scholarly journals Lowest eigenvalues of random Hamiltonians

2008 ◽  
Vol 77 (5) ◽  
Author(s):  
J. J. Shen ◽  
Y. M. Zhao ◽  
A. Arima ◽  
N. Yoshinaga
Keyword(s):  
Random Hamiltonians

"Universality" of Gaussian orthogonal ensemble fluctuations: the two-body random ensemble and shell model spectra

1990 ◽  
Vol 68 (3) ◽  
pp. 301-312 ◽  
Author(s):  
Gaetan J. H. Laberge ◽  
Rizwan U. Haq
Keyword(s):  
Energy Level ◽  
Shell Model ◽  
Detailed Analysis ◽  
Close Agreement ◽  
Level Density ◽  
Nuclear Interactions ◽  
Gaussian Orthogonal Ensemble ◽  
Random Hamiltonians

Starting from an appropriate decomposition of the level density into an average and fluctuating part, we studied the energy level fluctuations of an ensemble defined by two-body random Hamiltonians. A detailed analysis of several spectrally averaged fluctuation measures shows close agreement with the predictions of the Gaussian orthogonal ensemble (GOE). This confirms earlier indications that, except for noninteracting particles, fluctuation measures are insensitive to the rank of the interaction. Further, analysis of spectra obtained from realistic nuclear interactions agrees well with the GOE indicating that specific properties of the Hamiltonian have little or no influence on fluctuations. These results, therefore, strengthen our belief in the "universality" of GOE fluctuations.

scholarly journals LOCALIZATION FOR ONE DIMENSIONAL LONG RANGE RANDOM HAMILTONIANS

1999 ◽  
Vol 11 (01) ◽  
pp. 103-135 ◽  
Author(s):  
VOJKAN JAKŠIĆ ◽  
STANISLAV MOLCHANOV
Keyword(s):  
Long Range ◽  
Spectral Properties ◽  
Schrödinger Operators ◽  
Pure Point ◽  
Random Schrödinger Operators ◽  
Schrodinger Operators ◽  
One Dimensional ◽  
Free Part ◽  
Random Hamiltonians

We study spectral properties of random Schrödinger operators hω=h0+vω(n) on l2(Z) whose free part h0 is long range. We prove that the spectrum of hω is pure point for typical ω whenever the off-diagonal terms of h0 decay as |i-j|-γ for some γ>8.

Level density for some partially random Hamiltonians

1970 ◽  
Vol 69 (2) ◽  
pp. 181-208 ◽  
Author(s):  
A. Gervois
Keyword(s):  
Level Density ◽  
Random Hamiltonians

scholarly journals Generalized seniority from random Hamiltonians

1999 ◽  
Vol 61 (1) ◽  
Author(s):  
C. W. Johnson ◽  
G. F. Bertsch ◽  
D. J. Dean ◽  
I. Talmi
Keyword(s):  
Random Hamiltonians

REM Universality for Random Hamiltonians

2009 ◽  
pp. 45-84
Author(s):  
Gérard Ben Arous ◽  
Alexey Kuptsov
Keyword(s):  
Random Hamiltonians
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