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Related papers: Dysonian dynamics of the Ginibre ensemble

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We exhibit new functions of the eigenvectors of the Dyson Brownian motion which follow an equation similar to the Bourgade-Yau eigenvector moment flow. These observables can be seen as a Fermionic counterpart to the original (Bosonic) ones.…

Probability · Mathematics 2021-08-20 Lucas Benigni

The paper is concerned with the asymptotic behavior of the correlation functions of the characteristic polynomials of non-Hermitian random matrices with independent entries. It is shown that the correlation functions behave like that for…

Mathematical Physics · Physics 2022-01-04 Ievgenii Afanasiev

We prove that the tagged particles of infinitely many Brownian particles in $ \Rtwo $ interacting via a logarithmic (two-dimensional Coulomb) potential with inverse temperature $ \beta = 2 $ are sub-diffusive. The associated delabeled…

Probability · Mathematics 2023-11-28 Hirofumi Osada

We extend recent results on the asymptotic eigenvalue distribution of the SYK model to the multivariate case and relate the limit of a dynamical version of the SYK model with the q-Brownian motion, a non-commutative deformation of classical…

Operator Algebras · Mathematics 2020-09-09 Miguel Pluma , Roland Speicher

The random matrix ensembles (RME) of Hamiltonian matrices, e.g. Gaussian random matrix ensembles (GRME) and Ginibre random matrix ensembles (Ginibre RME), are applicable to following quantum statistical systems: nuclear systems, molecular…

Statistical Mechanics · Physics 2007-05-23 Maciej M. Duras

Embedding non-Markovian open quantum dynamics into an enlarged Markovian space offers a powerful route to nonperturbative simulations, where the dynamics of the extended space can be governed by multiple distinct Markovian equations. We…

Quantum Physics · Physics 2026-02-26 Meng Xu , J. T. Stockburger , J. Ankerhold

The random matrix ensembles (RMT) of quantum statistical Hamiltonian operators, e.g.Gaussian random matrix ensembles (GRME) and Ginibre random matrix ensembles (Ginibre RME), are applied to following quantum statistical systems: nuclear…

Statistical Mechanics · Physics 2007-05-23 Maciej M. Duras

We define a new diffusive matrix model converging towards the $\beta$-Dyson Brownian motion for all $\beta\in [0,2]$ that provides an explicit construction of $\beta$-ensembles of random matrices that is invariant under the…

Probability · Mathematics 2013-06-25 Romain Allez , Alice Guionnet

Spectral properties of evolution operators corresponding to random maps and quantized chaotic systems strongly interacting with an environment can be described by the ensemble of non-hermitian random matrices from the real Ginibre ensemble.…

Quantum Physics · Physics 2011-05-20 Wojciech Roga , Marek Smaczynski , Karol Zyczkowski

Non-Hermitian random matrices with statistical spectral characteristics beyond the standard Ginibre ensembles have recently emerged in the description of dissipative quantum many-body systems as well as in non-ergodic wave transport in…

Mathematical Physics · Physics 2025-11-27 Gernot Akemann , Yan V. Fyodorov , Dmitry V. Savin

A quantum statistical random system with energy dissipation is studied. Its statistics is governed by random complex-valued non-Hermitean Hamiltonians belonging to complex Ginibre ensemble of random matrices. The eigenenergies of…

Statistical Mechanics · Physics 2007-05-23 Maciej M. Duras

The eigenvalue spectrum of the sum of large random matrices that are mutually "free", i.e., randomly rotated, can be obtained using the formalism of R-transforms, with many applications in different fields. We provide a direct…

Disordered Systems and Neural Networks · Physics 2025-04-18 Pierre Bousseyroux , Jean-Philippe Bouchaud

The elliptic Ginibre ensemble of complex non-Hermitian random matrices allows to interpolate between the rotational invariant Ginibre ensemble and the Gaussian unitary ensemble of Hermitian random matrices. It corresponds to a…

Mathematical Physics · Physics 2023-02-09 G. Akemann , M. Duits , L. D. Molag

This is a concise review of the complex, real and quaternion real Ginibre random matrix ensembles and their elliptic deformations. Eigenvalue correlations are exactly reduced to two-point kernels and discussed in the strongly and weakly…

Mathematical Physics · Physics 2009-12-01 B. A. Khoruzhenko , H. -J. Sommers

We review some recent techniques for dealing with non-hermitian random matrix models based on generalized Green's functions. We introduce the diagrammatic methods in the hermitian case and generalize them to the non-hermitian case. The…

Disordered Systems and Neural Networks · Physics 2007-05-23 Romuald A. Janik , Maciej A. Nowak , Gabor Papp , Ismail Zahed

We study the dynamics of a transmon qubit that is capacitively coupled to an open multimode superconducting resonator. Our effective equations are derived by eliminating resonator degrees of freedom while encoding their effect in the…

Quantum Physics · Physics 2017-05-02 Moein Malekakhlagh , Alexandru Petrescu , Hakan E. Türeci

The Ginibre ensemble of complex random Hamiltonian matrices $H$ is considered. Each quantum system described by $H$ is a dissipative system and the eigenenergies $Z_{i}$ of the Hamiltonian are complex-valued random variables. For generic…

Statistical Mechanics · Physics 2007-05-23 Maciej M. Duras

The random matrix ensembles (RME) of Hamiltonian matrices, e.g. Gaussian random matrix ensembles (GRME) and Ginibre random matrix ensembles (Ginibre RME), are applicable to following quantum statistical systems: nuclear systems, molecular…

Statistical Mechanics · Physics 2007-05-23 Maciej M. Duras

We study non-Hermitian random matrices belonging to the symmetry classes of the complex and symplectic Ginibre ensemble, and present a unifying and systematic framework for analysing mixed spectral moments involving both holomorphic and…

Mathematical Physics · Physics 2026-04-10 Gernot Akemann , Sung-Soo Byun , Seungjoon Oh

The Ginibre ensemble of complex random Hamiltonian matrices $H$ is considered. Each quantum system described by $H$ is a dissipative system and the eigenenergies $Z_{i}$ of the Hamiltonian are complex-valued random variables. For generic…

Statistical Mechanics · Physics 2007-05-23 Maciej M. Duras