Related papers: Chaos and Scrambling in Quantum Small Worlds
Many quantitative approaches to the dynamical scrambling of information in quantum systems involve the study of out-of-time-ordered correlators (OTOCs). In this paper, we introduce an algebraic OTOC ($\mathcal{A}$-OTOC) that allows us to…
In closed generic many-body systems, unitary evolution disperses local quantum information into highly non-local objects, resulting in thermalization. Such a process is called information scrambling, whose swiftness is quantified by the…
How are the spatial and temporal patterns of information scrambling in locally interacting quantum many-body systems imprinted on the eigenstates of the system's time-evolution operator? We address this question by identifying statistical…
Quantum measurement is a process that involves the interaction between a quantum system and a macroscopic measurement apparatus containing many degrees of freedom. The photodetector is such an apparatus with many electrons interacting with…
The emergence of random matrix spectral correlations in interacting quantum systems is a defining feature of quantum chaos. We study such correlations in terms of the spectral form factor and its moments in interacting chaotic few- and…
Quantum Heisenberg spin chains with random couplings and spin sizes are studied using a real-space renormalization group technique. These systems belong to a new universality class of disordered quantum spin systems realized in {\it e.g.}…
Quantum chaos is presented as a paradigm of information processing by dynamical systems at the bottom of the range of phase-space scales. Starting with a brief review of classical chaos as entropy flow from micro- to macro-scales, I argue…
The field of quantum chaos originated in the study of spectral statistics for interacting many-body systems, but this heritage was almost forgotten when single-particle systems moved into the focus. In recent years new interest emerged in…
A simple model of small world quantum networks, in which a central node plays essential role, is introduced for sharing entanglement over long distances. In view of the challenges in setting up advanced quantum labs which allows only few…
The study of information scrambling in many-body systems has sharpened our understanding of quantum chaos, complexity and gravity. Here, we extend the framework for exploring information scrambling to infinite dimensional continuous…
Quantum dynamics is of fundamental interest and has implications in quantum information processing. The four-point out-of-time-ordered correlator (OTOC) is traditionally used to quantify quantum information scrambling under many-body…
Mesoscopic devices, with system sizes in the range of several to several dozens wavelengths, represent paradigmatic model systems for the observation of quantum chaotic behaviour based on semiclassical concepts. Those electronic and…
The fine grained energy spectrum of quantum chaotic systems is widely believed to be described by random matrix statistics. A basic scale in such a system is the energy range over which this behavior persists. We define the corresponding…
While a wealth of results has been obtained for chaos in single-particle quantum systems, much less is known about chaos in quantum many-body systems. We contribute to recent efforts to make a semiclassical analysis of such systems…
Information scrambling, the process by which quantum information spreads and becomes effectively inaccessible, is central to modern quantum statistical physics and quantum chaos. These lecture notes provide an introduction to information…
In a fast scrambling many-body quantum system, information is spread and entanglement is built up on a timescale that grows logarithmically with the system size. This is of fundamental interest in understanding the dynamics of many-body…
Fast scramblers are dynamical quantum systems that produce many-body entanglement on a timescale that grows logarithmically with the system size $N$. We propose and investigate a family of deterministic, fast scrambling quantum circuits…
We propose a characterization of quantum many-body chaos: given a collection of simple operators, the set of all possible pair-correlations between these operators can be organized into a matrix with random-matrix-like spectrum. This…
We systematically investigate scrambling (or delocalizing) processes of quantum information encoded in quantum many-body systems by using numerical exact diagonalization. As a measure of scrambling, we adopt the tripartite mutual…
Experimental progresses in the miniaturisation of electronic devices have made routinely available in the laboratory small electronic systems, on the micron or sub-micron scale, which at low temperature are sufficiently well isolated from…