Kinetic energy estimates for the accuracy of the time-dependent Hartree-Fock approximation with Coulomb interaction

Bach, Volker; Breteaux, Sébastien; Petrat, Sören P; Pickl, Peter; Tzaneteas, Tim

Kinetic energy estimates for the accuracy of the time-dependent Hartree-Fock approximation with Coulomb interaction

V. Bach, S. Breteaux, S.P. Petrat, P. Pickl, T. Tzaneteas, Journal de Mathématiques Pures et Appliquées 105 (2016) 1–30.

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IST-2016-581-v1+1_1-s2.0-S0021782415001191-main.pdf 658.49 KB

DOI

10.1016/j.matpur.2015.09.003

Journal Article | Published | English

Author

Bach, Volker ; Breteaux, Sébastien ; Petrat, Sören P^{IST Austria} ; Pickl, Peter ; Tzaneteas, Tim

Department

Seiringer Group

Grant

International IST Postdoc Fellowship Programme

Abstract

We study the time evolution of a system of N spinless fermions in R3 which interact through a pair potential, e.g., the Coulomb potential. We compare the dynamics given by the solution to Schrödinger's equation with the time-dependent Hartree-Fock approximation, and we give an estimate for the accuracy of this approximation in terms of the kinetic energy of the system. This leads, in turn, to bounds in terms of the initial total energy of the system.

Publishing Year

2016

Date Published

2016-01-01

Journal Title

Journal de Mathématiques Pures et Appliquées

Volume

105

Issue

Page

1 - 30

IST-REx-ID

1436

Cite this

Bach V, Breteaux S, Petrat SP, Pickl P, Tzaneteas T. Kinetic energy estimates for the accuracy of the time-dependent Hartree-Fock approximation with Coulomb interaction. Journal de Mathématiques Pures et Appliquées. 2016;105(1):1-30. doi:10.1016/j.matpur.2015.09.003

Bach, V., Breteaux, S., Petrat, S. P., Pickl, P., & Tzaneteas, T. (2016). Kinetic energy estimates for the accuracy of the time-dependent Hartree-Fock approximation with Coulomb interaction. Journal de Mathématiques Pures et Appliquées, 105(1), 1–30. https://doi.org/10.1016/j.matpur.2015.09.003

Bach, Volker, Sébastien Breteaux, Sören P Petrat, Peter Pickl, and Tim Tzaneteas. “Kinetic Energy Estimates for the Accuracy of the Time-Dependent Hartree-Fock Approximation with Coulomb Interaction.” Journal de Mathématiques Pures et Appliquées 105, no. 1 (2016): 1–30. https://doi.org/10.1016/j.matpur.2015.09.003.

V. Bach, S. Breteaux, S. P. Petrat, P. Pickl, and T. Tzaneteas, “Kinetic energy estimates for the accuracy of the time-dependent Hartree-Fock approximation with Coulomb interaction,” Journal de Mathématiques Pures et Appliquées, vol. 105, no. 1, pp. 1–30, 2016.

Bach V, Breteaux S, Petrat SP, Pickl P, Tzaneteas T. 2016. Kinetic energy estimates for the accuracy of the time-dependent Hartree-Fock approximation with Coulomb interaction. Journal de Mathématiques Pures et Appliquées. 105(1), 1–30.

Bach, Volker, et al. “Kinetic Energy Estimates for the Accuracy of the Time-Dependent Hartree-Fock Approximation with Coulomb Interaction.” Journal de Mathématiques Pures et Appliquées, vol. 105, no. 1, Elsevier, 2016, pp. 1–30, doi:10.1016/j.matpur.2015.09.003.

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