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We introduce a comprehensive analytical benchmark, relying on Fokker-Planck formalism, to study microbial dynamics in presence of both biotic and abiotic forces. In equilibrium, we observe a balance between the two kinds of forces, leading to no correlations between species abundances. This implies that real microbiomes, where correlations have been observed, operate out of equilibrium. Therefore, we analyze non-equilibrium dynamics, presenting an ansatz for an approximate solution that embodies the complex interplay of forces in the system. This solution is consistent with Taylor's law as a coarse-grained approximation of the relation between species abundance and variance, but implies subtler effects, predicting unobserved structure beyond Taylor's law. Motivated by this theoretical prediction, we refine the analysis of existing metagenomic data, unveiling a novel universal macroecological pattern. Finally, we speculate on the physical origin of Taylor's law: building upon an analogy with Brownian motion theory, we propose that Taylor's law emerges as a Fluctuation-Growth relation resulting from equipartition of environmental resources among microbial species., Comment: 14 pages, 6 figures, uses RevTeX 4.2

During the last decades macroecology has identified broad-scale patterns of abundances and diversity of microbial communities and put forward some potential explanations for them. However, these advances are not paralleled by a full understanding of the dynamical processes behind them. In particular, abundance fluctuations of different species are found to be correlated, both across time and across communities in metagenomic samples. Reproducing such correlations through appropriate population models remains an open challenge. The present paper tackles this problem and points to sparse species interactions as a necessary mechanism to account for them. Specifically, we discuss several possibilities to include interactions in population models and recognize Lotka-Volterra constants as a successful ansatz. For this, we design a Bayesian inference algorithm to extract sets of interaction constants able to reproduce empirical probability distributions of pairwise correlations for diverse biomes. Importantly, the inferred models still reproduce well-known single-species macroecological patterns concerning abundance fluctuations across both species and communities. Endorsed by the agreement with the empirically observed phenomenology, our analyses provide insights on the properties of the networks of microbial interactions, revealing that sparsity is a crucial feature.

The discourse surrounding the structural organization of mutualistic interactions mostly revolves around modularity and nestedness. The former is known to enhance the stability of communities, while the latter is related to their feasibility, albeit compromising the stability. However, it has recently been shown that the joint emergence of these structures poses challenges that can eventually lead to limitations in the dynamic properties of mutualistic communities. We hypothesize that considering compound arrangements -- modules with internal nested organization -- can offer valuable insights in this debate. We analyze the temporal structural dynamics of 20 plant-pollinator interaction networks and observe large structural variability throughout the year. Compound structures are particularly prevalent during the peak of the pollination season, often coexisting with nested and modular arrangements in varying degrees. Motivated by these empirical findings, we synthetically investigate the dynamics of the structural patterns across two control parameters -- community size and connectance levels -- mimicking the progression of the pollination season. Our analysis reveals contrasting impacts on the stability and feasibility of these mutualistic communities. We characterize the consistent relationship between network structure and stability, which follows a monotonic pattern. But, in terms of feasibility, we observe non-linear relationships. Compound structures exhibit a favorable balance between stability and feasibility, particularly in mid-sized ecological communities, suggesting they may effectively navigate the simultaneous requirements of stability and feasibility. These findings may indicate that the assembly process of mutualistic communities is driven by a delicate balance among multiple properties, rather than the dominance of a single one.

The quantitative study of traffic dynamics is crucial to ensure the efficiency of urban transportation networks. The current work investigates the spatial properties of congestion, that is, we aim to characterize the city areas where traffic bottlenecks occur. The analysis of a large amount of real road networks in previous works showed that congestion points experience spatial abrupt transitions, namely they shift away from the city center as larger urban areas are incorporated. The fundamental ingredient behind this effect is the entanglement of central and arterial roads, embedded in separated geographical regions. In this paper we extend the analysis of the conditions yielding abrupt transitions of congestion location. First, we look into the more realistic situation in which arterial and central roads, rather than lying on sharply separated regions, present spatial overlap. It results that this affects the position of bottlenecks and introduces new possible congestion areas. Secondly, we pay particular attention to the role played by the edge distribution, proving that it allows to smooth the transitions profile, and so to control the congestion displacement. Finally, we show that the aforementioned phenomenology may be recovered also as a consequence of a discontinuity in the nodes density, in a domain with uniform connectivity. Our results provide useful insights for the design and optimization of urban road networks, and the management of the daily traffic.

