of identical atoms. Here we restrict ourselves to the classical approach.…”
Section: Introductionmentioning
confidence: 99%