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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 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…
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…
Recently, the propagation of information through quantum many-body systems, developed to study quantum chaos, have found many application from black holes to disordered spin systems. Among other quantitative tools, Krylov complexity has…
In this work, we propose a quantum-mechanically measurable basis for the computation of spread complexity. Current literature focuses on computing different powers of the Hamiltonian to construct a basis for the Krylov state space and the…
Investigating the time evolution of complexity in quantum systems entails evaluating the spreading of the system's state across a defined basis in its corresponding Hilbert space. Recently, the Krylov basis has been identified as the one…
String theory provides a compact integral expression for the tree-level scattering amplitude of an arbitrary number of light strings. We focus on amplitudes involving a few tachyons and many photons, with a special choice of polarizations…
In this work, we investigate the impact of conserved charges on the dynamics of spread complexity of quantum states. Building on the notion of symmetry-resolved Krylov complexity [1], we extend the framework to general quantum states and…
Krylov complexity is a measure of operator growth in quantum systems, based on the number of orthogonal basis vectors needed to approximate the time evolution of an operator. In this paper, we study the Krylov complexity of a…
This Thesis explores the notion of Krylov complexity as a probe of quantum chaos and as a candidate for holographic complexity. The first Part is devoted to presenting the fundamental notions required to conduct research in this area.…
Quantum complexity is a measure of the minimal number of elementary operations required to approximately prepare a given state or unitary channel. Recently, this concept has found applications beyond quantum computing -- in studying the…
The concept of \emph{complexity} has become pivotal in multiple disciplines, including quantum information, where it serves as an alternative metric for gauging the chaotic evolution of a quantum state. This paper focuses on \emph{Krylov…
We study the holographic spread/Krylov complexity of operators with non-trivial internal structure and of genuinely extended operators. We first consider a massive particle in AdS$_5\times S^5$ carrying conserved $R$-charge, and show how…
Krylov complexity is a novel measure of operator complexity that exhibits universal behavior and bounds a large class of other measures. In this letter, we generalize Krylov complexity from a closed system to an open system coupled to a…
In this paper, we study the Krylov complexity in quantum field theory and make a connection with the holographic "Complexity equals Volume" conjecture. When Krylov basis matches with Fock basis, for several interesting settings, we observe…
In this work, we first examine the onset of thermodynamic chaos in Hayward AdS black holes with string fluids, emphasizing the effects of temporal and spatially periodic perturbations. We apply Melnikov's approach to examine the perturbed…
Considering the large-$q$ expansion of the Sachdev-Ye-Kitaev (SYK) model in the two-stage limit, we compute the Lanczos coefficients, Krylov complexity, and the higher Krylov cumulants in subleading order, along with the $t/q$ effects. The…
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…
In high-energy physics, confinement denotes the tendency of fundamental particles to remain bound together, preventing their observation as free, isolated entities. Interestingly, analogous confinement behavior emerges in certain condensed…
We analyze the amplitudes of one highly excited string (HES) state with two or three tachyons in open bosonic string theory. We argue that these processes are chaotic by showing that the spacing ratios of successive peaks in the angular…