Here we focus on a basic statistical measure of earthquake catalogs that has not been studied before, the asymmetry of interevent time series (e.g., reflecting the tendency to have more aftershocks than spontaneous earthquakes). We define the asymmetry metric as the ratio between the number of positive interevent time increments minus negative increments and the total (positive plus negative) number of increments. Such asymmetry commonly exists in time series data for nonlinear geophysical systems like river flow which decays slowly and increases rapidly. We find that earthquake interevent time series are significantly asymmetric, where the asymmetry function exhibits a significant crossover to weak asymmetry at large lag index. We suggest that the Omori law can be associated with the large asymmetry at short time intervals below the crossover whereas overlapping aftershock sequences and the spontaneous events can be associated with a fast decay of asymmetry above the crossover. We show that the asymmetry is better reproduced by a recently modified Epidemic-Type Aftershock Sequence (ETAS) model with two triggering processes in comparison to the standard ETAS model which only has one.

We present a detailed first-principles investigation of the response of a free-standing graphene sheet to an external perpendicular static electric field E. The charge density distribution in the vicinity of the graphene monolayer that is caused by E was determined using the pseudopotential density-functional theory approach. Different geometries were considered. The centroid of this extra density induced by an external electric field was determined as $z_{\mathrm{im}}$ = 1.048 Å at vanishing E, and its dependence on E has been obtained. The thus determined $z_{\mathrm{im}}$ was employed to construct the hybrid one-electron potential which generates a new set of energies for the image-potential states.

While Efimov physics in ultracold atoms is usually modeled with an isolated Feshbach resonance, many real world resonances appear in close vicinity to each other and are therefore overlapping. Here we derive a realistic model based on the mutual coupling of an open channel and two closed molecular channels while neglecting short-range physics as permitted by the narrow character of the considered resonances. The model is applied to three distinct scenarios with experimental relevance. We show that the effect of overlapping resonances is manifested most strikingly at a narrow resonance in whose vicinity there is a slightly narrower one. In this system the Efimov ground state extends not only over the scattering length zero crossing between the two resonances but also over the pole of the second resonance to finally meet the dissociation threshold below it. In the opposite scenario, when a narrow resonance is considered in the vicinity of a slightly broader one, we observe that the Efimov features are pushed to lower binding energies and smaller scattering lengths by a significant factor facilitating their experimental investigation. Both scenarios are compared with the case of two narrow resonances which are far enough away from each other to be effectively decoupled. In this case the two-channel model results are recovered. Finally, we analyze the rich excitation spectrum of the system and construct and explain its nodal pattern.

The interplay of interactions and disorder in low-dimensional superconductors supports the formation of multiple quantum phases as possible instabilities of the superconductor-insulator transition (SIT) at a singular quantum critical point. We explore a one-dimensional model which exhibits such a variety of phases in the strongly quantum fluctuations regime. Specifically, we study the effect of weak disorder on a two-leg Josephson ladder with comparable Josephson and charging energies $(E_J\sim E_C)$. An additional key feature of our model is the requirement of perfect $Z_2$ symmetry, respected by all parameters including the disorder. Using a perturbative renormalization-group (RG) analysis, we derive the phase diagram and identify at least one intermediate phase between a full-fledged superconductor and a disorder-dominated insulator. Most prominently, for repulsive interactions on the rungs we identify two distinct mixed phases: In both of them the longitudinal charge mode is a gapless superconductor, however one phase exhibits a dipolar charge density order on the rungs, while the other is disordered. This latter phase is characterized by coexisting superconducting (phase-locked) and charge-ordered rungs, and encompasses the potential of evolving into a Griffith's phase characteristic of the random-field Ising model in the strong disorder limit.

The Raychaudhuri equation is derived by assuming geometric flow in space–time M of $n+1$ dimensions. The equation turns into a harmonic oscillator form under suitable transformations. Thereby, a relation between geometrical entropy and mean geodesic deviation is established. This has a connection to chaos theory where the trajectories diverge exponentially. We discuss its application to cosmology and black holes. Thus, we establish a connection between chaos theory and general relativity.

