Multimarginal Optimal Transport Maps for One–dimensional Repulsive Costs

Colombo, Maria; Pascale, Luigi De; Marino, Simone Di

doi:10.4153/cjm-2014-011-x

Cited by 99 publications

(133 citation statements)

References 19 publications

(22 reference statements)

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“…On the other hand, it has been proved in [72] that the floating crystal, defined similarly as in (11), is the exact ground state of the indirect energy E Ind (1 [−N/2,N/2] ). Hence the computations in [8] imply that there is an energy shift:…”

Section: Extension To Riesz Potentials In All Space Dimensionsmentioning

confidence: 99%

Floating Wigner crystal with no boundary charge fluctuations

2019

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We modify the "floating crystal" trial state for the classical Homogeneous Electron Gas (also known as Jellium), in order to suppress the boundary charge fluctuations that are known to lead to a macroscopic increase of the energy. The argument is to melt a thin layer of the crystal close to the boundary and consequently replace it by an incompressible fluid. With the aid of this trial state we show that three different definitions of the ground state energy of Jellium coincide. In the first point of view the electrons are placed in a neutralizing uniform background. In the second definition there is no background but the electrons are submitted to the constraint that their density is constant, as is appropriate in Density Functional Theory. Finally, in the third system each electron interacts with a periodic image of itself, that is, periodic boundary conditions are imposed on the interaction potential.

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Section: Extension To Riesz Potentials In All Space Dimensionsmentioning

confidence: 99%

Floating Wigner crystal with no boundary charge fluctuations

2019

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“…91,92 This equivalence has triggered interest from the applied mathematics community working on optimal transport problems, which has led to the suggestion of several algorithms, 89,93−95 together with very interesting exact results. 96−98 …”

Section: Modeling the Local Acmentioning

confidence: 99%

Exchange–Correlation Functionals via Local Interpolation along the Adiabatic Connection

Vuckovic

Irons

Savin

et al. 2016

J. Chem. Theory Comput.

192

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The construction of density-functional approximations is explored by modeling the adiabatic connection locally, using energy densities defined in terms of the electrostatic potential of the exchange–correlation hole. These local models are more amenable to the construction of size-consistent approximations than their global counterparts. In this work we use accurate input local ingredients to assess the accuracy of a range of local interpolation models against accurate exchange–correlation energy densities. The importance of the strictly correlated electrons (SCE) functional describing the strong coupling limit is emphasized, enabling the corresponding interpolated functionals to treat strong correlation effects. In addition to exploring the performance of such models numerically for the helium and beryllium isoelectronic series and the dissociation of the hydrogen molecule, an approximate analytic model is presented for the initial slope of the local adiabatic connection. Comparisons are made with approaches based on global models, and prospects for future approximations based on the local adiabatic connection are discussed.

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“…(28) [17,79]. For spherically symmetric 2D and 3D problems, the radial components of the co-motion functions can also be found quite easily, while the angular components require minimizing the interaction energy over the electronic angles [15,35,78].…”

Section: Introductionmentioning

confidence: 99%

Electron avoidance: A nonlocal radius for strong correlation

Wagner

Gori‐Giorgi

2014

Phys. Rev. A

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We present here a model of the exchange-correlation hole for strongly correlated systems using a simple nonlocal generalization of the Wigner-Seitz radius. The model behaves similarly to the strictly correlated electron approach, which gives the infinitely correlated limit of density functional theory. Unlike the strictly correlated method, however, the energies and potentials of this model can be presently calculated for arbitrary geometries in three dimensions. We discuss how to evaluate the energies and potentials of the nonlocal model, and provide results for many systems where it is also possible to compare to the strictly correlated electron treatment.

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Multimarginal Optimal Transport Maps for One–dimensional Repulsive Costs

Cited by 99 publications

References 19 publications

Floating Wigner crystal with no boundary charge fluctuations

Floating Wigner crystal with no boundary charge fluctuations

Exchange–Correlation Functionals via Local Interpolation along the Adiabatic Connection

Electron avoidance: A nonlocal radius for strong correlation

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