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We propose a self-contained and accessible derivation of an exact formula for the $n$-point correlation functions of the signal measured when continuously observing a quantum system. The expression depends on the initial quantum state and…
A statistical physics model for the time evolutions of stock portfolios is proposed. In this model the time series of price changes are coded into the sequences of up and down spins. The Hamiltonian of the system is introduced and is…
Critical slowing down (CSD) is the phenomenon in which a system recovers more slowly from small perturbations. CSD, as evidenced by increasing signal variance and autocorrelation, has been observed in many dynamical systems approaching a…
The study of the low temperature phase of spin glass models by means of Monte Carlo simulations is a challenging task, because of the very slow dynamics and the severe finite size effects they show. By exploiting at the best the…
We propose to interpret machine learning functions as physical observables, opening up the possibility to apply "standard" statistical-mechanical methods to outputs from neural networks. This includes histogram reweighting and finite-size…
Ideal density-functional approximations (DFAs) should account for dynamic, static, and nondynamic correlation. While common DFAs struggle with the latter two, the Ziegler-Rauk-Baerends-Daul multiplet sum method (MSM) provides a pragmatic…
In many applications, the variables that characterize a stochastic system are measured along a second dimension, such as time. This results in multivariate functional data and the interest is in describing the statistical dependences among…
The development of quantum gas microscopy for two-dimensional optical lattices has provided an unparalleled tool to study the Fermi-Hubbard model (FHM) with ultracold atoms. Spin-resolved projective measurements, or snapshots, have played a…
The histogram reweighting technique, widely used to analyze Monte Carlo data, is shown to be applicable to dynamic properties obtained from Molecular Dynamics simulations. The theory presented here is based on the fact that the correlation…
Scanning tunneling microscopy (STM) has been a fundamental tool to characterize many-body effects in condensed matter systems, from extended solids to quantum dots. STM of molecules decoupled from the supporting conductive substrate has the…
In many complex molecular systems, the macroscopic ensemble's properties are controlled by microscopic dynamic events (or fluctuations) that are often difficult to detect via pattern-recognition approaches. Discovering the relationships…
We study various temporal correlation functions of a tagged particle in one-dimensional systems of interacting point particles evolving with Hamiltonian dynamics. Initial conditions of the particles are chosen from the canonical thermal…
We use a confocal microscope to examine the motion of individual particles in a dense colloidal suspension. Close to the glass transition, particle motion is strongly spatially correlated. The correlations decay exponentially with particle…
Quantum statistical correlations and momentum distributions are calculated for a spherically symmetric, three-dimensionally expanding finite fireballs, for non-relativistic expansions applying plane-wave approximation. The new concepts of…
We analyze the slow, glassy structural relaxation as measured through collective and tagged-particle density correlation functions obtained from Brownian dynamics simulations for a polydisperse system of quasi-hard spheres in the framework…
It is widely believed that the emergence of slow glassy dynamics is encoded in a material's microstructure. First-principles theory [mode-coupling theory (MCT)] is able to predict the dramatic slowdown of the dynamics from only static…
Non-Gaussian distributions in cosmology are commonly evaluated with Monte Carlo Markov-chain methods, as the Fisher-matrix formalism is restricted to the Gaussian case. The Metropolis-Hastings algorithm will provide samples from the…
We introduce the multivariate Log S-fBM model (mLog S-fBM), extending the univariate framework proposed by Wu \textit{et al.} to the multidimensional setting. We define the multidimensional Stationary fractional Brownian motion (mS-fBM),…
The crucial aspect of this demonstration is the discovery of renewal events, hidden in the computed dynamics of a multifractal metronome, which enables the replacement of the phenomenon of strong anticipation with a time delayed…
Symbolic dynamics has proven to be an invaluable tool in analyzing the mechanisms that lead to unpredictability and random behavior in nonlinear dynamical systems. Surprisingly, a discrete partition of continuous state space can produce a…