Related papers: Krylov complexity and chaos in quantum mechanics
We study the dynamics of a "kicked" quantum system undergoing repeated measurements of momentum. A diffusive behavior is obtained for a large class of Hamiltonians, even when the dynamics of the classical counterpart is not chaotic. These…
One of the fundamental manifestations of classical chaos is exponential sensitivity to initial conditions that is, two trajectories starting from nearly identical initial states diverge exponentially over time. This behavior is quantified…
We propose a formalism which defines chaos in both quantum and classical systems in an equivalent manner by means of \textit{adiabatic transformations}. The complexity of adiabatic transformations which preserve classical time-averaged…
Spread complexity uses the distribution of support of a time-evolving state in the Krylov basis to quantify dispersal across accessible dimensions of a Hilbert space. Here, we describe how variations in initial conditions, the Hamiltonian,…
We investigate the Krylov complexity of Schr\"odinger field theories, focusing on both bosonic and fermionic systems within the grand canonical ensemble that includes a chemical potential. Krylov complexity measures operator growth in…
We study classical and quantum dynamics of two spinless particles confined in a quantum wire with repulsive or attractive Coulomb interaction. The interaction induces irregular dynamics in classical mechanics, which reflects on the quantum…
In closed quantum systems, Krylov complexity admits a geometric description; operator growth is equivalent to Hamiltonian flow in an emergent phase space whose structure is fixed by the Lanczos coefficients. We show that this picture…
The spreading of quantum states in Krylov space under unitary dynamics provides a natural framework for characterizing quantum complexity. Quantifiers of this spreading, such as the spread complexity and the inverse participation ratio,…
We investigate signatures of quantum chaos within Ising spin chains subjected to transverse and longitudinal fields, incorporating both local (nearest-neighbor) and non-local (long-range) couplings. While local Ising models may exhibit…
Different aspects of the predictability problem in dynamical systems are reviewed. The deep relation among Lyapunov exponents, Kolmogorov-Sinai entropy, Shannon entropy and algorithmic complexity is discussed. In particular, we emphasize…
Krylov complexity is considered to provide a measure of the growth of operators evolving under Hamiltonian dynamics. The main strategy is the analysis of the structure of Krylov subspace $\mathcal{K}_M(\mathcal{H},\eta)$ spanned by the…
Quantifying complexity in quantum systems has witnessed a surge of interest in recent years, with Krylov-based measures such as Krylov complexity ($C_K$) and Spread complexity ($C_S$) gaining prominence. In this study, we investigate their…
We show that it is possible to associate univocally with each given solution of the time-dependent Schroedinger equation a particular phase flow ("quantum flow") of a non-autonomous dynamical system. This fact allows us to introduce a…
We study operator spreading in many-body quantum systems by its potential to generate an informationally complete measurement record in quantum tomography. We adopt continuous weak measurement tomography for this purpose. We generate the…
We ask whether Krylov complexity is mutually compatible with the circuit and Nielsen definitions of complexity. We show that the Krylov complexities between three states fail to satisfy the triangle inequality and so cannot be a measure of…
We study Krylov complexity in BMN Plane Wave Matrix Model at large mass deformation. We consider various consistent reductions of the matrix model that allow us to perform a Hamiltonian analysis which leads to different notions of the…
Recent studies have shown that there is a strong interplay between quantum complexity and quantum chaos. In this work, we consider a new method to study geometric complexity for interacting non-Gaussian quantum mechanical systems to…
We shortly review the progress in the domain of deterministic chaos for quantum dynamical systems. With the appropriately extended definition of quantum Lyapunov exponent we analyze various quantum dynamical maps. It is argued that, within…
The coupling of orbital and spin degrees of freedom is the source of many interesting phenomena. Here, we study the electron dynamics in a quantum billiard --a mesoscopic rectangular quantum dot-- with spin-orbit coupling driven by a…
The method of restricted path integrals allows one to effectively consider continuous (prolonged in time) measurements of quantum systems. Monitoring of the system coordinates is such a continuous measurement that allows one to describe a…