Abstract:Nonlinear statistics (i.e. statistics of permanents) on the eigenvalues of invariant random matrix models are considered for the three Dyson's symmetry classes β = 1, 2, 4. General formulas in terms of hyperdeterminants are found for β = 2. For specific cases and all βs, more computationally efficient results are obtained, based on symmetric functions expansions. As an application, we consider the case of quantum transport in chaotic cavities extending results from [D.V. Savin, H.-J. Sommers and W. Wieczorek, … Show more
“…Exact results appeared for small n in [11,12,13,14] and for general n in [15,16]. In this last work the present author used a result of Kaneko [2] and Kadell [17] which gives the average value of any Schur function of the eigenvalues, an approach that was later taken further in [18,19]. For large numbers of channels, a generating function for the average value of ( 4) was presented in [20], and an explicit expression appeared in [13].…”
We obtain explicit expressions for positive integer moments of the
probability density of eigenvalues of the Jacobi and Laguerre random matrix
ensembles, in the asymptotic regime of large dimension. These densities are
closely related to the Selberg and Selberg-like multidimensional integrals. Our
method of solution is combinatorial: it consists in the enumeration of certain
classes of lattice paths associated to the solution of recurrence relations
“…(A.2) in principle allows for a complete characterization of statistical properties of experimental observables. For most recent analytical results, we refer to [30,31,32,33,46,47,48,49,50,51,52,53,54,55].…”
Section: Electronic Transport In Open Cavitiesmentioning
confidence: 99%
“…In particular, the study of higher moments of the transmission matrix τ n = Tr[T n ] has recently seen many analytical progresses 5 [24,25,30,31,32,33,48,49,53]. In particular, we now have two different (but equivalent) formulae for higher moments for β = 2 and arbitrary N 1 , N 2 :…”
Section: Electronic Transport In Open Cavitiesmentioning
We collect explicit and user-friendly expressions for one-point densities of the real eigenvalues {λ i } of N ×N Wishart-Laguerre and Jacobi random matrices with orthogonal, unitary and symplectic symmetry. Using these formulae, we compute integer moments τ n = N i=1 λ n i for all symmetry classes without any large N approximation. In particular, our results provide exact expressions for moments of transmission eigenvalues in chaotic cavities with time-reversal or spin-flip symmetry and supporting a finite and arbitrary number of electronic channels in the two incoming leads.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.