Related papers: Euclidean operator growth and quantum chaos
We study cutoff and lattice effects in the O(n) symmetric $\phi^4$ theory for a $d$-dimensional cubic geometry of size $L$ with periodic boundary conditions. In the large-N limit above $T_c$, we show that $\phi^4$ field theory at finite…
We establish pointwise estimates expressed in terms of a nonlinear potential of a generalized Wolff type for $A$-superharmonic functions with nonlinear operator $A:\Omega\times\mathbb{R}^n\to\mathbb{R}^n$ having measurable dependence on the…
It has been conjectured by Maldacena, Shenker, and Stanford [J. High Energy Phys.~08 (2016) 106] that the exponential growth rate of the out-of-time-ordered correlator (OTOC) $F(t)$ has a universal upper bound $2\pi k_B T/\hbar$. Here we…
We study the asymptotic shape of the occupied region for monotone deterministic dynamics in d-dimensional Euclidean space parametrized by a threshold theta, and a Borel set N with positive and finite Lebesgue measure. If A_n denotes the…
Krylov methods have reappeared recently, connecting physically sensible notions of complexity with quantum chaos and quantum gravity. In these developments, the Hamiltonian and the Liouvillian are tridiagonalized so that…
Predictability is ensured by causality while lost in chaos. To reconcile these two popular notions, we study chaos in geodesic motions in generic curved spacetimes with external potentials, where causality is controlled by a scalar…
We study expansive dynamical systems in the setting of distributive lattices and their automorphisms, the usual notion of expansiveness for a homeomorphism of a compact metric space being the particular case when the lattice is the topology…
Krylov subspace methods quantify operator growth in quantum many-body systems through Lanczos coefficients that encode how operators spread under time evolution. Although these diagnostics were originally motivated by questions of chaos and…
We study Krylov complexity in Lifshitz-type Dirac field theories with a generic dynamical critical exponent $z$. By computing the Lanczos coefficients for massless and massive cases, we analyze the growth and saturation behavior of Krylov…
A simple probe of chaos and operator growth in many-body quantum systems is the out of time ordered four point function. In a large class of local systems, the effects of chaos in this correlator build up exponentially fast inside the so…
We prove an abstract result giving a $\langle t \rangle^\varepsilon$ upper bound on the growth of the Sobolev norms of a time-dependent Schr\"odinger equation of the form ${i} \dot \psi = H_0 \psi + V (t)\psi$. Here $H_0$ is assumed to be…
We report on a result on quantum electrodynamics on a three dimensional Euclidean spacetime. The model is formulated on a toroidal lattice with unit volume and variable lattice spacing. The result is that the renormalized partition function…
Operator scrambling is a crucial ingredient of quantum chaos. Specifically, in the quantum chaotic system, a simple operator can become increasingly complicated under unitary time evolution. This can be diagnosed by various measures such as…
Everything you ever wanted to know about what has come to be known as ``chaotic mixing:'' This paper describes the evolution of localised ensembles of initial conditions in 2- and 3-D time-independent potentials which admit both regular and…
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…
The space of density matrices is embedded in a Euclidean space to deduce the dynamical equation satisfied by the state of an open quantum system. The Euclidean norm is used to obtain an explicit expression for the speed of the evolution of…
We consider infinite harmonic chain with completely deterministic dynamics. Initial data are assumed absolutely bounded. Nevertheless maximum of the variables can grow infinitely in time. We give conditions for this phenomenon. It coincides…
We explore the high-dimensional chaotic dynamics of the Lorenz-96 model by computing the variation of the fractal dimension with system parameters. The Lorenz-96 model is a continuous in time and discrete in space model first proposed by…
For many quantum systems of interest, the classical computational cost of simulating their time evolution scales exponentially in the system size. At the same time, quantum computers have been shown to allow for simulations of some of these…
We show that the known bound on the growth rate of the out-of-time-order four-point correlator in chaotic many-body quantum systems follows directly from the general structure of operator matrix elements in systems that obey the eigenstate…