Related papers: Dissipative spectral form factor for elliptic Gini…
We study the dissipative spectral form factor (DSFF) at complex time $T e^{i\theta}$ for the complex elliptic Ginibre ensemble with non-Hermiticity parameter $\tau \in [0,1)$. As the matrix dimension $N \to \infty$, we consider the natural…
We propose a measure, which we call the dissipative spectral form factor (DSFF), to characterize the spectral statistics of non-Hermitian (and non-Unitary) matrices. We show that DSFF successfully diagnoses dissipative quantum chaos, and…
The Dissipative Spectral Form Factor (DSFF), recently introduced in [arXiv:2103.05001] for the Ginibre ensemble, is a key tool to study universal properties of dissipative quantum systems. In this work we compute the DSFF for a large class…
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…
We show that non-Hermitian Ginibre random matrix behaviors emerge in spatially-extended many-body quantum chaotic systems in the space direction, just as Hermitian random matrix behaviors emerge in chaotic systems in the time direction.…
We numerically study the spectral statistics of open quantum many-body systems (OQMBS) as signatures of quantum chaos (or the lack thereof), using the dissipative spectral form factor (DSFF), a generalization of the spectral form factor to…
We explore the connections between dissipative quantum phase transitions and non-Hermitian random matrix theory. For this, we work in the framework of the dissipative Dicke model which is archetypal of symmetry-breaking phase transitions in…
The Dicke model, renowned for its superradiant quantum phase transition, also exhibits a transition from regular to chaotic dynamics. In this work, we provide a systematic, comparative study of static and dynamical indicators of chaos for…
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…
The complex elliptic Ginibre ensemble with coupling $\tau$ is a complex Gaussian matrix interpolating between the Gaussian Unitary Ensemble (GUE) and the Ginibre ensemble. It has been known for some time that its eigenvalues form a…
For an additive perturbation of the complex Ginibre ensemble under a deterministic matrix $X_0$, under certain assumption on $X_0$, we observe that there are only two kinds of local statistical patterns at the spectral edge: GinUE…
We investigate crystalline-like behavior of the spectral form factor (SFF) in unitary quantum systems with extremely strong eigenvalue repulsion. Using a low-temperature Coulomb gas as a model of repulsive eigenvalues, we derive the…
The spectral form factor (SFF) is a powerful diagnostic of random matrix behavior in quantum many-body systems. We introduce a family of random circuit ensembles whose SFFs can be computed \textit{exactly}. These ensembles describe the…
Spectral form factor (SFF), one of the key quantity from random matrix theory, serves as an important tool to probe universality in disordered quantum systems and quantum chaos. In this work, we present exact closed-form expressions for the…
Dynamic structure factor (DSF) is important for understanding excitations in many-body physics; it reveals information about the spectral and spatial correlations of fluctuations in quantum systems. Collective phenomena like quantum phase…
Quantum chaotic systems with one-dimensional spectra follow spectral correlations of orthogonal (OE), unitary (UE), or symplectic ensembles (SE) of random matrices depending on their invariance under time reversal and rotation. In this…
This is a collection of notes that are about spectral form factors of standard ensembles in the random matrix theory, written for the practical usage of current study of late time quantum chaos. More precisely, we consider Gaussian Unitary…
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…
We consider the finite-temperature dynamical structure factor (DSF) of gapped quantum spin chains such as the spin one Heisenberg model and the transverse field Ising model in the disordered phase. At zero temperature the DSF in these…
We systematically study the short range spectral fluctuation properties of three non-hermitian spin chain hamiltonians using complex spacing ratios. In particular we focus on the non-hermitian version of the standard one-dimensional…