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Autor:
Panin, Ivan I.
Publikováno v:
Electron. J. Statist. 15 (2021), no. 1, 235--281
Sobol' sensitivity indices allow to quantify the respective effects of random input variables and their combinations on the variance of mathematical model output. We focus on the problem of Sobol' indices estimation via a metamodeling approach where
Externí odkaz:
http://arxiv.org/abs/1912.11070
Autor:
Panin, Andrej I.
This work completes the construction of purely algebraic version of the theory of non-linear quantum chemistry methods. It is shown that at the heart of these methods there lie certain algebras close in their definition to the well-known Clifford alg
Externí odkaz:
http://arxiv.org/abs/1007.1736
Autor:
Panin, A. I.
Hamiltonian and Schrodinger evolution equations on finite-dimensional projective space are analyzed in detail. Hartree-Fock (HF) manifold is introduced as a submanifold of many electron projective space of states. Evolution equations, exact and linea
Externí odkaz:
http://arxiv.org/abs/0707.3796
Autor:
Panin, A. I.
Interrelation of the Coleman's representabilty theory for 1-density operators and abstract algebraic form of the Hohenberg-Kohn theorem is studied in detail. Convenient realization of the Hohenberg-Kohn set of classes of 1-electron operators and the
Externí odkaz:
http://arxiv.org/abs/physics/0607037
Autor:
Panin, A. I.
New algebraic structure on electronic Fock space is studied in detail. This structure is defined in terms of a certain multiplication of many electron wave functions and has close interrelation with coupled cluster and similar approaches. Its study c
Externí odkaz:
http://arxiv.org/abs/physics/0503236
Autor:
Panin, A. I.
Efficient technique of manipulation with phase prefactors in electronic Fock spaces is developed. Its power is demonstrated on example of both relatively simple classic configuration interaction matrix element evaluation and essentially more complica
Externí odkaz:
http://arxiv.org/abs/physics/0503234
Autor:
Panin, A. I., Petrov, A. N.
General theorem describing a relation between diagonal of one-electron density matrix and a certain class of many-electron ensembles of determinant states is proved. As a corollary to this theorem a constructive proof of sufficiency of Coleman's repr
Externí odkaz:
http://arxiv.org/abs/physics/0310043
Autor:
Panin, A. I.
General properties of new models of the electronic Fock spaces based on the notion of (p,q)-sheaves are studied. Interrelation between simple sheaves and density operators is established. Explicit expressions for the transformed reduced Hamiltonians
Externí odkaz:
http://arxiv.org/abs/physics/0210070
Autor:
Panin, A. I.
New models of the Fock space sector corresponding to some fixed number of electrons are introduced. These models originate from the representability theory and their practical implementation may lead to essential reduction of dimensions of intermedia
Externí odkaz:
http://arxiv.org/abs/physics/0108007