REAL SOLUTION OF THE COMPLEX RANDOM PHASE APPROXIMATION EQUATION

1993 ◽  
Vol 02 (01) ◽  
pp. 265-271
Author(s):  
N. TERUYA ◽  
M. KYOTOKU ◽  
H. DIAS
Keyword(s):  
Eigenvalue Problem ◽  
Random Phase Approximation ◽  
Original Problem ◽  
Hermitian Matrix ◽  
Random Phase ◽  
Linear Response Theory ◽  
Collective Excitations ◽  
Real Eigenvalue ◽  
Complex Eigenvalue ◽  
Physical Phenomena

The description of several physical phenomena may require the solution of a complex eigenvalue problem of a non-Hermitian matrix. This problem may be met in the description of some nuclear and plasmon collective excitations using the linear-response theory. It is shown that there exists a related real matrix which satisfies the usual standard real eigenvalue problem whose solution yields directly the solution of the original problem.

scholarly journals Two-dimensional parabolic Dirac system in the presence of nonmagnetic and magnetic impurities

2021 ◽  
pp. 2150159
Author(s):  
Chen-Huan Wu
Keyword(s):  
Random Phase Approximation ◽  
Random Phase ◽  
Linear Response Theory ◽  
Magnetic Impurities ◽  
Transition Metal Dichalcogenide ◽  
Dirac System ◽  
Rkky Interaction ◽  
Dirac Materials ◽  
Induced Charge Density ◽  
Anisotropic Dispersion

We theoretically investigate the effect of the nonmagnetic and magnetic impurities to the 2D parabolic Dirac system. The induced charge density by the charged impurity is obtained by the linear response theory within the random phase approximation. We also calculate in-detail, the Ruderman–Kittel–Kasuya–Yosida (RKKY) interaction between two magnetic impurities placed within the 2D sheet of the Dirac materials with isotropic and anisotropic dispersion. For the anisotropic dispersion, the RKKY interaction is also anisotropic and related to the lattice parameters which can be obtained through the DFT calculation or the experiments. The features of the RKKY interaction also can be treated as a signature of the topological phase transition as well as the change of Berry curvature. Our results are also illuminating to the study of the static screening and the RKKY interaction of the isotropic or anisotropic 3D Dirac/Weyl semimetals or the 2D transition metal dichalcogenide family.

scholarly journals Collective excitations in Random Phase Approximation and beyond

2011 ◽  
Vol 267 ◽  
pp. 012047
Author(s):  
F Catara ◽  
D Gambacurta ◽  
M Grasso ◽  
M Sambataro
Keyword(s):  
Random Phase Approximation ◽  
Random Phase ◽  
Collective Excitations ◽  
Phase Approximation

scholarly journals PHỔ PLASMON TRONG HỆ 3 LỚP GRAPHENE LỚP KÉP

2021 ◽  
Vol 11 (1) ◽  
pp. 104
Author(s):  
Nguyen Van Men ◽  
Dong Thi Kim Phuong ◽  
Vu Dong Duong
Keyword(s):  
Carrier Density ◽  
Random Phase Approximation ◽  
Layer Structure ◽  
Random Phase ◽  
Collective Excitations ◽  
Lower Branch ◽  
Zero Temperature ◽  
Optical Branch ◽  
Single Particle Excitation ◽  
Plasmon Modes

Recent research demonstrates that graphene has unique properties and applications in many technological fields. This paper presents results calculated within random phase approximation at zero temperature for collective excitations, an important characteristic of materials, in a three-layer structure consisting of three bilayer graphene sheets in an inhomogeneous background dielectric. Numerical calculations show that one optical and two acoustic branches exist in the system. The optical branch becomes overdamped quickly while the two acoustic branches continue and disappear at single-particle excitation boundaries. The increase in carrier density in the layers significantly decreases the frequencies of plasmon modes. The inhomogeneity of the background dielectric decreases the frequency of the higher branches but increases that of the lower branch. The effects of interlayer separation on plasmon modes are similar to those in homogeneous systems. Our results may provide more information and contribute to improving the theory of graphene.

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