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Related Concept Videos

Current Density01:21

Current Density

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The total amount of current flowing through one unit value of a cross-sectional area is referred to as current density. If the current flow is uniform, the amount of current flowing through a conductor is the same at all points along the conductor, even if the conductor area varies. The current density consists of the local magnitude and direction of the charge flow, which varies from point to point. Current density is measured in amperes per meter square, and direction is defined as the net...
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The total amount of current flowing per unit cross-sectional area is called the current density. Hence, the current passing through a cross-sectional area can be written as the surface integral of the current density.
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Boundary Conditions for Current Density01:25

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Current density becomes discontinuous across an interface of materials with different electrical conductivities. The normal component of the current density is continuous across the boundary.
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Carrier Transport01:21

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The generation of electrical current in semiconductors is fundamentally driven by two mechanisms: drift and diffusion. These processes are essential for the functionality and performance of semiconductor-based devices.
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Ampere's Law in Matter01:22

Ampere's Law in Matter

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The total current density in magnetized material is the sum of the free and bound current densities. The free current arises due to the motion of free electrons within the material, while the bound current arises due to the alignment of magnetic dipole moments.
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Energy Associated With a Charge Distribution01:21

Energy Associated With a Charge Distribution

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The work done to bring a charge through a distance r is given by the potential difference between the initial and the final position. To assemble a collection of point charges, the total work done can be expressed in terms of the product of each pair of charges divided by their separation distance, defined with respect to a suitable origin. Solving this expression gives the energy stored in a point charge distribution.
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Revisiting density-functional theory of the total current density.

Andre Laestadius1, Markus Penz2, Erik I Tellgren1

  • 1Hylleraas Centre for Quantum Molecular Sciences, Department of Chemistry, University of Oslo, PO Box 1033 Blindern, N-0315 Oslo, Norway.

Journal of Physics. Condensed Matter : an Institute of Physics Journal
|April 13, 2021
PubMed
Summary

This study reinterprets Diener's density-functional theory (DFT) formulation for magnetic fields. The research proves Diener's approach incorrectly calculates ground-state energy and contains a fundamental error in its Hohenberg-Kohn map construction.

Keywords:
Hohenberg–Kohn theoremcurrent-density-functional theorydensity-functional theorymagnetic systems

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Area of Science:

  • Quantum Chemistry
  • Condensed Matter Physics
  • Computational Materials Science

Background:

  • Density-functional theory (DFT) typically uses electron density as the sole variable.
  • Incorporating magnetic fields into DFT requires an additional variable, often the total current density in time-dependent cases.
  • In static ground-state DFT, the gauge-dependent paramagnetic current density has been used, posing theoretical challenges.

Purpose of the Study:

  • To reinterpret and clarify Diener's proposed exact reformulation of ground-state DFT using total current density.
  • To analyze the validity of Diener's unorthodox variational principle for ground-state DFT.
  • To assess the correctness of Diener's Hohenberg-Kohn-like mapping for total current density.

Main Methods:

  • Reinterpretation of Diener's formulation using a maximin variational principle.
  • Analysis of convexity properties derived from the variational expressions.
  • Mathematical proof of the limitations of Diener's approach.

Main Results:

  • Diener's formulation, based on a maximin variational principle, is shown to be incapable of reproducing the correct ground-state energy.
  • The proposed construction of a Hohenberg-Kohn map within Diener's framework contains an irreparable mistake.
  • The gauge-dependent paramagnetic current density, not the gauge-invariant total current density, incorrectly appears as the additional variable in the static ground-state setting.

Conclusions:

  • Diener's proposed exact ground-state density-functional theory reformulation using total current density is fundamentally flawed.
  • The theoretical framework requires further development to accurately incorporate magnetic-field effects within DFT.
  • The study highlights critical issues in existing theoretical approaches to magnetic DFT.