A classical random walker starting on a node of a finite graph will always reach any other node since the search is ergodic, namely it fully explores space, hence the arrival probability is unity. For quantum walks, destructive interference may induce effectively non-ergodic features in such search processes. Under repeated projective local measurements, made on a target state, the final detection of the system is not guaranteed since the Hilbert space is split into a bright subspace and an orthogonal dark one. Using this we find an uncertainty relation for the deviations of the detection probability from its classical counterpart, in terms of the energy fluctuations.

We study large networks of parametric oscillators as heuristic solvers of random Ising models. In these networks, known as coherent Ising machines, the model to be solved is encoded in the coupling between the oscillators, and a solution is offered by the steady state of the network. This approach relies on the assumption that mode competition steers the network to the ground-state solution of the Ising model. By considering a broad family of frustrated Ising models, we show that the most efficient mode does not correspond generically to the ground state of the Ising model. We infer that networks of parametric oscillators close to threshold are intrinsically not Ising solvers. Nevertheless, the network can find the correct solution if the oscillators are driven sufficiently above threshold, in a regime where nonlinearities play a predominant role. We find that for all probed instances of the model, the network converges to the ground state of the Ising model with a finite probability.

Global warming, extreme climate events, earthquakes and their accompanying socioeconomic disasters pose significant risks to humanity. Yet due to the nonlinear feedbacks, multiple interactions and complex structures of the Earth system, the understanding and, in particular, the prediction of such disruptive events represent formidable challenges to both scientific and policy communities. During the past years, the emergence and evolution of Earth system science has attracted much attention and produced new concepts and frameworks. Especially, novel statistical physics and complex networks-based techniques have been developed and implemented to substantially advance our knowledge of the Earth system, including climate extreme events, earthquakes and geological relief features, leading to substantially improved predictive performances. We present here a comprehensive review on the recent scientific progress in the development and application of how combined statistical physics and complex systems science approaches such as critical phenomena, network theory, percolation, tipping points analysis, and entropy can be applied to complex Earth systems. Notably, these integrating tools and approaches provide new insights and perspectives for understanding the dynamics of the Earth systems. The overall aim of this review is to offer readers the knowledge on how statistical physics concepts and theories can be useful in the field of Earth system science.

We study a two state “jumping diffusivity” model for a Brownian process alternating between two different diffusion constants, $D_{+}>D_{-}$ , with random waiting times in both states whose distribution is rather general. In the limit of long measurement times, Gaussian behavior with an effective diffusion coefficient is recovered. We show that, for equilibrium initial conditions and when the limit of the diffusion coefficient $D_{-}⟶0$ is taken, the short time behavior leads to a cusp, namely a non-analytical behavior, in the distribution of the displacements $P(x,t)$ for $x⟶0$ . Visually this cusp, or tent-like shape, resembles similar behavior found in many experiments of diffusing particles in disordered environments, such as glassy systems and intracellular media. This general result depends only on the existence of finite mean values of the waiting times at the different states of the model. Gaussian statistics in the long time limit is achieved due to ergodicity and convergence of the distribution of the temporal occupation fraction in state $D_{+}$ to a $\delta$ -function. The short time behavior of the same quantity converges to a uniform distribution, which leads to the non-analyticity in $P(x,t)$ . We demonstrate how super-statistical framework is a zeroth order short time expansion of $P(x,t)$ , in the number of transitions, that does not yield the cusp like shape. The latter, considered as the key feature of experiments in the field, is found with the first correction in perturbation theory.

