Related papers: Krylov complexity in saddle-dominated scrambling
Out-of-time-order correlators (OTOCs) that capture maximally chaotic properties of a black hole are determined by scattering processes near the horizon. This prompts the question to what extent OTOCs display chaotic behaviour in horizonless…
Out-of-time-order correlators (OTOC) being explored as a measure of quantum chaos, is studied here in a coupled bipartite system. Each of the subsystems can be chaotic or regular and lead to very different OTOC growths both before and after…
We investigate Krylov complexity of the fermion chain operator which consists of multiple Majorana fermions in the double-scaled SYK (DSSYK) model with finite temperature. Using the fact that Krylov complexity is computable from two-point…
The non-integrability of quantum systems, often associated with chaotic behavior, is a concept typically applied to cases with a high-dimensional Hilbert space Among different indicators signaling this behavior, the study of the long-time…
The out-of-time-order correlator (OTOC), recently analyzed in several physical contexts, is studied for low-dimensional chaotic systems through semiclassical expansions and numerical simulations. The semiclassical expansion for the OTOC…
Previous studies show that, in quantum chaotic and integrable systems, the so-called out-of-time-ordered correlator (OTOC) generically behaves differently at long times, while, it may show similar early growth in one-body systems. In this…
In this work, we investigate the Krylov complexity in quantum optical systems subject to time--dependent classical external fields. We focus on various interacting quantum optical models, including a collection of two--level atoms, photonic…
OTOC has been used to characterize the information scrambling in quantum systems. Recent studies showed that local conserved quantities play a crucial role in governing the relaxation dynamics of OTOC in non-integrable systems. In…
Quantum information stored in local operators spreads over other degrees of freedom of the system during time evolution, known as scrambling. This process is conveniently characterized by the out-of-time-order commutators (OTOC), whose time…
We discuss the predictability of a conservative system that drives a chaotic system with positive maximum Lyapunov exponent $\lambda_0$, such as the erratic motion of an asteroid in the gravitational field of two bodies of much larger mass.…
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 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…
We study upper bounds on the growth of operator entropy $S_K$ in operator growth. Using uncertainty relation, we first prove a dispersion bound on the growth rate $|\partial_t S_K|\leq 2b_1 \Delta S_K$, where $b_1$ is the first Lanczos…
Much recent work has been devoted to the study of information scrambling in quantum systems. In this paper, we study the long-time properties of the algebraic out-of-time-order-correlator ("$\mathcal{A}$-OTOC") and derive an analytical…
We explore the physics of scrambling in the moving mirror models, in which a two-dimensional CFT is subjected to a time-dependent boundary condition. It is well-known that by choosing an appropriate mirror profile, one can model quantum…
Quantum chaos is an intriguing topic and has attracted a great deal of interests in quantum mechanics and black hole physics. Recently, the exponential growth of out-of-time-ordered correlator (OTOC) has been proposed to diagnose quantum…
We show that Hall's exact uncertainty relation acquires a simple geometric form in the Krylov basis generated by the Liouvillian. In this canonical operator frame, the uncertainty equality implies that the operator amplitude vector evolves…
In the context of chaotic quantum many-body systems, we show that operator growth, as diagnosed by out-of-time-order correlators of local operators, also leaves a sharp imprint in out-of-time-order correlators of global operators. In…
In this study, we analyze Krylov Complexity in two-dimensional conformal field theories subjected to deformed SL$(2,\mathbb{R})$ Hamiltonians. In the vacuum state, we find that the K-complexity exhibits a universal phase structure. The…
Krylov complexity provides a powerful framework for characterizing the dynamical evolution of quantum systems through the spreading of states in Krylov space. The motivation for this is rooted in the optimality of the Krylov basis for the…