Dynamics of band electrons in electric and magnetic fields: rigorous justification of the effective Hamiltonians
G Nenciu - Reviews of Modern Physics, 1991 - APS
Results concerning the rigorous justification of the effective Hamiltonians for band electrons
in the presence of weak homogeneous electric and magnetic fields are reviewed. In the …
in the presence of weak homogeneous electric and magnetic fields are reviewed. In the …
[图书][B] Noncommutative geometry
A Connes - 1994 - Springer
Our geometric concepts evolved first through the discovery of Non-Euclidean geometry. The
discovery of quantum mechanics in the form of the noncommuting coordinates on the phase …
discovery of quantum mechanics in the form of the noncommuting coordinates on the phase …
The ten martini problem
A Avila, S Jitomirskaya - Annals of mathematics, 2009 - JSTOR
The Ten Martini Problem Page 1 Annals of Mathematics, 170 (2009), 303-342 The Ten
Martini Problem By Artur Avila and Svetlana Jitomirskaya Abstract We prove the conjecture (known …
Martini Problem By Artur Avila and Svetlana Jitomirskaya Abstract We prove the conjecture (known …
Spectral theory of Sturm-Liouville operators on infinite intervals: a review of recent developments
Y Last - Sturm-Liouville Theory: Past and Present, 2005 - Springer
This review discusses some of the central developments in the spectral theory of Sturm-
Liouville operators on infinite intervals over the last thirty years or so. We discuss some of …
Liouville operators on infinite intervals over the last thirty years or so. We discuss some of …
On the measure of the spectrum for the almost Mathieu operator
On the measure of the spectrum for the almost Mathieu operator Page 1 Commun. Math. Phys.
132, 103-118 (1990) Communications in Mathematical Physics 9 Springer-Verlag 1990 On the …
132, 103-118 (1990) Communications in Mathematical Physics 9 Springer-Verlag 1990 On the …
Cantor spectrum for the almost Mathieu operator
J Puig - Communications in mathematical physics, 2004 - Springer
In this paper we use results on reducibility, localization and duality for the Almost Mathieu
operator,\left (H_ b, ϕ x\right) _n= x_ n+ 1+ x_ n-1+ b\left (2 π n ω+ ϕ\right) x_n on l 2 (ℤ) and …
operator,\left (H_ b, ϕ x\right) _n= x_ n+ 1+ x_ n-1+ b\left (2 π n ω+ ϕ\right) x_n on l 2 (ℤ) and …
Discrete magnetic laplacian
MA Shubin - Communications in mathematical physics, 1994 - Springer
We consider a 2-dimensional discrete operator which we call the Discrete Magnetic
Laplacian (DML); it is an analogue of the magnetic Schrödinger operator. It follows from well …
Laplacian (DML); it is an analogue of the magnetic Schrödinger operator. It follows from well …
An algebraic semi-classical approach to Bloch electrons in a magnetic field
R Rammal, J Bellissard - Journal de Physique, 1990 - jphys.journaldephysique.org
Starting from Heisenberg's point of view, a semi-classical quantization method is introduced
for 2D Bloch electrons in a magnetic field. The underlying lattice structure is used to define …
for 2D Bloch electrons in a magnetic field. The underlying lattice structure is used to define …
[图书][B] The geometry of algebraic Fermi curves
D Gieseker - 2012 - books.google.com
The Geometry of Algebraic Fermi Curves deals with the geometry of algebraic Fermi curves,
with emphasis on the inverse spectral problem. Topics covered include the periodic …
with emphasis on the inverse spectral problem. Topics covered include the periodic …
Microlocal analysis for the periodic magnetic Schrodinger equation and related questions
JM Bony, G Grubb, L Hörmander, H Komatsu… - … at the 2nd Session of the …, 1991 - Springer
Quantum mechanics has been from the beginning (with the work of VP. Maslov and others)
one of the main motivations for microlocal analysis. These notes deal with some questions …
one of the main motivations for microlocal analysis. These notes deal with some questions …