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Computation 2018, 6(1), 25; https://doi.org/10.3390/computation6010025

Dissipation Effects in Schrödinger and Quantal Density Functional Theories of Electrons in an Electromagnetic Field

1
Department of Physics, Ningbo University, Ningbo 315211, China
2
Department of Physics, The Graduate Center of the City University of New York, New York, NY 10016, USA
*
Author to whom correspondence should be addressed.
Received: 19 January 2018 / Revised: 23 February 2018 / Accepted: 25 February 2018 / Published: 6 March 2018
(This article belongs to the Special Issue In Memory of Walter Kohn—Advances in Density Functional Theory)
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Abstract

Dissipative effects arise in an electronic system when it interacts with a time-dependent environment. Here, the Schrödinger theory of electrons in an electromagnetic field including dissipative effects is described from a new perspective. Dissipation is accounted for via the effective Hamiltonian approach in which the electron mass is time-dependent. The perspective is that of the individual electron: the corresponding equation of motion for the electron or time-dependent differential virial theorem—the ‘Quantal Newtonian’ second law—is derived. According to the law, each electron experiences an external field comprised of a binding electric field, the Lorentz field, and the electromagnetic field. In addition, there is an internal field whose components are representative of electron correlations due to the Pauli exclusion principle and Coulomb repulsion, kinetic effects, and density. There is also an internal contribution due to the magnetic field. The response of the electron is governed by the current density field in which a damping coefficient appears. The law leads to further insights into Schrödinger theory, and in particular the intrinsic self-consistent nature of the Schrödinger equation. It is proved that in the presence of dissipative effects, the basic variables (gauge-invariant properties, knowledge of which determines the Hamiltonian) are the density and physical current density. Finally, a local effective potential theory of dissipative systems—quantal density functional theory (QDFT)—is developed. This constitutes the mapping from the interacting dissipative electronic system to one of noninteracting fermions possessing the same dissipation and basic variables. Attributes of QDFT are the separation of the electron correlations due to the Pauli exclusion principle and Coulomb repulsion, and the determination of the correlation contributions to the kinetic energy. Hence, Schrödinger theory in conjunction with QDFT leads to additional insights into the dissipative system. View Full-Text
Keywords: dissipation effects in quantum mechanics; dissipation in Schrödinger theory; dissipation in quantal density functional theory; density functional theory dissipation effects in quantum mechanics; dissipation in Schrödinger theory; dissipation in quantal density functional theory; density functional theory
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Pan, X.-Y.; Sahni, V. Dissipation Effects in Schrödinger and Quantal Density Functional Theories of Electrons in an Electromagnetic Field. Computation 2018, 6, 25.

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