The impact of Machine Learning (ML) algorithms in the age of big data and platform capitalism has not spared scientific research in academia. In this work, we will analyse the use of ML in fundamental physics and its relationship to other cases that directly affect society. We will deal with different aspects of the issue, from a bibliometric analysis of the publications, to a detailed discussion of the literature, to an overview on the productive and working context inside and outside academia. The analysis will be conducted on the basis of three key elements: the non-neutrality of science, understood as its intrinsic relationship with history and society; the non-neutrality of the algorithms, in the sense of the presence of elements that depend on the choices of the programmer, which cannot be eliminated whatever the technological progress is; the problematic nature of a paradigm shift in favour of a data-driven science (and society). The deconstruction of the presumed universality of scientific thought from the inside becomes in this perspective a necessary first step also for any social and political discussion. This is the subject of this work in the case study of ML., Comment: Originally published in Italian on the journal The Lab's Quarterly

During the last decades, the study of cities has been transformed by new approaches combining engineering and complexity sciences. Network theory is playing a central role, facilitating the quantitative analysis of crucial urban dynamics, such as mobility, city growth or urban planning. In this work, we focus on the spatial aspects of congestion. Analyzing a large amount of real city networks, we show that the location of the onset of congestion changes according to the considered urban area, defining, in turn, a set of congestion regimes separated by abrupt transitions. To help unveiling these spatial dependencies of congestion (in terms of network betweenness analysis), we introduce a family of planar road network models composed of a dense urban center connected to an arboreal periphery. These models, coined as GT and DT-MST models, allow us to analytically, numerically and experimentally describe how and why congestion emerges in particular geographical areas of monocentric cities and, subsequently, to describe the congestion regimes and the factors that promote the appearance of their abrupt transitions. We show that the fundamental ingredient behind the observed abrupt transitions is the spatial separation between the urban center and the periphery, and the number of separate areas that form the periphery. Elaborating on the implications of our results, we show that they may have an influence on the design and optimization of road networks regarding urban growth and the management of daily traffic dynamics., Comment: 32 pages, 25 figures

We revisit decoherence process of a qubit register interacting with a thermal bosonic bath. We generalize the previous studies by considering not only the register's behavior but also of a part of its environment. In particular, we are interested in information flow from the register to the environment, which we describe using recently introduced multipartite quantum state structures called Spectrum Broadcast Structures. Working in two specific cases of: i) two-qubit register and ii) collective decoherence, we identify the regimes where the environment acquires almost complete information about the register state. We also study in more detail the interesting causal aspects, related to the finite propagation time of the field disturbances between the qubits. Finally, we describe quantum state structures which appear due to the presence of protected spaces., Comment: 10 pages, v2: references added

We introduce a novel minimally-disturbing method for sub-nK thermometry in a Bose-Einstein condensate (BEC). Our technique is based on the Bose-polaron model; namely, an impurity embedded in the BEC acts as the thermometer. We propose to detect temperature fluctuations from measurements of the position and momentum of the impurity. Crucially, these cause minimal back-action on the BEC and hence, realize a non-demolition temperature measurement. Following the paradigm of the emerging field of \textit{quantum thermometry}, we combine tools from quantum parameter estimation and the theory of open quantum systems to solve the problem in full generality. We thus avoid \textit{any} simplification, such as demanding thermalization of the impurity atoms, or imposing weak dissipative interactions with the BEC. Our method is illustrated with realistic experimental parameters common in many labs, thus showing that it can compete with state-of-the-art \textit{destructive} techniques, even when the estimates are built from the outcomes of accessible (sub-optimal) quadrature measurements., Comment: New references added

We study entanglement and squeezing of two uncoupled impurities immersed in a Bose-Einstein condensate. We treat them as two quantum Brownian particles interacting with a bath composed of the Bogoliubov modes of the condensate. The Langevin-like quantum stochastic equations derived exhibit memory effects. We study two scenarios: (i) In the absence of an external potential, we observe sudden death of entanglement; (ii) In the presence of an external harmonic potential, entanglement survives even at the asymptotic time limit. Our study considers experimentally tunable parameters., Comment: 38 pages, 7 figures

