scholarly journals Breakdown of the Fermi Liquid picture in one dimensional fermion systems: connection with the energy level statistics

1994 ◽  
Vol 4 (5) ◽  
pp. 737-756 ◽  
Author(s):  
R. Mélin ◽  
B. Douçot ◽  
P. Butaud
Keyword(s):  
Energy Level ◽  
Fermi Liquid ◽  
One Dimensional ◽  
Fermion Systems ◽  
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.

Quantum Boxes, Stringed Instruments

2017 ◽  
Author(s):  
Frank S. Levin
Keyword(s):  
Energy Level ◽  
Schrödinger Equation ◽  
Quantum System ◽  
Schrodinger Equation ◽  
Probability Distributions ◽  
Wave Functions ◽  
Energy Level Diagram ◽  
One Dimensional ◽  
Stringed Instruments ◽  
Symmetry Properties

Chapter 7 illustrates the results obtained by applying the Schrödinger equation to a simple pedagogical quantum system, the particle in a one-dimensional box. The wave functions are seen to be sine waves; their wavelengths are evaluated and used to calculate the quantized energies via the de Broglie relation. An energy-level diagram of some of the energies is constructed; on it are illustrations of the corresponding wave functions and probability distributions. The wave functions are seen to be either symmetric or antisymmetric about the midpoint of the line representing the box, thereby providing a lead-in to the later exploration of certain symmetry properties of multi-electron atoms. It is next pointed out that the Schrödinger equation for this system is identical to Newton’s equation describing the vibrations of a stretched musical string. The different meaning of the two solutions is discussed, as is the concept and structure of linear superpositions of them.

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

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
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