Related papers: Weakly universal dynamical correlations between ei…
The paper addresses the calculation of correlation functions of permanental polynomials of matrices with random entries. By exploiting a convenient contour integral representation of the matrix permanent some explicit results are provided…
The density matrix of a non-relativistic quantum system, divided into $N$ sub-systems, is rewritten in terms of the set of all partitioned density matrices for the system. For the case where the different sub-systems are distinguishable, we…
We study purification dynamics in monitored quantum processes governed by ensembles of quantum circuits in different random-matrix symmetry classes. We analyze the universal aspects that emerge away from the measurement induced phase…
Universality often emerges in low-energy equilibrium physics of quantum many-body systems, despite their microscopic complexity and variety. Recently, there has been a growing interest in studying far-from-equilibrium dynamics of quantum…
Universality in physics describes how disparate systems can exhibit identical low-energy behavior. Here, we reveal a rich landscape of new universal scattering phenomena governed by the interplay between an interaction and a system's…
We consider the many-body ground state of polarized fermions interacting via zero-range $\mathfrak{p}$-wave forces in a one-dimensional geometry. We rigorously prove that in the limit of infinite attractions spectral properties of any-order…
The statistical distribution of levels of an integrable system is claimed to be a Poisson distribution. In this paper, we numerically generate an ensemble of N dimensional random diagonal matrices as a model for regular systems. We evaluate…
Time-dependent response and correlation functions are studied in random quantum systems composed of infinitely many parts without mutual interaction and defined with statistically independent random matrices. The latter are taken within the…
In this paper we calculate, in the large N limit, the eigenvalue density of an infinite product of random unitary matrices, each of them generated by a random hermitian matrix. This is equivalent to solving unitary diffusion generated by a…
Wishart random matrix theory is of major importance for the analysis of correlated time series. The distribution of the smallest eigenvalue for Wishart correlation matrices is particularly interesting in many applications. In the complex…
The eigenvalue densities of two random matrix ensembles, the Wigner Gaussian matrices and the Wishart covariant matrices, are decomposed in the contributions of each individual eigenvalue distribution. It is shown that the fluctuations of…
Correlation matrices are the sub-class of positive definite real matrices with all entries on the diagonal equal to unity. Earlier work has exhibited a parametrisation of the corresponding Cholesky factorisation in terms of partial…
Density-dependent diffusion is a widespread phenomenon in nature. We have examined the density-dependent diffusion behavior of some biological processes such as tumor growth and invasion [23]. Here, we extend our previous work by developing…
We develop a technique for finding the dynamical evolution in time of an averaged density matrix. The result is an equation of evolution that includes an Effective Hamiltonian, as well as decoherence terms in Lindblad form. Applying the…
Using a character expansion method, we calculate exactly the eigenvalue density of random matrices of the form M^\dagger M where M is a complex matrix drawn from a normalized distribution P(M) ~ exp(-\Tr(A M B M^\dagger) with A and B…
Modeling correlation (and covariance) matrices can be challenging due to the positive-definiteness constraint and potential high-dimensionality. Our approach is to decompose the covariance matrix into the correlation and variance matrices…
It is shown that the matrix models which give non-perturbative definitions of string and M theory may be interpreted as non-local hidden variables theories in which the quantum observables are the eigenvalues of the matrices while their…
We consider the correlation functions of eigenvalues of a unidimensional chain of large random hermitian matrices. An asymptotic expression of the orthogonal polynomials allows to find new results for the correlations of eigenvalues of…
We consider low--dimensional dynamical systems with a mixed phase space and discuss the typical appearance of slow, polynomial decay of correlations: in particular we emphasize how this mixing rate is related to large deviations properties.
Putting dynamics into random matrix models leads to finitely many nonintersecting Brownian motions on the real line for the eigenvalues, as was discovered by Dyson. Applying scaling limits to the random matrix models, combined with Dyson's…