scholarly journals Geometry, number theory, and the butterfly spectrum of two-dimensional Bloch electrons

2021 ◽  
Vol 104 (4) ◽  
Author(s):  
Indubala I. Satija
Keyword(s):  
Number Theory ◽  
Two Dimensional ◽  
Bloch Electrons

Thermodynamic formalism for certain nonhyperbolic maps

1999 ◽  
Vol 19 (5) ◽  
pp. 1365-1378 ◽  
Author(s):  
MICHIKO YURI
Keyword(s):  
Number Theory ◽  
Gibbs Measure ◽  
Existence And Uniqueness ◽  
Thermodynamic Formalism ◽  
Periodic Points ◽  
Two Dimensional ◽  
Absolutely Continuous ◽  
One Dimensional ◽  
Conformal Measures ◽  
One Dimensional Maps

We establish a generalized thermodynamic formalism for certain nonhyperbolic maps with countably many preimages. We study existence and uniqueness of conformal measures and statistical properties of the equilibrium states absolutely continuous with respect to the conformal measures. We will see that such measures are not Gibbs but satisfy a version of Gibbs property (weak Gibbs measure). We apply our results to a one-parameter family of one-dimensional maps and a two-dimensional nonconformal map related to number theory. Both of them admit indifferent periodic points.

Withdrawal of a stratified fluid from a vertical two-dimensional duct

1975 ◽  
Vol 70 (2) ◽  
pp. 321-332 ◽  
Author(s):  
Jorg Imberger ◽  
Chris Fandry
Keyword(s):  
Number Theory ◽  
Free Surface ◽  
Froude Number ◽  
Stratified Fluid ◽  
Two Dimensional ◽  
Tank Bottom ◽  
Vertical Duct

On the basis of a small Froude number theory it is shown that previous horizontalduct models of the withdrawal of fluid from a stratified tank with a free surface and a fixed bottom are inappropriate at large times and that the flow should be modelled by that from an infinite vertical duct. The falling horizontal free surface in the tank is replaced by a vertically moving column of stratified fluid and the tank bottom is modelled by a stagnant pool of fluid below. This model is analysed and a solution uniformly valid in time is presented. The properties of the solution are then compared with existing theories and experiments.

Effect of magnetic modulation on Bloch electrons on a two-dimensional square lattice

1995 ◽  
Vol 52 (20) ◽  
pp. 14755-14760 ◽  
Author(s):  
Godfrey Gumbs ◽  
Desiré Miessein ◽  
Danhong Huang
Keyword(s):  
Square Lattice ◽  
Two Dimensional ◽  
Bloch Electrons

Applying the 1/N-Energy Solution of the Harper Equation to the Derivation of Thermodynamic Properties of Bloch Electrons

1998 ◽  
Vol 12 (32) ◽  
pp. 3503-3520 ◽  
Author(s):  
C. Micu ◽  
E. Papp
Keyword(s):  
Thermodynamic Properties ◽  
Electron Gas ◽  
Energy Solution ◽  
The Novel ◽  
Two Dimensional ◽  
Quantum Gas ◽  
Dimensional Electron ◽  
Dimensional Electron Gas ◽  
Bloch Electrons ◽  
Harper Equation

The novel 1/N-energy solution to the Harper equation presented recently is applied to the derivation of thermodynamic properties of Bloch electrons on a two-dimensional lattice penetrated by a perpendicular uniform magnetic field. One procceeds by using an almost typical density of states such as proposed previously for a two-dimensional electron gas. Comparisons with recent data concerning rare earth componds as well as with results obtained before with the help of Dingle- and quantum-gas densities are done. One assumes that the Fermi level is fixed.

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