{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,31]],"date-time":"2025-10-31T07:39:40Z","timestamp":1761896380980,"version":"build-2065373602"},"reference-count":25,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2016,8,16]],"date-time":"2016-08-16T00:00:00Z","timestamp":1471305600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Natural National Science Foundation of China","award":["11275100"],"award-info":[{"award-number":["11275100"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Computation"],"abstract":"<jats:p>Local effective potential theory, both stationary-state and time-dependent, constitutes the mapping from a system of electrons in an external field to one of the noninteracting fermions possessing the same basic variable such as the density, thereby enabling the determination of the energy and other properties of the electronic system. This paper is a description via Quantal Density Functional Theory (QDFT) of the electron correlations that must be accounted for in such a mapping. It is proved through QDFT that independent of the form of external field, (a) it is possible to map to a model system possessing all the basic variables; and that (b) with the requirement that the model fermions are subject to the same external fields, the only correlations that must be considered are those due to the Pauli exclusion principle, Coulomb repulsion, and Correlation\u2013Kinetic effects. The cases of both a static and time-dependent electromagnetic field, for which the basic variables are the density and physical current density, are considered. The examples of solely an external electrostatic or time-dependent electric field constitute special cases. An efficacious unification in terms of electron correlations, independent of the type of external field, is thereby achieved. The mapping is explicated for the example of a quantum dot in a magnetostatic field, and for a quantum dot in a magnetostatic and time-dependent electric field.<\/jats:p>","DOI":"10.3390\/computation4030030","type":"journal-article","created":{"date-parts":[[2016,8,16]],"date-time":"2016-08-16T10:03:21Z","timestamp":1471341801000},"page":"30","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":11,"title":["Electron Correlations in Local Effective Potential Theory"],"prefix":"10.3390","volume":"4","author":[{"given":"Viraht","family":"Sahni","sequence":"first","affiliation":[{"name":"The Graduate School of the City University of New York, New York, NY 10016, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xiao-Yin","family":"Pan","sequence":"additional","affiliation":[{"name":"Department of Physics, Ningbo University, Ningbo 315211, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Tao","family":"Yang","sequence":"additional","affiliation":[{"name":"Department of Physics, Ningbo University, Ningbo 315211, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2016,8,16]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"A 1133","DOI":"10.1103\/PhysRev.140.A1133","article-title":"Self-consistent equations including exchange and correlation effects","volume":"140","author":"Kohn","year":"1965","journal-title":"Phys. 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Quantum Chem."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"042508","DOI":"10.1103\/PhysRevA.63.042508","article-title":"Sum rules and properties in time-dependent density-functional theory","volume":"63","author":"Qian","year":"2001","journal-title":"Phys. Rev. A"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1007\/3-540-61132-0_1","article-title":"Quantum-mechanical interpretation of density functional theory","volume":"182","author":"Sahni","year":"1996","journal-title":"Top. Curr. Chem."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"1846","DOI":"10.1103\/PhysRevA.55.1846","article-title":"Physical Interpretation of Density Functional Theory and of Its Representation of the Hartree-Fock and Hartree Theories","volume":"55","author":"Sahni","year":"1997","journal-title":"Phys. Rev. A"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"2040","DOI":"10.1103\/PhysRevA.51.2040","article-title":"Exact exchange-correlation potential and approximate exchange potential in terms of density matrices","volume":"51","author":"Holas","year":"1995","journal-title":"Phys. Rev. A"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"B864","DOI":"10.1103\/PhysRev.136.B864","article-title":"Inhomogeneous electron gas","volume":"136","author":"Hohenberg","year":"1994","journal-title":"Phys. Rev."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"997","DOI":"10.1103\/PhysRevLett.52.997","article-title":"Density-functional theory for time-dependent systems","volume":"52","author":"Runge","year":"1984","journal-title":"Phys. Rev. Lett."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"174105","DOI":"10.1063\/1.4934800","article-title":"Hohenberg-Kohn Theorems in Electrostatic and Uniform Magnetostatic Fields","volume":"143","author":"Pan","year":"2015","journal-title":"J. Chem. Phys."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"042518","DOI":"10.1103\/PhysRevA.83.042518","article-title":"Quantal Density Functional Theory in the Presence of a Magnetic Field","volume":"83","author":"Yang","year":"2011","journal-title":"Phys. Rev. A"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"2785","DOI":"10.1103\/RevModPhys.82.2785","article-title":"Vortices in quantum droplets: Analogies between boson and fermion systems","volume":"82","author":"Saarikovski","year":"2010","journal-title":"Rev. Mod. Phys."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"4595","DOI":"10.1103\/PhysRevA.56.4595","article-title":"Density matrices and density functionals in strong magnetic fields","volume":"56","author":"Holas","year":"1997","journal-title":"Phys. Rev. A"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"4723","DOI":"10.1088\/0305-4470\/27\/13\/047","article-title":"Two electrons in a homogeneous magnetic field: Particular analytical solutions","volume":"27","author":"Taut","year":"1994","journal-title":"Corrigenda J. Phys. A"},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"631","DOI":"10.1524\/zpch.2010.6128","article-title":"Exact solutions for a two-electron Quantum Dot model in a magnetic field and application to more complex systems","volume":"224","author":"Taut","year":"2010","journal-title":"Z. Phys. Chem."},{"key":"ref_18","first-page":"357","article-title":"Study of a Quantum Dot in an Excited State","volume":"61","author":"Slamet","year":"2016","journal-title":"Bull. Am. Phys. Soc."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"1149","DOI":"10.1103\/PhysRevA.38.1149","article-title":"Density-functional theory of many-electron systems subjected to time-dependent electric and magnetic fields","volume":"38","author":"Ghosh","year":"1988","journal-title":"Phys. Rev. A"},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"201102","DOI":"10.1103\/PhysRevB.70.201102","article-title":"Mapping from current densities to vector potentials in time-dependent current density functional theory","volume":"70","author":"Vignale","year":"2004","journal-title":"Phys. Rev. B"},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"024318","DOI":"10.1063\/1.4858463","article-title":"Wave Function for Harmonically Confined Electrons in Time-Dependent Electric and Magnetostatic Fields","volume":"140","author":"Zhu","year":"2014","journal-title":"J. Chem. Phys."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"1242","DOI":"10.1103\/PhysRev.123.1242","article-title":"Cyclotron Resonance and de Haas-Van Alphen Oscillations of an Interacting Electron Gas","volume":"123","author":"Kohn","year":"1961","journal-title":"Phys. Rev."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"2244","DOI":"10.1103\/PhysRevLett.73.2244","article-title":"Harmonic-Potential Theorem: Implications for Approximate Many-Body Theories","volume":"73","author":"Dobson","year":"1994","journal-title":"Phys. Rev. Lett."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"14","DOI":"10.1016\/j.comptc.2014.02.020","article-title":"Wigner High Electron Correlation Regime in Nonuniform Electron Density Systems: Kinetic and Correlation-Kinetic Aspects","volume":"1035","author":"Achan","year":"2014","journal-title":"Comput. Theor. Chem."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"022502","DOI":"10.1103\/PhysRevA.90.022502","article-title":"Wigner High Electron Correlation Regime of Nonuniform Density Systems: A Quantal Density Functional Theory Study","volume":"90","author":"Achan","year":"2014","journal-title":"Phys. Rev. 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