scholarly journals Eigenvectors distribution and quantum unique ergodicity for deformed Wigner matrices

2020 ◽  
Vol 56 (4) ◽  
pp. 2822-2867
Author(s):  
L. Benigni
Keyword(s):  
Unique Ergodicity ◽  
Wigner Matrices

Limiting Behavior of Eigenvectors of Large Wigner Matrices

2011 ◽  
Vol 146 (3) ◽  
pp. 519-549 ◽  
Author(s):  
Z. D. Bai ◽  
G. M. Pan
Keyword(s):  
Limiting Behavior ◽  
Wigner Matrices

Teichmüller dynamics and unique ergodicity via currents and Hodge theory

2020 ◽  
Vol 2020 (768) ◽  
pp. 39-54
Author(s):  
Curtis T. McMullen
Keyword(s):  
Hodge Theory ◽  
Unique Ergodicity ◽  
Polygonal Billiards ◽  
Teichmuller Dynamics

AbstractWe present a cohomological proof that recurrence of suitable Teichmüller geodesics implies unique ergodicity of their terminal foliations. This approach also yields concrete estimates for periodic foliations and new results for polygonal billiards.

scholarly journals Equipartition principle for Wigner matrices

2021 ◽  
Vol 9 ◽  
Author(s):  
Zhigang Bao ◽  
László Erdős ◽  
Kevin Schnelli
Keyword(s):  
High Precision ◽  
Quantum Systems ◽  
Wigner Matrices ◽  
Very High

Abstract We prove that the energy of any eigenvector of a sum of several independent large Wigner matrices is equally distributed among these matrices with very high precision. This shows a particularly strong microcanonical form of the equipartition principle for quantum systems whose components are modelled by Wigner matrices.

scholarly journals On a Unique Ergodicity of Some Markov Processes

2011 ◽  
Vol 36 (4) ◽  
pp. 589-606 ◽  
Author(s):  
Rafał Kapica ◽  
Tomasz Szarek ◽  
Maciej Ślȩczka
Keyword(s):  
Markov Processes ◽  
Unique Ergodicity

scholarly journals Local laws for polynomials of Wigner matrices

2020 ◽  
Vol 278 (12) ◽  
pp. 108507
Author(s):  
László Erdős ◽  
Torben Krüger ◽  
Yuriy Nemish
Keyword(s):  
Wigner Matrices

scholarly journals Non-unique ergodicity, observers' topology and the dual algebraic lamination for $\Bbb R$-trees

2007 ◽  
Vol 51 (3) ◽  
pp. 897-911 ◽  
Author(s):  
Thierry Coulbois ◽  
Arnaud Hilion ◽  
Martin Lustig
Keyword(s):  
Unique Ergodicity
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