scholarly journals Transseries for the ground state density and generalized Bloch equation: Double-well potential case

2018 ◽  
Vol 98 (10) ◽  
Author(s):  
E. Shuryak ◽  
A. V. Turbiner
Keyword(s):  
Ground State ◽  
Bloch Equation ◽  
State Density ◽  
Potential Case ◽  
Double Well Potential ◽  
Ground State Density

scholarly journals Moments of the ground state density for the d-dimensional Fermi gas in an harmonic trap

2020 ◽  
pp. 2150018
Author(s):  
Peter J. Forrester
Keyword(s):  
Ground State ◽  
Matrix Theory ◽  
Fermi Gas ◽  
State Density ◽  
Harmonic Trap ◽  
Second Order ◽  
Closed Form Expression ◽  
Gaussian Unitary Ensemble ◽  
Linear Differential ◽  
Ground State Density

We consider properties of the ground state density for the [Formula: see text]-dimensional Fermi gas in an harmonic trap. Previous work has shown that the [Formula: see text]-dimensional Fourier transform has a very simple functional form. It is shown that this fact can be used to deduce that the density itself satisfies a third-order linear differential equation, previously known in the literature but from other considerations. It is shown too how this implies a closed form expression for the [Formula: see text]th non-negative integer moments of the density, and a second-order recurrence. Both can be extended to general Re[Formula: see text]. The moments, and the smoothed density, permit expansions in [Formula: see text], where [Formula: see text], with [Formula: see text] denoting the shell label. The moment expansion substituted in the second-order recurrence gives a generalization of the Harer–Zagier recurrence, satisfied by the coefficients of the [Formula: see text] expansion of the moments of the spectral density for the Gaussian unitary ensemble in random matrix theory.

Some Fundamental Issues in Ground-State Density Functional Theory: A Guide for the Perplexed

2009 ◽  
Vol 5 (4) ◽  
pp. 902-908 ◽  
Author(s):  
John P. Perdew ◽  
Adrienn Ruzsinszky ◽  
Lucian A. Constantin ◽  
Jianwei Sun ◽  
Gábor I. Csonka
Keyword(s):  
Density Functional Theory ◽  
Ground State ◽  
Density Functional ◽  
State Density ◽  
Functional Theory ◽  
Ground State Density

Local ground state density in metal-dielectric-semiconductor structures

1983 ◽  
Vol 26 (3) ◽  
pp. 288-292
Author(s):  
D. I. Sheka ◽  
A. M. Voskoboinikov ◽  
V. I. Strikha
Keyword(s):  
Ground State ◽  
State Density ◽  
Semiconductor Structures ◽  
Ground State Density

Comment on Inverse problem from discrete spectrum in the D = 2 dimensional space (2014 Phys. Scr. 989 085201)

2022 ◽  
Author(s):  
Francisco Marcelo Fernandez
Keyword(s):  
Inverse Problem ◽  
Potential Energy ◽  
Ground State ◽  
Dimensional Space ◽  
Potential Energy Function ◽  
State Density ◽  
Energy Functions ◽  
Sum Rule ◽  
Potential Energy Functions ◽  
Ground State Density

Abstract We analyse a method for the construction of the potential-energy function from the moments of the ground-state density. The sum rule on which some expressions are based appear to be wrong, as well as the moments and potential-energy functions derived for some illustrative examples.

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