Although the sizes of business firms have been a subject of intensive research, the definition of a “size” of a firm remains unclear. In this study, we empirically characterize in detail the scaling relations between size measures of business firms, analyzing them based on allometric scaling. Using a large dataset of Japanese firms that tracked approximately one million firms annually for two decades (1994–2015), we examined up to the trivariate relations between corporate size measures: annual sales, capital stock, total assets, and numbers of employees and trading partners. The data were examined using a multivariate generalization of a previously proposed method for analyzing bivariate scalings. We found that relations between measures other than the capital stock are marked by allometric scaling relations. Power–law exponents for scalings and distributions of multiple firm size measures were mostly robust throughout the years but had fluctuations that appeared to correlate with national economic conditions. We established theoretical relations between the exponents. We expect these results to allow direct estimation of the effects of using alternative size measures of business firms in regression analyses, to facilitate the modeling of firms, and to enhance the current theoretical understanding of complex systems.

Networks are finite metric spaces, with distances defined by the shortest paths between nodes. However, this is not the only form of network geometry: two others are the geometry of latent spaces underlying many networks and the effective geometry induced by dynamical processes in networks. These three approaches to network geometry are intimately related, and all three of them have been found to be exceptionally efficient in discovering fractality, scale invariance, self-similarity and other forms of fundamental symmetries in networks. Network geometry is also of great use in a variety of practical applications, from understanding how the brain works to routing in the Internet. We review the most important theoretical and practical developments dealing with these approaches to network geometry and offer perspectives on future research directions and challenges in this frontier in the study of complexity.

We investigate the overdamped Langevin motion for particles in a potential well that is asymptotically flat. When the potential well is deep as compared to the temperature, physical observables, like the mean square displacement, are essentially time-independent over a long time interval, the stagnation epoch. However, the standard Boltzmann–Gibbs (BG) distribution is non-normalizable, given that the usual partition function is divergent. For this regime, we have previously shown that a regularization of BG statistics allows for the prediction of the values of dynamical and thermodynamical observables in the non-normalizable quasi-equilibrium state. In this work, based on the eigenfunction expansion of the time-dependent solution of the associated Fokker–Planck equation with free boundary conditions, we obtain an approximate time-independent solution of the BG form, being valid for times that are long, but still short as compared to the exponentially large escape time. The escaped particles follow a general free-particle statistics, where the solution is an error function, which is shifted due to the initial struggle to overcome the potential well. With the eigenfunction solution of the Fokker–Planck equation in hand, we show the validity of the regularized BG statistics and how it perfectly describes the time-independent regime though the quasi-stationary state is non-normalizable.

In a previous paper, we have shown how the classical and quantum relativistic dynamics of the Stueckelberg–Horwitz–Piron [SHP] theory can be embedded in general relativity (GR). We briefly review the SHP theory here and, in particular, the formulation of the theory of spin in the framework of relativistic quantum theory. We show here how the quantum theory of relativistic spin can be embedded, using a theorem of Abraham, Marsden and Ratiu and also explicit derivation, into the framework of GR by constructing a local induced representation. The relation to the work of Fock and Ivanenko is also discussed. We show that in a gravitational field there is a highly complex structure for the spin distribution in the support of the wave function. We then discuss entanglement for the spins in a two body system.

Single crystal diamond (<5 ppm nitrogen) containing native NV centers with coherence time of 150 μs was irradiated with 2 MeV alpha particles, with doses ranging from 10¹² ion/cm² to 10¹⁵ ion/cm². The effect of ion damage on the coherence time of NV centers was studied using optically detected magnetic resonance and supplemented by fluorescence and Raman microscopy. A cross-sectional geometry was employed so that the NV coherence time could be measured as a function of increasing defect concentration along the ion track. Surprisingly, although the ODMR contrast was found to decrease with increasing ion induced vacancy concentration, the measured decoherence time remained undiminished at 150us despite the estimated vacancy concentration reaching a value of 40 ppm at the end of range. These results suggest that ion induced damage in the form of an increase in vacancy concentration does not necessarily result in a significant increase in the density of the background spin bath.