We study the dynamics of an impurity embedded in a trapped Bose-Einstein condensate (Bose polaron), by recalling the quantum Brownian motion model. It is crucial that the model considers a parabolic trapping potential to resemble the experimental conditions. Thus, we detail here how the formal derivation changes due to the gas trap, in comparison to the homogeneous gas. We first find that the presence of a gas trap leads to a new form of the bath-impurity coupling constant and a larger degree in the super-ohmicity of the spectral density. This is manifested as a different dependence of the system dynamics on the past history. To quantify this, we introduce several techniques to compare the different amount of memory effects arising in the homogeneous and inhomogeneous gas. We find that it is higher in the second case. Moreover, we calculate the position variance of the impurity, represenitng a measurable quantity. We show that the impurity experiences super-diffusion and genuine position squeezing. Wdetail how both effects can be enhanced or inhibited by tuning the Bose-Einstein condensate trap frequency.

We study the small mass limit (or: the Smoluchowski-Kramers limit) of a class of quantum Brownian motions with inhomogeneous damping and diffusion. For Ohmic bath spectral density with a Lorentz-Drude cutoff, we derive the Heisenberg-Langevin equations for the particle's observables using a quantum stochastic calculus approach. We set the mass of the particle to equal $m = m_{0} \epsilon$, the reduced Planck constant to equal $\hbar = \epsilon$ and the cutoff frequency to equal $\Lambda = E_{\Lambda}/\epsilon$, where $m_0$ and $E_{\Lambda}$ are positive constants, so that the particle's de Broglie wavelength and the largest energy scale of the bath are fixed as $\epsilon \to 0$. We study the limit as $\epsilon \to 0$ of the rescaled model and derive a limiting equation for the (slow) particle's position variable. We find that the limiting equation contains several drift correction terms, the quantum noise-induced drifts, including terms of purely quantum nature, with no classical counterparts., Comment: 29 pages

We study the dynamics of a quantum impurity immersed in a Bose-Einstein condensate as an open quantum system in the framework of the quantum Brownian motion model. We derive a generalized Langevin equation for the position of the impurity. The Langevin equation is an integrodifferential equation that contains a memory kernel and is driven by a colored noise. These result from considering the environment as given by the degrees of freedom of the quantum gas, and thus depend on its parameters, e.g. interaction strength between the bosons, temperature, etc. We study the role of the memory on the dynamics of the impurity. When the impurity is untrapped, we find that it exhibits a super-diffusive behavior at long times. We find that back-flow in energy between the environment and the impurity occurs during evolution. When the particle is trapped, we calculate the variance of the position and momentum to determine how they compare with the Heisenberg limit. One important result of this paper is that we find position squeezing for the trapped impurity at long times. We determine the regime of validity of our model and the parameters in which these effects can be observed in realistic experiments., Comment: 16 pages, 9 figures

Objectivity constitutes one of the main features of the macroscopic classical world. An important aspect of the quantum-to-classical transition issue is to explain how such a property arises from the microscopic quantum world. Recently, within the framework of open quantum systems, there has been proposed such a mechanism in terms of the, so-called, Spectrum Broadcast Structures. These are multipartite quantum states of the system of interest and a part of its environment, assumed to be under an observation. This approach requires a departure from the standard open quantum systems methods, as the environment cannot be completely neglected. In the present work we study the emergence of such a state-structures in one of the canonical models of the condensed matter theory: Spin-boson model, describing the dynamics of a two-level system coupled to an environment made up by a large number of harmonic oscillators. We pay much attention to the behavior of the model in the non-Markovian regime, in order to provide a testbed to analyze how the non-Markovian nature of the evolution affects the surfacing of a spectrum broadcast structure., Comment: 11 pages, 13 figures

The theory of quantum Brownian motion describes the properties of a large class of open quantum systems. Nonetheless, its description in terms of a Born-Markov master equation, widely used in the literature, is known to violate the positivity of the density operator at very low temperatures. We study an extension of existing models, leading to an equation in the Lindblad form, which is free of this problem. We study the dynamics of the model, including the detailed properties of its stationary solution, for both constant and position-dependent coupling of the Brownian particle to the bath, focusing in particular on the correlations and the squeezing of the probability distribution induced by the environment, Comment: 15 pages, 10 figures