The Gaussian orthogonal ensemble with missing and spurious levels: A model for experimental level‐spacing distributions

1987 ◽  
Vol 87 (9) ◽  
pp. 5415-5418 ◽  
Author(s):  
Kevin K. Lehmann ◽  
Stephen L. Coy
Keyword(s):  
Level Spacing ◽  
Gaussian Orthogonal Ensemble ◽  
Experimental Level

GAUSSIAN ORTHOGONAL ENSEMBLE FOR THE LEVEL SPACING STATISTICS OF THE QUANTUM FOUR-STATE CHIRAL POTTS MODEL

2002 ◽  
Vol 16 (14n15) ◽  
pp. 2047-2053
Author(s):  
J.-Ch. ANGLÈS d'AURIAC ◽  
S. DOMMANGE ◽  
J.-M. MAILLLARD ◽  
C. M. VIALLET
Keyword(s):  
Random Matrix ◽  
Potts Model ◽  
Matrix Theory ◽  
Level Spacing ◽  
Chiral Potts Model ◽  
Quantum Chain ◽  
Ensemble Statistics ◽  
Higher Genus ◽  
Gaussian Orthogonal Ensemble ◽  
Potts Chain

We have performed a Random Matrix Theory (RMT) analysis of the quantum four state chiral Potts chain for different sizes of the quantum chain up to eight sites, and for different unfolding methods. Our analysis shows that one generically has a Gaussian Orthogonal Ensemble statistics for the unfolded spectrum instead of the GUE statistics one could expect. Furthermore a change from the generic GOE distribution to a Poisson distribution occurs when the hamiltonian becomes integrable. Therefore, the RMT analysis can be seen as a detector of "higher genus integrability".

Inelastic Electron-Matter Interactions

1978 ◽  
Vol 36 (3) ◽  
pp. 259-267
Author(s):  
J. Silcox
Keyword(s):  
Electron Microscope ◽  
Energy Loss ◽  
Chemical Structure ◽  
Inelastic Electron ◽  
Primary Concern ◽  
Unique Probe ◽  
Introductory Paper ◽  
Elastic Processes ◽  
Experimental Level ◽  
Inelastic Processes

In this introductory paper, my primary concern will be in identifying and outlining the various types of inelastic processes resulting from the interaction of electrons with matter. Elastic processes are understood reasonably well at the present experimental level and can be regarded as giving information on spatial arrangements. We need not consider them here. Inelastic processes do contain information of considerable value which reflect the electronic and chemical structure of the sample. In combination with the spatial resolution of the electron microscope, a unique probe of materials is finally emerging (Hillier 1943, Watanabe 1955, Castaing and Henri 1962, Crewe 1966, Wittry, Ferrier and Cosslett 1969, Isaacson and Johnson 1975, Egerton, Rossouw and Whelan 1976, Kokubo and Iwatsuki 1976, Colliex, Cosslett, Leapman and Trebbia 1977). We first review some scattering terminology by way of background and to identify some of the more interesting and significant features of energy loss electrons and then go on to discuss examples of studies of the type of phenomena encountered. Finally we will comment on some of the experimental factors encountered.

scholarly journals Optical Thouless conductance and level-spacing statistics in two-dimensional Anderson localizing systems

2019 ◽  
Vol 100 (6) ◽  
Author(s):  
Sandip Mondal ◽  
Randhir Kumar ◽  
Martin Kamp ◽  
Sushil Mujumdar
Keyword(s):  
Two Dimensional ◽  
Level Spacing

"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.

Level Spacing Distributions of Random Matrix Ensembles

1993 ◽  
Vol 62 (7) ◽  
pp. 2248-2259 ◽  
Author(s):  
Masahiro Shiroishi ◽  
Taro Nagao ◽  
Miki Wadati
Keyword(s):  
Random Matrix ◽  
Level Spacing ◽  
Random Matrix Ensembles ◽  
Matrix Ensembles

scholarly journals Level spacing of random matrices in an external source

1998 ◽  
Vol 58 (6) ◽  
pp. 7176-7185 ◽  
Author(s):  
E. Brézin ◽  
S. Hikami
Keyword(s):  
Random Matrices ◽  
External Source ◽  
Level Spacing
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