INFINITE NETWORK OF IDENTICAL CAPACITORS BY GREEN'S FUNCTION

2005 ◽  
Vol 19 (24) ◽  
pp. 3713-3721 ◽  
Author(s):  
J. H. ASAD ◽  
R. S. HIJJAWI ◽  
A. J. SAKAJI ◽  
J. M. KHALIFEH
Keyword(s):  
Green’S Function ◽  
Green's Function ◽  
Lattice Site ◽  
Linear Chain ◽  
Tight Binding ◽  
Square Lattice ◽  
Van Hove Singularity ◽  
Infinite Network ◽  
Infinite Networks ◽  
Infinite Linear

The capacitance between arbitrary nodes in perfect infinite networks of identical capacitors is studied. We calculate the capacitance between the origin and the lattice site (l, m) for an infinite linear chain, and for an infinite square network consisting of identical capacitors using the Lattice Green's Function. The asymptotic behavior of the capacitance for an infinite square lattice is investigated for infinite separation between the origin and the site (l, m). We point out the relation between the capacitance of the lattice and the van Hove singularity of the tight-binding Hamiltonian. This method can be applied directly to other lattice structures.

PERTURBATION OF AN INFINITE NETWORK OF IDENTICAL CAPACITORS

2007 ◽  
Vol 21 (02) ◽  
pp. 199-209 ◽  
Author(s):  
R. S. HIJJAWI ◽  
J. H. ASAD ◽  
A. J. SAKAJI ◽  
J. M. KHALIFEH
Keyword(s):  
Asymptotic Behavior ◽  
Green’S Function ◽  
Green's Function ◽  
Numerical Results ◽  
Square Lattice ◽  
Infinite Network ◽  
Arbitrary Lattice ◽  
Lattice Green's Function ◽  
Lattice Green’S Function

The capacitance between any two arbitrary lattice sites in an infinite square lattice is studied when one bond is removed (i.e. perturbed). A connection is made between the capacitance and the lattice Green's function of the perturbed network, where they are expressed in terms of those of the perfect network. The asymptotic behavior of the perturbed capacitance is investigated as the separation between the two sites goes to infinity. Finally, numerical results are obtained along different directions and a comparison is made with the perfect capacitances.

On the perturbation of a uniform tiling with resistors

2016 ◽  
Vol 30 (24) ◽  
pp. 1650166 ◽  
Author(s):  
M. Q. Owaidat ◽  
J. H. Asad ◽  
Zhi-Zhong Tan
Keyword(s):  
Green’S Function ◽  
Green's Function ◽  
Square Lattice ◽  
Resistor Network ◽  
Theoretical Results

The perturbation of a uniformly tiled resistor network by adding an edge (a resistor) to the network is considered. The two-point resistance on the perturbed tiling in terms of that on the perfect tiling is obtained using Green’s function. Some theoretical results are presented for an infinite modified square lattice. These results are confirmed experimentally by constructing an actual resistor lattice of size 13 × 13.

Electronic Properties of Ultrathin Isoelectronic Intralayers in Semiconductors

1991 ◽  
Vol 240 ◽  
Author(s):  
K. A. Mäder ◽  
A. Baldereschi
Keyword(s):  
Quantum Well ◽  
Quantum Wells ◽  
Green’S Function ◽  
Electronic Properties ◽  
Green's Function ◽  
Tight Binding ◽  
Function Approach ◽  
Diamond Structure ◽  
Two Dimensional ◽  
Host Materials

ABSTRACTAn empirical tight-binding Koster-Slater approach is used to determine the electronic properties of ultrathin“quantum wells”in semiconducting host materials of the zincblende or diamond structure. The“quantum well”is viewed as a giant two-dimensional isoelectronic impurity, and treated in a perturbational Green's function approach. We present results on the AlAs/GaAs and on the InP/InAs systems.

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