Related papers: Arbitrary relaxation rate under non-Hermitian matr…
Two-dimensional networks of ordered quantum dots beyond the percolation threshold are studied, as typical example of conducting nanostructures with quenched random disorder. Theory predicts anomalous diffusion with stretched-exponential…
In non-Hermitian crystal systems under open boundary condition (OBC), it is generally believed that the OBC modes with frequencies containing positive imaginary parts, when excited by external driving, will experience exponential growth in…
Quantum systems with discrete symmetries can usually be desymmetrized, but this strategy fails when considering transport in open systems with a symmetry that maps different openings onto each other. We investigate the joint probability…
We study the transport and spectral properties of a non-Hermitian one-dimensional disordered lattice, the diagonal matrix elements of which are random complex variables taking both positive (loss) and negative (gain) imaginary values: Their…
The spatiotemporal evolution of the out-of-time-order correlator (OTOC) measures the propagation and scrambling of local quantum information. For the transverse field Ising model with open boundaries, the local operator $\sigma^{x}$ shows…
We consider the time evolution of the out-of-time-ordered correlator (OTOC) of two general observables $A$ and $B$ in a mean field chaotic quantum system described by a random Wigner matrix as its Hamiltonian. We rigorously identify three…
We investigate the spectral properties of non-Hermitian real random matrices whose entries exhibit long-range correlations decaying as~$|r-r'|^{-\alpha}$. We find a progressive breakdown of the circular law, controlled by the decrease…
It has been conjectured by Maldacena, Shenker, and Stanford [J. High Energy Phys.~08 (2016) 106] that the exponential growth rate of the out-of-time-ordered correlator (OTOC) $F(t)$ has a universal upper bound $2\pi k_B T/\hbar$. Here we…
We show for generic quantum non-Hermitian tight-binding models that relaxation timescales of local observables are not controlled by the localization length $\xi_{\rm loc}$ associated with the non-Hermitian skin effect, contrary to popular…
Thermalization of chaotic quantum many-body systems under unitary time evolution is related to the growth in complexity of initially simple Heisenberg operators. Operator growth is a manifestation of information scrambling and can be…
We consider the standard overlap $\mathcal{O}_{ij}: =\langle \mathbf{r}_j, \mathbf{r}_i\rangle\langle \mathbf{l}_j, \mathbf{l}_i\rangle$ of any bi-orthogonal family of left and right eigenvectors of a large random matrix $X$ with centred…
We study the spectral properties of a class of random matrices where the matrix elements depend exponentially on the distance between uniformly and randomly distributed points. This model arises naturally in various physical contexts, such…
Delocalization transition is numerically found in a non-Hermitian extension of a discrete-time quantum walk on a one-dimensional random medium. At the transition, an eigenvector gets delocalized and at the same time the corresponding energy…
Consider a Hermitian matrix model under an external potential with spiked external source. When the external source is of rank one, we compute the limiting distribution of the largest eigenvalue for general, regular, analytic potential for…
Random Hermitian matrices are used to model complex systems without time-reversal invariance. Adding an external source to the model can have the effect of shifting some of the matrix eigenvalues, which corresponds to shifting some of the…
Out-of-time-ordered correlators (OTOCs) have emerged as powerful tools for diagnosing quantum chaos and information scrambling. While extensively studied in closed quantum systems, their behavior in dissipative environments remains less…
We investigate quantum dynamics of a quantum walker on a finite bipartite non-Hermitian lattice, in which the particle can leak out with certain rate whenever it visits one of the two sublattices. Quantum walker initially located on one of…
We investigate the asymptotic behavior of the eigenvalues of spiked perturbations of Wigner matrices when the dimension goes to infinity. The entries of the Hermitian Wigner matrix have a distribution which is symmetric and satisfies a…
The dynamics of spontaneous emission of an atomic system is studied in the framework of an open quantum system. The resulting quantum master equation for the atomic system is non hermitian. The generator $\mathcal{L}$ can possess…
A generalized Wigner matrix perturbed by a finite-rank deterministic matrix is considered. The fluctuations of the largest eigenvalues, which emerge outside the bulk of the spectrum, and the corresponding eigenvectors, are studied. Under…