Related papers: Correlation dimension and phase space contraction …
Recovering properties of correlation functions is typically challenging. On one hand, experimentally, it requires measurements with a temporal resolution finer than the system's dynamics. On the other hand, analytical or numerical analysis…
Many natural and physical processes display long memory and extreme events. In these systems, the measured time series is invariably contaminated by noise. As the extreme events display large deviation from the mean behaviour, the noise…
We consider stochastic processes arising from dynamical systems by evaluating an observable function along the orbits of the system. The novelty is that we will consider observables achieving a global maximum value (possible infinite) at…
Correlations between electrons and the effective dimensionality are crucial factors that shape the properties of an interacting electron system. For example, the onsite Coulomb repulsion, U, may inhibit, or completely block the intersite…
We review the theory of entanglement measures, concentrating mostly on the finite dimensional two-party case. Topics covered include: single-copy and asymptotic entanglement manipulation; the entanglement of formation; the entanglement…
We present the complete phase diagram for one-dimensional binary mixtures of bosonic ultracold atomic gases in a harmonic trap. We obtain exact results with direct numerical diagonalization for small number of atoms, which permits us to…
Fractal dimensions are tools for probing the structure of quantum states and identifying whether they are localized or delocalized in a given basis. These quantities are commonly extracted through finite-size scaling, which limits the…
Models in which dark energy interacts with dark matter have been proposed in the literature to help explain why dark energy should only come to dominate in recent times. In this paper, we present a dynamical framework to calculate…
This paper develops a variational inference framework for control of infinite dimensional stochastic systems. We employ a measure theoretic approach which relies on the generalization of Girsanov's theorem, as well as the relation between…
Entanglement entropy appears as a central property of quantum systems in broad areas of physics. However, its precise value is often sensitive to unknown microphysics, rendering it incalculable. By considering parametric dependence on…
Lyapunov exponents describe the asymptotic behavior of the singular values of large products of random matrices. A direct computation of these exponents is however often infeasible. By establishing a link between Lyapunov exponents and an…
Coupled oscillators are prevalent throughout the physical world. Dynamical system formulations of weakly coupled oscillator systems have proven effective at capturing the properties of real-world systems. However, these formulations usually…
We develop and generalize the theory of extreme value for non-stationary stochastic processes, mostly by weakening the uniform mixing condition that was previously used in this setting. We apply our results to non-autonomous dynamical…
Phase transitions and critical phenomena are among the most intriguing phenomena in nature and their renormalization-group theory is one of the greatest achievements of theoretical physics. However, the predictions of the theory above an…
Complex systems are characterised by a tight, nontrivial interplay of their constituents, which gives rise to a multi-scale spectrum of emergent properties. In this scenario, it is practically and conceptually difficult to identify those…
The recent years have witnessed a growing interest for covariant Lyapunov vectors (CLVs) which span local intrinsic directions in the phase space of chaotic systems. Here we review the basic results of ergodic theory, with a specific…
Extreme values of real phenomena are events that occur with low frequency, but can have a large impact on real life. These are, in many practical problems, high-dimensional by nature (e.g. Tawn, 1990; Coles and Tawn, 1991). To study these…
To understand an emergent spacetime is to understand the emergence of locality. Entanglement entropy is a powerful diagnostic of locality, because locality leads to a large amount of short distance entanglement. Two dimensional string…
Extreme value theory for univariate and low-dimensional observations has been explored in considerable detail, but the field is still in an early stage regarding high-dimensional settings. This paper focuses on H\"usler-Reiss models, a…
We describe an algorithm for studying the entanglement entropy and spectrum of 2D systems, as a coupled array of $N$ one dimensional chains in their continuum limit. Using the algorithm to study the quantum Ising model in 2D, (both in its…