Spectral statistics for Anderson models with sporadic potentials

2020 ◽  
Vol 10 (2) ◽  
pp. 581-597
Author(s):  
Werner Kirsch ◽  
Maddaly Krishna
Keyword(s):  
Spectral Statistics ◽  
Anderson Models

scholarly journals Chaos on the hypercube

2020 ◽  
Vol 2020 (11) ◽  
Author(s):  
Yiyang Jia ◽  
Jacobus J. M. Verbaarschot
Keyword(s):  
Magnetic Flux ◽  
Spectral Density ◽  
Hermite Polynomials ◽  
Weighted Sums ◽  
Majorana Fermions ◽  
Chord Diagrams ◽  
Magnetic Inversion ◽  
Constant Magnitude ◽  
Kitaev Model ◽  
Spectral Statistics

Abstract We analyze the spectral properties of a d-dimensional HyperCubic (HC) lattice model originally introduced by Parisi. The U(1) gauge links of this model give rise to a magnetic flux of constant magnitude ϕ but random orientation through the faces of the hypercube. The HC model, which also can be written as a model of 2d interacting Majorana fermions, has a spectral flow that is reminiscent of Maldacena-Qi (MQ) model, and its spectrum at ϕ = 0, actually coincides with the coupling term of the MQ model. As was already shown by Parisi, at leading order in 1/d, the spectral density of this model is given by the density function of the Q-Hermite polynomials, which is also the spectral density of the double-scaled Sachdev-Ye-Kitaev model. Parisi demonstrated this by mapping the moments of the HC model to Q-weighted sums on chord diagrams. We point out that the subleading moments of the HC model can also be mapped to weighted sums on chord diagrams, in a manner that descends from the leading moments. The HC model has a magnetic inversion symmetry that depends on both the magnitude and the orientation of the magnetic flux through the faces of the hypercube. The spectrum for fixed quantum number of this symmetry exhibits a transition from regular spectra at ϕ = 0 to chaotic spectra with spectral statistics given by the Gaussian Unitary Ensembles (GUE) for larger values of ϕ. For small magnetic flux, the ground state is gapped and is close to a Thermofield Double (TFD) state.

scholarly journals From closed to open one-dimensional Anderson model: Transport versus spectral statistics

2012 ◽  
Vol 86 (1) ◽  
Author(s):  
S. Sorathia ◽  
F. M. Izrailev ◽  
V. G. Zelevinsky ◽  
G. L. Celardo
Keyword(s):  
Anderson Model ◽  
One Dimensional ◽  
Spectral Statistics

scholarly journals Transitions in spectral statistics

1994 ◽  
Vol 27 (16) ◽  
pp. L563-L568 ◽  
Author(s):  
C Blecken ◽  
Y Chen ◽  
K A Muttalib
Keyword(s):  
Spectral Statistics

scholarly journals Direct Scaling Analysis of Fermionic Multiparticle Correlated Anderson Models with Infinite-Range Interaction

2016 ◽  
Vol 2016 ◽  
pp. 1-17 ◽  
Author(s):  
Victor Chulaevsky
Keyword(s):  
Dynamical Localization ◽  
Scaling Analysis ◽  
Range Interaction ◽  
Direct Scaling ◽  
Strongly Mixing ◽  
Optimal Decay ◽  
Decay Bounds ◽  
Multiparticle Systems ◽  
Infinite Range ◽  
Anderson Models

We adapt the method of direct scaling analysis developed earlier for single-particle Anderson models, to the fermionic multiparticle models with finite or infinite interaction on graphs. Combined with a recent eigenvalue concentration bound for multiparticle systems, the new method leads to a simpler proof of the multiparticle dynamical localization with optimal decay bounds in a natural distance in the multiparticle configuration space, for a large class of strongly mixing random external potentials. Earlier results required the random potential to be IID.

scholarly journals Long-Term Spectral Statistics for Voice Presentation Attack Detection

2017 ◽  
Vol 25 (11) ◽  
pp. 2098-2111 ◽  
Author(s):  
Hannah Muckenhirn ◽  
Pavel Korshunov ◽  
Mathew Magimai-Doss ◽  
Sebastien Marcel
Keyword(s):  
Attack Detection ◽  
Spectral Statistics ◽  
Presentation Attack Detection
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