Energy Level Statistics, Lattice Point Problems, and Almost Modular Functions

2007 ◽  
pp. 163-181 ◽  
Author(s):  
Jens Marklof
Keyword(s):  
Energy Level ◽  
Lattice Point ◽  
Modular Functions ◽  
Level Statistics ◽  
Lattice Point Problems

Arithmetical chaos and violation of universality in energy level statistics

1992 ◽  
Vol 69 (15) ◽  
pp. 2188-2191 ◽  
Author(s):  
J. Bolte ◽  
G. Steil ◽  
F. Steiner
Keyword(s):  
Energy Level ◽  
Level Statistics

Some Applications of Fourier series in the Analytic Theory of Numbers

1928 ◽  
Vol 24 (4) ◽  
pp. 585-596 ◽  
Author(s):  
L. J. Mordell
Keyword(s):  
Fourier Series ◽  
Class Number ◽  
Lattice Point ◽  
Zeta Functions ◽  
Gauss Sums ◽  
Analytic Theory ◽  
Quadratic Fields ◽  
Lattice Point Problems ◽  
Theory Of Numbers

It is a familiar fact that an important part is played in the Analytic Theory of Numbers by Fourier series. There are, for example, applications to Gauss' sums, to the zeta functions, to lattice point problems, and to formulae for the class number of quadratic fields.

scholarly journals Energy-level statistics and localization of 2d electrons in random magnetic fields

1998 ◽  
Vol 249-251 ◽  
pp. 792-795 ◽  
Author(s):  
M. Batsch ◽  
L. Schweitzer ◽  
B. Kramer
Keyword(s):  
Magnetic Fields ◽  
Energy Level ◽  
Level Statistics

Effects of bifurcations on the energy level statistics for oval billiards

1999 ◽  
Vol 59 (4) ◽  
pp. 4026-4035 ◽  
Author(s):  
H. Makino ◽  
T. Harayama ◽  
Y. Aizawa
Keyword(s):  
Energy Level ◽  
Level Statistics

scholarly journals GAP PROBABILITY OF A ONE-DIMENSIONAL GAS MODEL

1996 ◽  
Vol 10 (16) ◽  
pp. 1989-1997
Author(s):  
Y. CHEN ◽  
S.M. MANNING
Keyword(s):  
Energy Level ◽  
Thermodynamic Limit ◽  
Gap Formation ◽  
Mobility Edge ◽  
One Dimensional ◽  
Disordered Solids ◽  
Formation Probability ◽  
Level Statistics ◽  
Correct Form ◽  
Gap Probability

We investigate the gap formation probability of the effective one-dimensional gas model recently proposed for the energy level statistics for disordered solids at the mobility edge. It is found that in order to get the correct form for the gap probability of this model, the thermodynamic limit must be taken very carefully.

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