Related papers: On the quantum variance of matrix elements for the…
We consider the properties of an observable (such as a single spin component that squares to the identity) when expressed as a matrix in the basis of energy eigenstates, and then truncated to a microcanonical slice of energies of varying…
We discuss the semiclassical approximation to transport problems in quantum chaotic systems. The figures of merit are moments of the transmission matrix and of the time delay matrix. After reviewing a few results obtained by treating these…
The quantitative contributions of a mixed phase-space to the mean characterizing the distribution of diagonal transition matrix elements and to the variance characterizing the distributions of non-diagonal transition matrix elements are…
Transmon qubits arise from the quantization of nonlinear resonators, systems that are prone to the buildup of strong, possibly chaotic, fluctuations. Such instabilities will likely affect fast gate operations which involve the transient…
We connect quantum graphs with infinite leads, and turn them to scattering systems. We show that they display all the features which characterize quantum scattering systems with an underlying classical chaotic dynamics: typical poles, delay…
The statistical properties of the quantum chaotic spectra have been studied, so far, only up to the second order correlation effects. The numerical as well as the analytical evidence that random matrix theory can successfully model the…
We study the decrease of fluctuations of diagonal matrix elements of observables and of Husimi densities of quantum mechanical wave functions around their mean value upon approaching the semi-classical regime ($\hbar \rightarrow 0$). The…
The fundamental correspondence between quantum chaotic single-particle systems and random matrix theory is well-understood via periodic orbit theory. In contrast, we show that many-body systems with explicit subsystem structure possess…
Quantum-classical correspondence for the average shape of eigenfunctions and the local spectral density of states are well-known facts. In this paper, the fluctuations that quantum mechanical wave functions present around the classical…
Classically chaotic systems relax to coarse grained states of equilibrium. Here we numerically study the quantization of such bounded relaxing systems, in particular the quasi-periodic fluctuations associated with the correlation between…
Measurement choices in weakly-measured open quantum systems can affect quantum trajectory chaos. We consider this scenario semi-classically and show that measurement acts as nonlinear generalized fluctuation and dissipation forces. These…
Typical eigenstates of quantum systems, whose classical limit is chaotic, are well approximated as random states. Corresponding eigenvalue spectra is modeled through appropriate ensemble of random matrix theory. However, a small subset of…
In quantum chaos, the spectral statistics generally follows the predictions of Random Matrix Theory (RMT). A notable exception is given by scar states, that enhance probability density around unstable periodic orbits of the classical…
When an isolated quantum system is driven out of equilibrium, expectation values of general observables start oscillating in time. This article reviews the general theory of such temporal fluctuations. We first survey some results on the…
The nonequilibrium dynamics in chaotic quantum systems denies a fully understanding up to now, even if thermalization in the long-time asymptotic state has been explained by the eigenstate thermalization hypothesis which assumes a universal…
We propose a possible resolution for the problem of why the semicircular law is not observed, whilst the random matrix hypothesis describes well the fluctuation of energy spectra. We show in the random 2-matrix model that the interactions…
Random matrix theory is used to represent generic loss of coherence of a fixed central system coupled to a quantum-chaotic environment, represented by a random matrix ensemble, via random interactions. We study the average density matrix…
The energy level statistics of uniform random graphs are studied, by treating the graphs as random tight-binding lattices. The inherent random geometry of the graphs and their dynamical spatial dimensionality, leads to various quantum…
We show that, in the semiclassical limit and whenever the elements of the Hamiltonian matrix are random enough, the eigenvectors of strongly chaotic time-independent systems in ordered bases can on average be exponentially localized across…
We study the universal fluctuations of the Wigner-Smith time delay for systems which exhibit chaotic dynamics in their classical limit. We present a new derivation of the semiclassical relation of the quantum time delay to properties of the…