Related papers: Krylov Winding and Emergent Coherence in Operator …
We study information scrambling -- a spread of initially localized quantum information into the system's many degree of freedom -- in discrete-time quantum walks. We consider out-of-time-ordered correlators (OTOC) and K-complexity as a…
Operator spreading under unitary time evolution has attracted a lot of attention recently, as a way to probe many-body quantum chaos. While quantities such as out-of-time-ordered correlators (OTOC) do distinguish interacting from…
We discuss the probability distribution for the "size" of a time-evolving operator in the SYK model. Scrambling is related to the fact that as time passes, the distribution shifts towards larger operators. Initially, the rate is exponential…
We demonstrate that time-evolved operators can construct a Krylov space to compute Operator complexity and introduce Krylov observability as a measure of effective phase space dimension in quantum systems. We test Krylov observability in…
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…
Krylov complexity measures the spread of an evolved state in a natural basis, induced by the generator of the dynamics and the initial state. Here, we study the spread in Hilbert space of the state of an Ising chain subject to a…
We give a detailed theory for the leading coarse-grained dynamics of entanglement entropy of states and of operators in generic short-range interacting quantum many-body systems. This includes operators spreading under Heisenberg time…
Recent theoretical studies have predicted the existence of caustics in many-body quantum dynamics, where they manifest as extended regions of enhanced probability density that obey temporal and spatial scaling relations. Focusing on the…
We demonstrate on a representative example of a planar hybrid system with digital sampling a sudden transition from a stable limit cycle to the onset of chaotic dynamics. We show that the scaling law in the size of the attractor is…
In a quantum many-body system, autocorrelation functions can determine linear responses nearby equilibrium and quantum dynamics far from equilibrium. In this letter, we bring out the connection between the operator complexity and the…
We study the coherent dynamics of globally coupled maps showing macroscopic chaos. With this term we indicate the hydrodynamical-like irregular behaviour of some global observables, with typical times much longer than the times related to…
Information in a chaotic quantum system will scramble across the system, preventing any local measurement from reconstructing it. The scrambling dynamics is key to understanding a wide range of quantum many-body systems. Here we use Holevo…
An important parameter characterising the synchronisation of turbulent flows is the threshold coupling wavenumber. This study investigates the relationship between the threshold coupling wavenumber and the leading Lyapunov vector using…
We perform a systematic holographic study of Krylov complexity for a wide class of confining quantum field theories. Using the geometric prescription that identifies the time derivative of the complexity with the proper momentum of a…
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…
We study a periodically driven macrospin system with anisotropic long-range interactions and collective dissipation, described by a Lindblad master equation. In the thermodynamic limit ($N\to\infty$), a mean-field treatment yields classical…
The concepts of operator size and computational complexity play important roles in the study of quantum chaos and holographic duality because they help characterize the structure of time-evolving Heisenberg operators. It is particularly…
We study the out-of-time-ordered correlator (OTOC) in a zero temperature two dimensional conformal field theory (CFT) under evolution by a Liouvillian composed of the Virasoro generators. A bound was conjectured in arXiv:1812.08657 on the…
In this work, we develop a quantum metrological framework for quantum chaos by showing that local subsystems of information scrambling systems naturally function as quantum stopwatches. The reduced quantum state of a subsystem encodes the…
Causal diamonds are known to have thermal behavior that can be probed by finite-lifetime observers equipped with energy-scaled detectors. This thermality can be attributed to the time evolution of observers within the causal diamond,…