scholarly journals Large N Expansion for Normal and Complex Matrix Ensembles

2007 ◽  
pp. 213-229 ◽  
Author(s):  
P. Wiegmann ◽  
A. Zabrodin
Keyword(s):  
Complex Matrix ◽  
Large N ◽  
Matrix Ensembles ◽  
Large N Expansion

scholarly journals A large N expansion for gravity

2005 ◽  
Vol 731 (3) ◽  
pp. 389-405 ◽  
Author(s):  
F. Canfora
Keyword(s):  
Large N ◽  
Large N Expansion

scholarly journals Modelling equilibration of local many-body quantum systems by random graph ensembles

Quantum ◽  
2020 ◽  
Vol 4 ◽  
pp. 273 ◽  
Author(s):  
Daniel Nickelsen ◽  
Michael Kastner
Keyword(s):  
Hilbert Space ◽  
Random Matrices ◽  
Network Theory ◽  
Maximum Flow ◽  
Quantum Systems ◽  
Complex Matrix ◽  
Many Body ◽  
Random Matrix Ensembles ◽  
Matrix Ensembles ◽  
Exact Diagonalisation

We introduce structured random matrix ensembles, constructed to model many-body quantum systems with local interactions. These ensembles are employed to study equilibration of isolated many-body quantum systems, showing that rather complex matrix structures, well beyond Wigner's full or banded random matrices, are required to faithfully model equilibration times. Viewing the random matrices as connectivities of graphs, we analyse the resulting network of classical oscillators in Hilbert space with tools from network theory. One of these tools, called the maximum flow value, is found to be an excellent proxy for equilibration times. Since maximum flow values are less expensive to compute, they give access to approximate equilibration times for system sizes beyond those accessible by exact diagonalisation.

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