Related papers: Krylov Complexity in Quantum Field Theory
We study Krylov complexity in various models of quantum field theory: free massive bosons and fermions on flat space and on spheres, holographic models, and lattice models with the UV-cutoff. In certain cases we find asymptotic behavior of…
Krylov complexity, or K-complexity for short, has recently emerged as a new probe of chaos in quantum systems. It is a measure of operator growth in Krylov space, which conjecturally bounds the operator growth measured by the out of time…
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.…
We introduce and review a new complexity measure, called `Krylov complexity', which takes its origins in the field of quantum-chaotic dynamics, serving as a canonical measure of operator growth and spreading. Krylov complexity, underpinned…
One of the important open problems in quantum black hole physics is a dual interpretation of holographic complexity proposals. To date the only quantitative match is the equality between the Krylov spread complexity in triple-scaled SYK at…
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…
This paper establishes that Krylov complexity contains the entire information about the dynamics of a quantum operator, extending the list of equivalent quantities that can serve this purpose, such as the Lanczos coefficients, the return…
We examine the complexity of quasi-static chaotic open quantum systems. As a prototypical example, we analytically compute the Krylov complexity of a slowly leaking hard-sphere gas using Berry's conjecture. We then connect it to the…
Krylov complexity characterizes the operator growth in the quantum many-body systems or quantum field theories. The existing literatures have studied the Krylov complexity in the low temperature limit in the quantum field theories. In this…
We point out an interesting connection between the mathematical framework of the Krylov basis, which is used to quantify quantum complexity, and the entanglement entropy in high-energy QCD. In particular, we observe that the cascade…
We study holographic Krylov complexity in the Coulomb branch of ${\cal N}=4$ SYM. Adopting the proposal that the time derivative of the Krylov complexity is dual to the proper radial momentum of a massive particle, we investigate two probe…
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…
This paper investigates the notion of Krylov complexity, a measure of operator growth, within the framework of 1-matrix quantum mechanics (1-MQM). Krylov complexity quantifies how an operator evolves over time by expanding it in a series of…
Krylov complexity has emerged as an important tool in the description of quantum information and, in particular, quantum chaos. Here we formulate Krylov complexity $K(t)$ for quantum mechanical systems as a path integral, and argue that at…
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…
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…
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…
There are various definitions of the concept of complexity in Quantum Field Theory as well as for finite quantum systems. For several of them there are conjectured holographic bulk duals. In this work we establish an entry in the AdS/CFT…
We study holographic Krylov complexity in the Anabalon-Ross solitonic background, a top-down Type IIB solution describing a twisted-circle compactification of ${\cal N}=4$ SYM that flows to a confining, gapped three-dimensional theory.…
Within the framework of the "complexity equals action" and "complexity equals volume" conjectures, we study the properties of holographic complexity for rotating black holes. We focus on a class of odd-dimensional equal-spinning black holes…