Tunable 
                
                  
                
                
                  
                    χ
                    /
                    P
                    T
                  
                
                $\chi /\mathcal {P}\mathcal {T}$
               Symmetry in Noisy Graphene

Silva, E. Frade; Barbosa, A. L. R.; Hussein, M. S.; Ramos, J. Galvão

doi:10.1007/s13538-018-0576-6

Cited by 3 publications

(11 citation statements)

References 35 publications

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“…Inverted potentials v nad t ½q A ; q tot ðrÞ cannot only be used as a reference guiding the development of improved explicit approximations but if they could be generated inexpensively, they could be used instead of explicit density approximations for the functional v nad t ½q A ; q tot ðrÞ in practical simulations. Concerning the domain of the admissible densities, for which the functional v nad t ½q A ; q tot ðrÞ is defined, we notice that the necessary condition for Equation 6 to hold is that the corresponding energy functional T nad s ½q A ; q tot exists (see the derivation of Equation 6 in Refs. [18,27]).…”

Section: Implicit Definition Of the Functional For Nonadditive Kinementioning

confidence: 99%

“…Another possibility is to chose the inverted potential corresponding to the smoothest orbital. [6] Several authors proposed methods to invert numerically the Kohn-Sham equation for an arbitrarily chosen target density: (i) generally applicable iterative procedures which use linear responses, [75][76][77][78] (ii) methods hinging on solving coupled equations applicable only for small model systems comprising only a few electrons. [79][80][81][82][83][84][85] Below, we provide a brief overview of the key elements of the methods used in the literature for inverting the Kohn-Sham equations.…”

Section: Numerical Inversion Of the Kohn-sham Equation With Finite mentioning

confidence: 99%

“…The exact (at the limit of complete basis set) v s ½q o ðrÞ is nothing else as the Kohn-Sham potential, obtained at the end of the self-consistent procedure to solve Kohn-Sham equation. It is, therefore, available and can be used in Equation 6. q B ðrÞ for various partitioning of the ground-state electron densities for beryllium atom, He-Li 1 diatomic, and Be-H 2 and B 1 -H 2 complexes.…”

Section: Numerical Inversion Of the Kohn-sham Equation With Finite mentioning

confidence: 99%

“…q B ðrÞ for various partitioning of the ground-state electron densities for beryllium atom, He-Li 1 diatomic, and Be-H 2 and B 1 -H 2 complexes. [6] In the construction of the potential, instead of the numerically available Kohn-Sham potential needed for the second term in Equation 6, it was obtained (up to a constant) from the lowest Kohn-Sham orbital density (q 1 ðrÞ52j/ 1 ðrÞj 2 ) using analytic inversion always applicable for spin-compensated two-electron densities.…”

Section: Numerical Inversion Of the Kohn-sham Equation With Finite mentioning

confidence: 99%

“…[3] Other authors used accurate inverted potentials to detect flaws of explicit approximations to v nad t ½q A ; q tot ðrÞ and to determine their limits of applicability. [4][5][6][7] Inverted potentials are key elements of various simulation methods. [3,[8][9][10][11][12][13][14][15][16] Such studies provide frequently direct or indirect (through calculated observables) information about the quality of the inverted nonadditive kinetic potential.…”

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Nonadditive kinetic potentials from inverted Kohn–Sham problem

Banafsheh¹,

Wesołowski²

2017

Int J of Quantum Chemistry

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The nonadditive kinetic potential is a key element in density-dependent embedding methods. The correspondence between the ground-state density and the total effective Kohn-Sham potential provides the basis for various methods to construct the nonadditive kinetic potential for any pair of electron densities. Several research groups used numerical or analytical inversion procedures to explore this strategy which overcomes the failures of known explicit density functional approximations. The numerical inversions, however, apply additional approximations/simplifications. The relations known for the exact quantities cannot be assumed to hold for quantities obtained in numerical inversions. The exact relations are discussed with special emphasis on such issues as: the admissibility of the densities for which the potential is constructed, the choice of densities to be used as independent variables, self-consistency between the potentials and observables calculated using the embedded wavefunction, and so forth. The review focuses on how these issues are treated in practice. The review is supplemented with the analysis of the inverted potentials for weakly overlapping pairs of electron densities-the case not studied previously.density embedding, density functional theory, electron density overlap | I N TR ODU C TI ONThe nonadditive kinetic energy (T nad s ) and potential (v nad t ðrÞ) are key ingredients in numerical simulation methods exploring the density embedding strategy (see section 1.2). Both quantities are defined as functionals of admissible pairs of electron densities: where W s denotes a N-electron single-determinant trial wavefunction. Atomic units are used throughout this work.In practical applications, q A ðrÞ is the density corresponding to the wavefunction W emb associated with the embedded subsystem and q tot ðrÞ is electron density of the total system comprising the part represented by W emb and its "environment." Usually, explicit density functionals approximate the functionals v nad t ½q A ; q tot ðrÞ and/or T nad s ½q A ; q tot . Simulations and studies on model systems reported by several researchers revealed many cases where the currently known explicit density functionals fail (see section 1.2). These failures resulted in recent interest in an alternative -implicit -strategy to construct v nad t ½q A ; q tot ðrÞ (and T nad s ½q A ; q tot ) for arbitrarily chosen pairs of densities q A ðrÞ and q tot ðrÞ. Such constructions are based on the Levy correspondence [1] between the Kohn-Sham potential [2] and the electron density. This correspondence exists for admissible electron Int J Quantum Chem. 2018;118:e25410.

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Section: Implicit Definition Of the Functional For Nonadditive Kinementioning

confidence: 99%

Section: Numerical Inversion Of the Kohn-sham Equation With Finite mentioning

confidence: 99%

Section: Numerical Inversion Of the Kohn-sham Equation With Finite mentioning

confidence: 99%

Section: Numerical Inversion Of the Kohn-sham Equation With Finite mentioning

confidence: 99%

mentioning

confidence: 99%

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Nonadditive kinetic potentials from inverted Kohn–Sham problem

Banafsheh¹,

Wesołowski²

2017

Int J of Quantum Chemistry

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Duality quantum simulation of a general parity-time-symmetric two-level system

Zheng

2018

EPL

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The evolution of a two-level quantum system with a general parity-time-reversalinvariant Hamiltonian is reinterpreted as a subsystem in a four-dimensional Hilbert space, which makes it possible to simulate any two-level parity-time-symmetric (PT-symmetric) quantum system using a conventional quantum mechanics system. We studied the ability to simulate and investigate novel quantum systems and phenomena using a nowadays-available Hermitian quantum computer or a duality quantum computer. The quantum circuits are given for a qubit and two qudit systems, and they would be useful for experimental implementation and applications in the future.

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