scholarly journals Rational invariant tori and band edge spectra for non-selfadjoint operators

2018 ◽  
Vol 20 (2) ◽  
pp. 391-457 ◽  
Author(s):  
Michael Hitrik ◽  
Johannes Sjöstrand
Keyword(s):  
Invariant Tori ◽  
Band Edge ◽  
Selfadjoint Operators ◽  
Rational Invariant

Autonomous Geometrical Mechanics

2018 ◽  
Author(s):  
Peter Mann
Keyword(s):  
Phase Space ◽  
Contact Structure ◽  
Invariant Tori ◽  
Time Dependent ◽  
Contact Structures ◽  
Natural Setting ◽  
Adiabatic Invariance ◽  
Jet Bundle ◽  
Integrability Theorem ◽  
Extended Phase

This chapter examines the structure of the phase space of an integrable system as being constructed from invariant tori using the Arnold–Liouville integrability theorem, and periodic flow and ergodic flow are investigated using action-angle theory. Time-dependent mechanics is formulated by extending the symplectic structure to a contact structure in an extended phase space before it is shown that mechanics has a natural setting on a jet bundle. The chapter then describes phase space of integrable systems and how tori behave when time-dependent dynamics occurs. Adiabatic invariance is discussed, as well as slow and fast Hamiltonian systems, the Hannay angle and counter adiabatic terms. In addition, the chapter discusses foliation, resonant tori, non-resonant tori, contact structures, Pfaffian forms, jet manifolds and Stokes’s theorem.

Tailored Electronic Band Gap and Valance Band Edge of Nickel Oxide via p-Type Incorporation

2021 ◽  
Vol 125 (13) ◽  
pp. 7495-7501
Author(s):  
Gang Wang ◽  
Jinju Zheng ◽  
Boyi Xu ◽  
Chaonan Zhang ◽  
Yue Zhu ◽  
...  
Keyword(s):  
Nickel Oxide ◽  
Band Gap ◽  
Band Edge ◽  
Electronic Band ◽  
Electronic Band Gap ◽  
P Type

Parabolic invariant tori in quasi-periodically forced skew-product maps

2021 ◽  
Vol 277 ◽  
pp. 234-274
Author(s):  
Xinyu Guan ◽  
Jianguo Si ◽  
Wen Si
Keyword(s):  
Invariant Tori ◽  
Skew Product ◽  
Product Maps

scholarly journals Calculation of Band Offsets of Mg(OH)2-Based Heterostructures

2021 ◽  
Vol 2 (3) ◽  
pp. 274-283
Author(s):  
Masaya Ichimura
Keyword(s):  
Solar Cells ◽  
Valence Band ◽  
Dye Sensitized Solar Cells ◽  
Band Alignment ◽  
First Principles Calculation ◽  
Band Edge ◽  
Level Energy ◽  
Type I ◽  
Valence Band Edge ◽  
Generalized Gradient

The band alignment of Mg(OH)2-based heterostructures is investigated based on first-principles calculation. (111)-MgO/(0001)-Mg(OH)2 and (0001)-wurtzite ZnO/(0001)-Mg(OH)2 heterostructures are considered. The O 2s level energy is obtained for each O atom in the heterostructure supercell, and the band edge energies are evaluated following the procedure of the core-level spectroscopy. The calculation is based on the generalized gradient approximation with the on-site Coulomb interaction parameter U considered for Zn. For MgO/Mg(OH)2, the band alignment is of type II, and the valence band edge of MgO is higher by 1.6 eV than that of Mg(OH)2. For ZnO/Mg(OH)2, the band alignment is of type I, and the valence band edge of ZnO is higher by 0.5 eV than that of Mg(OH)2. Assuming the transitivity rule, it is expected that Mg(OH)2 can be used for certain types of heterostructure solar cells and dye-sensitized solar cells to improve the performance.

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