Related papers: Discrete Hessians in study of Quantum Statistical …
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 apply a new formalism to derive the higher-order quantum kinetic expansion (QKE) for studying dissipative dynamics in a general quantum network coupled with an arbitrary thermal bath. The dynamics of system population is described by a…
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…
We rederive in a simplified version the Lehmann-Sommers eigenvalue distribution for the Gaussian ensemble of asymmetric real matrices, invariant under real orthogonal transformations, as a basis for a detailed derivation of a Pfaffian…
The conjectured three generic local bulk statistics amongst all non-Hermitian random matrix symmetry classes have recently been extended to three generic local edge statistics. We study analytically and numerically complex spacing ratios…
We investigate the dynamics of Entanglement Hamiltonians (EHs) in dissipative free-fermionic systems using a recent operator-based formulation of the quasiparticle picture. Focusing on gain and loss dissipation, we study the post-quench…
We study the ensemble of complex symmetric matrices. The ensemble is useful in the study of effect of dissipation on systems with time reversal invariance. We consider the nearest neighbor spacing distribution and spacing ratio to…
. We study the statistical properties of the eigenvalues of non-Hermitian operators assoicated with the dissipative complex systems. By considering the Gaussian ensembles of such operators, a hierarchical relation between the correlators is…
Schroedinger equation on a Hilbert space ${\cal H}$, represents a linear Hamiltonian dynamical system on the space of quantum pure states, the projective Hilbert space $P {\cal H}$. Separable states of a bipartite quantum system form a…
Statistics over the Gaussian unitary ensemble and the Wishart ensemble of random matrices often have nice closed-form expressions. These are related to multivariate extensions of the Hermite, Laguerre, and Jacobi polynomials, which often…
The dynamical algebra associated to a family of isospectral oscillator Hamiltonians is studied through the analysis of its representation in the basis of energy eigenstates. It is shown that this representation becomes similar to that of…
We investigate circuit complexity of unitaries generated by time evolution of randomly chosen strongly interacting Hamiltonians in finite dimensional Hilbert spaces. Specifically, we focus on two ensembles of random generators -- the so…
Discrete and continuous variables oftentimes require different treatments in many learning tasks. Identifying the Hamiltonian governing the evolution of a quantum system is a fundamental task in quantum learning theory. While previous works…
Just like decent classical difference-difference systems define symplectic maps on suitable phase spaces, their counterparts with properly ordered noncommutative entries come as Heisenberg equations of motion for corresponding quantum…
A non-Hermitean extension of paradigmatic Wishart random matrices is introduced to set up a theoretical framework for statistical analysis of (real, complex and real quaternion) stochastic time series representing two "remote" complex…
This is part II of a review relating to the three classes of random non-Hermitian Gaussian matrices introduced by Ginibre in 1965. While part I restricted attention to the GinUE (Ginibre unitary ensemble) case of complex elements, in this…
A class of pseudo-hermitian quantum system with an explicit form of the positive-definite metric in the Hilbert space is presented. The general method involves a realization of the basic canonical commutation relations defining the quantum…
Non hermitian Hamiltonians play an important role in the study of dissipative quantum systems. We show that using states with time dependent normalization can simplify the description of such systems especially in the context of the…
Control of quantum dissipative systems can be challenging because control variables are typically part of the system Hamiltonian, which can only generate motion along unitary orbits of the system. To transit between orbits, one must harness…
The Eigenstate Thermalization Hypothesis implies that for a thermodynamically large system in one of its eigenstates, the reduced density matrix describing any finite subsystem is determined solely by a set of {\it relevant} conserved…