Wavelet-basis calculation of Wannier functions

2003 ◽  
Vol 68 (23) ◽  
Author(s):  
Stephen D. Clow ◽  
Bruce R. Johnson
Keyword(s):  
Wavelet Basis ◽  
Wannier Functions ◽  
Basis Calculation

Wavelet Basis In The Space C∞[-1; 1]

2008 ◽  
Vol 1 (1) ◽  
pp. 19-24
Author(s):  
Alexander P. Goncharov ◽  
Ali Samil Kavruk
Keyword(s):  
Wavelet Basis

scholarly journals Discrete Nonlinear Schrödinger Systems for Periodic Media with Nonlocal Nonlinearity: The Case of Nematic Liquid Crystals

2021 ◽  
Vol 11 (10) ◽  
pp. 4420
Author(s):  
Panayotis Panayotaros
Keyword(s):  
Differential Equation ◽  
Infinite System ◽  
Linear Part ◽  
Optical Power ◽  
Explicit Construction ◽  
Translation Invariance ◽  
Nonlocal Nonlinearity ◽  
Wannier Functions ◽  
Nonlinear Schrödinger ◽  
Nonlinear Schrödinger Systems

We study properties of an infinite system of discrete nonlinear Schrödinger equations that is equivalent to a coupled Schrödinger-elliptic differential equation with periodic coefficients. The differential equation was derived as a model for laser beam propagation in optical waveguide arrays in a nematic liquid crystal substrate and can be relevant to related systems with nonlocal nonlinearities. The infinite system is obtained by expanding the relevant physical quantities in a Wannier function basis associated to a periodic Schrödinger operator appearing in the problem. We show that the model can describe stable beams, and we estimate the optical power at different length scales. The main result of the paper is the Hamiltonian structure of the infinite system, assuming that the Wannier functions are real. We also give an explicit construction of real Wannier functions, and examine translation invariance properties of the linear part of the system in the Wannier basis.

Wavelets in the Solution of Nongray Radiative Heat Transfer Equation

1998 ◽  
Vol 120 (1) ◽  
pp. 133-139 ◽  
Author(s):  
Y. Bayazitoglu ◽  
B. Y. Wang
Keyword(s):  
Transfer Equation ◽  
Solution Method ◽  
Radiative Heat ◽  
Radiative Transfer Equation ◽  
Basis Functions ◽  
Wavelet Basis ◽  
System Of Equations ◽  
Heat Transfer Equation ◽  
One Dimensional ◽  
The One

The wavelet basis functions are introduced into the radiative transfer equation in the frequency domain. The intensity of radiation is expanded in terms of Daubechies’ wrapped-around wavelet functions. It is shown that the wavelet basis approach to modeling nongrayness can be incorporated into any solution method for the equation of transfer. In this paper the resulting system of equations is solved for the one-dimensional radiative equilibrium problem using the P-N approximation.

scholarly journals Linear scaling calculation of maximally localized Wannier functions with atomic basis set

2006 ◽  
Vol 124 (23) ◽  
pp. 234108 ◽  
Author(s):  
H. J. Xiang ◽  
Zhenyu Li ◽  
W. Z. Liang ◽  
Jinlong Yang ◽  
J. G. Hou ◽  
...  
Keyword(s):  
Basis Set ◽  
Linear Scaling ◽  
Wannier Functions

scholarly journals Construction and solution of a Wannier-functions based Hamiltonian in the pseudopotential plane-wave framework for strongly correlated materials

2008 ◽  
Vol 65 (1) ◽  
pp. 91-98 ◽  
Author(s):  
Dm. Korotin ◽  
A. V. Kozhevnikov ◽  
S. L. Skornyakov ◽  
I. Leonov ◽  
N. Binggeli ◽  
...  
Keyword(s):  
Plane Wave ◽  
Strongly Correlated ◽  
Wannier Functions ◽  
Strongly Correlated Materials

scholarly journals Some examples related to Kato's conjecture

1996 ◽  
Vol 60 (2) ◽  
pp. 274-286 ◽  
Author(s):  
Rhonda J. Hughes ◽  
Paul R. Chernoff
Keyword(s):  
Wavelet Basis ◽  
Accretive Operators ◽  
Singular Coefficients

AbstractWe show that the Kato conjecture is true for m-accretive operators with highly singular coefficients. For operators of the form A = *F, where formally corresponds to d/dx + zδ on L2 (R), we prove that Dom (A1/2) = Dom() = e-zHH1(R) where H is the Heavysied function. By adapting recent methods of Auscher and Tchamitchian, we characterize Dom (A) in terms of an unconditional wavelet basis for L2(R).

Spontaneous polarization and piezoelectric properties of AlN nanowires: Maximally localized Wannier functions analysis

2015 ◽  
Vol 111 (6) ◽  
pp. 67003 ◽  
Author(s):  
Haibo Niu ◽  
Guangde Chen ◽  
Yelong Wu ◽  
Honggang Ye ◽  
Youzhang Zhu
Keyword(s):  
Spontaneous Polarization ◽  
Piezoelectric Properties ◽  
Wannier Functions
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