Related papers: Universality for random matrices and log-gases
In previous articles we have developed a theory of down conversion in nonlinear crystals, based on the Wigner representation of the radiation field. Taking advantage of the fact that the Wigner function is always positive in parametric down…
The paper continues the development of the rigorous supersymmetric transfer matrix approach to the random band matrices started in J Stat Phys 164:1233 -- 1260, 2016; Commun Math Phys 351:1009 -- 1044, 2017. We consider random Hermitian…
Wigner functions, allowing for a reformulation of quantum mechanics in phase space, are of central importance for the study of the quantum-classical transition. A full understanding of the quantum-classical transition, however, also…
We consider large non-Hermitian real or complex random matrices $X$ with independent, identically distributed centred entries. We prove that their local eigenvalue statistics near the spectral edge, the unit circle, coincide with those of…
We generalize Wigner's causality bounds and Bethe's integral formula for the effective range to arbitrary dimension and arbitrary angular momentum. Moreover, we discuss the impact of these constraints on the separation of low- and…
In this paper we describe a strategy to study the Anderson model of an electron in a random potential at weak coupling by a renormalization group analysis. There is an interesting technical analogy between this problem and the theory of…
This is a continuation of our earlier paper on the universality of the eigenvalues of Wigner random matrices. The main new results of this paper are an extension of the results in that paper from the bulk of the spectrum up to the edge. In…
The eigenvalues of quantum chaotic systems have been conjectured to follow, in the large energy limit, the statistical distribution of eigenvalues of random ensembles of matrices of size $N\rightarrow\infty$. Here we provide semiclassical…
We consider symmetric and Hermitian random matrices whose entries are independent and symmetric random variables with an arbitrary variance pattern. Under a novel Short-to-Long Mixing condition, which is sharp in the sense that it precludes…
We study entanglement dynamics in quantum Brownian motion (QBM) models. Our main tool is the Wigner function propagator. Time evolution in the Wigner picture is physically intuitive and it leads to a simple derivation of a master equation…
We consider $N\times N$ Hermitian random matrices with i.i.d. entries. The matrix is normalized so that the average spacing between consecutive eigenvalues is of order $1/N$. We study the connection between eigenvalue statistics on…
Recent work has proposed fading ergodicity as a mechanism for many-body ergodicity breaking. Here, we show that two paradigmatic random matrix ensembles -- the Rosenzweig-Porter model and the ultrametric model -- fall within the same…
We investigate the eigenvalues statistics of ensembles of normal random matrices when their order N tends to infinite. In the model the eigenvalues have uniform density within a region determined by a simple analytic polynomial curve. We…
The equation of motion for the reduced Wigner function of a system coupled to an external quantum system is presented for the specific case when the external quantum system can be modeled as a set of harmonic oscillators. The result is…
Universality of local eigenvalue statistics is one of the most striking phenomena of Random Matrix Theory, that also accounts for a lot of the attention that the field has attracted over the past 15 years. In this paper we focus on the…
We show that if the non Gaussian part of the cumulants of a random matrix model obey some scaling bounds in the size of the matrix, then Wigner's semicircle law holds. This result is derived using the replica technique and an analogue of…
This paper first surveys the connection of integrable systems of the Painleve type to various distribution functions appearing in Wigner-Dyson random matrix theory. A short discussion is then given of the appearance of these same…
We consider eigenvalues of generalized Wishart processes as well as particle systems, of which the empirical measures converge to deterministic measures as the dimension goes to infinity. In this paper, we obtain central limit theorems to…
We propose a new Wigner inequality suitable for test of the hypothesis of realism. We show that this inequality is not identical neither to the well-known Wigner inequality nor to the Leggett-Garg inequality in Wigner form. The obtained…
We consider random Hermitian matrices made of complex or real $M\times N$ rectangular blocks, where the blocks are drawn from various ensembles. These matrices have $N$ pairs of opposite real nonvanishing eigenvalues, as well as $M-N$ zero…