Related papers: Lanczos-Pascal approach to correlation functions i…
We study many-body chaos in a (2+1)D relativistic scalar field theory at high temperatures in the classical statistical approximation, which captures the quantum critical regime and the thermal phase transition from an ordered to a…
We investigate three different methods for systematically approximating the diffusion coefficient of a deterministic random walk on the line which contains dynamical correlations that change irregularly under parameter variation. Capturing…
For appropriately chosen weights, temporal averages in chaotic systems can be approximated as a weighted sum of averages over reference states, such as unstable periodic orbits. Under strict assumptions, such as completeness of the orbit…
This tutorial article introduces the physics of quantum information scrambling in quantum many-body systems. The goals are to understand how to precisely quantify the spreading of quantum information and how causality emerges in complex…
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…
The out-of-time-ordered correlation (OTOC) function is an important new probe in quantum field theory which is treated as a significant measure of random quantum correlations. In this paper, with the slogan "Cosmology meets Condensed Matter…
We give elementary and explicit sufficient conditions (in particular, a functional correlation bound) for deterministic homogenisation (convergence to a stochastic differential equation) for discrete-time fast-slow systems of the form \[…
The apparent randomness of chaotic eigenstates in interacting quantum systems hides subtle correlations dynamically imposed by their finite energy per particle. These correlations are revealed when Berrys approach for chaotic eigenfunctions…
In a quantum many-body system, autocorrelation functions can determine linear responses nearby equilibrium and quantum dynamics far from equilibrium. In this letter, we bring out the connection between the operator complexity and the…
Performance of quantum process estimation is naturally limited to fundamental, random, and systematic imperfections in preparations and measurements. These imperfections may lead to considerable errors in the process reconstruction due to…
Self-consistent N-body simulations are efficient tools to study galactic dynamics. However, using them to study individual trajectories (or ensembles) in detail can be challenging. Such orbital studies are important to shed light on global…
We present a rigorous and efficient approach to the calculation of classical lattice-dynamical quantities from simulations that do not require an explicit solution of the time evolution. We focus on the temperature-dependent vibrational…
In this paper, we present a quasi-polynomial time classical algorithm that estimates the partition function of quantum many-body systems at temperatures above the thermal phase transition point. It is known that in the worst case, the same…
Out-of-time-ordered correlation functions (OTOC's) are presently being extensively debated as quantifiers of dynamical chaos in interacting quantum many-body systems. We argue that in quantum spin and fermionic systems, where all local…
Many-body densities and correlation functions are of paramount importance for understanding quantum many-body physics. Here, we present a method to compute them; our approach is general and based on the action of bosonic or fermionic…
We study correlations of observables in energy eigenstates of chaotic systems of a large size $N$. We show that the bipartite entanglement of two subsystems is quite strong, whereas macroscopic entanglement of the total system is absent. It…
We present and validate simple and efficient methods to estimate the chaoticity of orbits in low dimensional dynamical systems from computations of Lagrangian descriptors (LDs) on short time scales. Two quantities are proposed for…
We provide a protocol to measure out-of-time-order correlation functions. These correlation functions are of theoretical interest for diagnosing the scrambling of quantum information in black holes and strongly interacting quantum systems…
Diffusion is an ubiquitous phenomenon. It is a widespread belief that as long as the area under a current autocorrelation function converges in time, the corresponding spatiotemporal density dynamics should be diffusive. This may be viewed…
We show how to generalise the zero temperature Lanczos method for calculating dynamical correlation functions to finite temperatures. The key is the microcanonical ensemble, which allows us to replace the involved canonical ensemble with a…