A spectral identity for the multidimensional Schr�dinger equation with periodic potential

1992 ◽  
Vol 91 (3) ◽  
pp. 692-695
Author(s):  
S. V. Frolov
Keyword(s):  
Periodic Potential ◽  
Dinger Equation ◽  
Spectral Identity

EXCITON INSULATOR STATES IN MATERIALS WITH ‘MEXICAN HAT’ BAND STRUCTURE DISPERSION AND IN GRAPHENE

2015 ◽  
Vol 11 (1) ◽  
pp. 2927-2949
Author(s):  
Lyubov E. Lokot
Keyword(s):  
Band Structure ◽  
Three Dimensional ◽  
Dimensional Sphere ◽  
Electron Hole ◽  
Dinger Equation ◽  
Fermi Sphere ◽  
Zinc Blende ◽  
Bulk Gan ◽  
Structure Dispersion ◽  
Excitonic States

In the paper a theoretical study the both the quantized energies of excitonic states and their wave functions in grapheneand in materials with "Mexican hat" band structure dispersion as well as in zinc-blende GaN is presented. An integral twodimensionalSchrödinger equation of the electron-hole pairing for a particles with electron-hole symmetry of reflection isexactly solved. The solutions of Schrödinger equation in momentum space in studied materials by projection the twodimensionalspace of momentum on the three-dimensional sphere are found exactly. We analytically solve an integral twodimensionalSchrödinger equation of the electron-hole pairing for particles with electron-hole symmetry of reflection. Instudied materials the electron-hole pairing leads to the exciton insulator states. Quantized spectral series and lightabsorption rates of the excitonic states which distribute in valence cone are found exactly. If the electron and hole areseparated, their energy is higher than if they are paired. The particle-hole symmetry of Dirac equation of layered materialsallows perfect pairing between electron Fermi sphere and hole Fermi sphere in the valence cone and conduction cone andhence driving the Cooper instability. The solutions of Coulomb problem of electron-hole pair does not depend from a widthof band gap of graphene. It means the absolute compliance with the cyclic geometry of diagrams at justification of theequation of motion for a microscopic dipole of graphene where >1 s r . The absorption spectrums for the zinc-blendeGaN/(Al,Ga)N quantum well as well as for the zinc-blende bulk GaN are presented. Comparison with availableexperimental data shows good agreement.

Study of potential oscillations during reaction of an aluminium single crystal with an aqueous KOH solution

1990 ◽  
Vol 55 (2) ◽  
pp. 345-353 ◽  
Author(s):  
Ivan Halaša ◽  
Milica Miadoková
Keyword(s):  
Aqueous Solutions ◽  
Single Crystal ◽  
Single Crystals ◽  
Periodic Potential ◽  
Optimum Conditions ◽  
Potential Oscillations ◽  
Dilute Aqueous Solutions ◽  
Experimental Findings ◽  
Kinetics Of

The authors investigated periodic potential changes measured on oriented sections of Al single crystals during spontaneous dissolution in dilute aqueous solutions of KOH, with the aim to find optimum conditions for the formation of potential oscillations. It was found that this phenomenon is related with the kinetics of the reaction investigated, whose rate also changed periodically. The mechanism of the oscillations is discussed in view of the experimental findings.

Chern Numbers and Green's Functions in Solid State Physics

1997 ◽  
Vol 11 (11) ◽  
pp. 1389-1410
Author(s):  
Xiao-Rong Wu-Morrow ◽  
Cecile Dewitt-Morette ◽  
Lev Rozansky
Keyword(s):  
Periodic Potential ◽  
Solid State Physics ◽  
Hall Conductance ◽  
Energy Eigenvalues ◽  
Finite Dimensional ◽  
Topological Quantum ◽  
Chern Numbers ◽  
Density Response ◽  
Physical Quantities ◽  
Noninteracting Electron

Using the energy Green's function formulation proposed by Niu 1 for particle densities, we construct and clarify the nature of the topological invariant assigned to the Hall conductance in the Hall system of 2-dimensional noninteracting electron gas; we identify this topological quantum number explicitly as the first Chern number of a complex vector bundle over a 2-torus parametrized by the magnetic potential (a1, a2); the fibres are finite dimensional spaces spanned by eigenfunctions of the system with energy eigenvalues below the Fermi energy. Other cases can be treated by a similar procedure, namely, by recognizing that some physical quantities are integrals of curvatures defined on a nontrivial finite dimensional complex bundle. Therefore, in suitable units, they take integer values. We treat, as an example, the electron density response to a dilation of a periodic potential. The integer in this case is the number of Bloch bands. The quantization of the Hall conductance and density response is also shown in the presence of disorder.

Motion of microscopic grains in a periodic potential of plate acoustic waves

2003 ◽  
Vol 15 (43) ◽  
pp. 7201-7211 ◽  
Author(s):  
A M Gorb ◽  
A B Nadtochii ◽  
O A Korotchenkov
Keyword(s):  
Acoustic Waves ◽  
Periodic Potential ◽  
Plate Acoustic Waves
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