相关论文: Quantum chaos, integrability, and late times in th…
We study the statistical properties of Lanczos coefficients over an ensemble of random initial operators generating the Krylov space. We propose two statistical quantities that are important in characterizing the complexity: the average…
The complexity of quantum evolutions can be understood by examining their dispersion in a chosen basis. Recent research has stressed the fact that the Krylov basis is particularly adept at minimizing this dispersion [V. Balasubramanian et…
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…
Krylov complexity measures the spread of the wavefunction in the Krylov basis, which is constructed using the Hamiltonian and an initial state. We investigate the evolution of the maximally entangled state in the Krylov basis for both…
We apply a notion of quantum complexity, called "Krylov complexity", to study the evolution of systems from integrability to chaos. For this purpose we investigate the integrable XXZ spin chain, enriched with an integrability breaking…
In Hermitian systems, Krylov complexity has emerged as a powerful diagnostic of quantum dynamics, capable of distinguishing chaotic from integrable phases, in agreement with established probes such as spectral statistics and…
A characteristic feature of "quantum chaotic" systems is that their eigenspectra and eigenstates display universal statistical properties described by random matrix theory (RMT). However, eigenstates of local systems also encode structure…
We study whether a generic isolated quantum system initially set out of equilibrium can be considered as localized close to its initial state. Our approach considers the time evolution in the Krylov basis, which maps the dynamics onto that…
Previous results indicate that while chaos can lead to substantial entropy production, thereby maximizing dynamical entanglement, this still falls short of maximality. Random Matrix Theory (RMT) modeling of composite quantum systems,…
The eigenvalues of quantum chaotic systems have been conjectured to follow, in the large energy limit, the statistical distribution of eigenvalues of random ensembles of matrices of size $N\rightarrow\infty$. Here we provide semiclassical…
Quantum chaotic systems are often defined via the assertion that their spectral statistics coincides with, or is well approximated by, random matrix theory. In this paper we explain how the universal content of random matrix theory emerges…
Recently, Krylov complexity was proposed as a measure of complexity and chaoticity of quantum systems. We consider the stadium billiard as a typical example of the quantum mechanical system obtained by quantizing a classically chaotic…
The statistics of the resonance widths and the behavior of the survival probability is studied in a particular model of quantum chaotic scattering (a particle in a periodic potential subject to static and time-periodic forces) introduced…
Random matrix theory (RMT) provides a successful model for quantum systems, whose classical counterpart has a chaotic dynamics. It is based on two assumptions: (1) matrix-element independence, and (2) base invariance. Last decade witnessed…
This article tackles a fundamental long-standing problem in quantum chaos, namely, whether quantum chaotic systems can exhibit sensitivity to initial conditions, in a form that directly generalizes the notion of classical chaos in phase…
Krylov complexity, as a novel measure of operator complexity under Heisenberg evolution, exhibits many interesting universal behaviors and also bounds many other complexity measures. In this work, we study Krylov complexity $\mathcal{K}(t)$…
The most general and versatile defining feature of quantum chaotic systems is that they possess an energy spectrum with correlations universally described by random matrix theory (RMT). This feature can be exhibited by systems with a well…
We propose a measure of quantum state complexity defined by minimizing the spread of the wave-function over all choices of basis. Our measure is controlled by the "survival amplitude" for a state to remain unchanged, and can be efficiently…
The concept of structural invariance previously introduced by the authors is used to argue that the connection between random matrix theory and quantum systems with a chaotic classical counterpart is in fact largely exact in the…
We investigate minimal two-body Hamiltonians with random interactions that generate spectra resembling those of Gaussian random matrices, a phenomenon we term quadratic quantum chaos. Unlike integrable two-body fermionic systems, the…