arXiv subjects

Francesco Caravelli

Publications and source records attributed to Francesco Caravelli.

At least 55 records · Page 3Linked to original sources

arXiv2023

On the combinatorics of Lotka-Volterra equations

We study an approach to obtaining the exact formal solution of the 2-species Lotka-Volterra equation based on combinatorics and generating functions. By employing a combination of Carleman linearization and Mori-Zwanzig reduction techniques, we transform the nonlinear equations into a linear system, allowing for the derivation of a formal solution. The Mori-Zwanzig reduction reduces to an expansion which we show can be interpreted as a directed and weighted lattice path walk, which we use to obtain a representation of the system dynamics as walks of fixed length. The exact solution is then shown to be dependent on the generator of weighted walks. We show that the generator can be obtained by the solution of PDE which in turn is equivalent to a particular Koopman evolution of nonlinear observables.

cond-mat.stat-mech↗

arXiv2023

Cycle equivalence classes, orthogonal Weingarten calculus, and the mean field theory of memristive systems

It has been recently noted that for a class of dynamical systems with explicit conservation laws represented via projector operators the dynamics can be understood in terms of lower dimensional equations This is the case for instance of memristive circuits Memristive systems are important classes of devices with wide ranging applications in electronic circuits artificial neural networks and memory storage We show that such mean field theories can emerge from averages over the group of orthogonal matrices interpreted as cycle preserving transformations applied to the projector operator describing Kirchhoffs laws Our results provide insights into the fundamental principles underlying the behavior of resistive and memristive circuits and highlight the importance of conservation laws for their meanf ield theories In addition we argue that our results shed light on the nature of the critical avalanches observed in quasi-two dimensional nanowires as boundary phenomena

cond-mat.stat-mech↗

arXiv2023

Complex field reversal dynamics in nanomagnetic systems

Nanomagnetic materials, built from thin, patterned films of ferromagnetic materials, began as analogues to frustrated magnetism. Their low energy of operation and emergent properties make them strong candidates for physics based devices. A recent model of how nanomagnetic domains flip, the Glauber mean-field model, is used here to understand how systems of nanomagnets evolve when opposed by external field. This reversal can be expressed in an analytical form in the case of one-dimensional chains and trees at zero temperature, where the cascade of spin flips gives rise to harmonic power spectra. The same cascades in two and three dimensions form fractal field reversal clusters whose shape depends on the strength of the field and the tuning of interactions between nanomagnets.

cond-mat.stat-mech↗

arXiv2023

Mean field theory of self-organizing memristive connectomes

Biological neuronal networks are characterized by nonlinear interactions and complex connectivity. Given the growing impetus to build neuromorphic computers, understanding physical devices that exhibit structures and functionalities similar to biological neural networks is an important step toward this goal. Self-organizing circuits of nanodevices are at the forefront of the research in neuromorphic computing, as their behavior mimics synaptic plasticity features of biological neuronal circuits. However, an effective theory to describe their behavior is lacking. This study provides for the first time an effective mean field theory for the emergent voltage-induced polymorphism of \textit{circuits} of a nanowire connectome, showing that the behavior of these circuits can be explained by a low-dimensional dynamical equation. The equation can be derived from the microscopic dynamics of a single memristive junction in analytical form. We test our effective model on experiments of nanowire networks and show that it fits both the potentiation and depression of these synapse-mimicking circuits. We show that our theory applies beyond the case of nanowire networks by formulating a general mean-field theory of conductance transitions in self-organizing memristive connectomes.

cond-mat.soft↗

arXiv2022

Ranking influential nodes in networks from partial information

Many complex systems exhibit a natural hierarchy in which elements can be ranked according to a notion of "influence". While the complete and accurate knowledge of the interactions between constituents is ordinarily required for the computation of nodes' influence, using a low-rank approximation we show that in a variety of contexts local information about the neighborhoods of nodes is enough to reliably estimate how influential they are, without the need to infer or reconstruct the whole map of interactions. Our framework is successful in approximating with high accuracy different incarnations of influence in systems as diverse as the WWW PageRank, trophic levels of ecosystems, upstreamness of industrial sectors in complex economies, and centrality measures of social networks, as long as the underlying network is not exceedingly sparse. We also discuss the implications of this "emerging locality" on the approximate calculation of non-linear network observables.

physics.soc-ph↗

arXiv2022

The Computational Capacity of LRC, Memristive and Hybrid Reservoirs

Reservoir computing is a machine learning paradigm that uses a high-dimensional dynamical system, or \emph{reservoir}, to approximate and predict time series data. The scale, speed and power usage of reservoir computers could be enhanced by constructing reservoirs out of electronic circuits, and several experimental studies have demonstrated promise in this direction. However, designing quality reservoirs requires a precise understanding of how such circuits process and store information. We analyze the feasibility and optimal design of electronic reservoirs that include both linear elements (resistors, inductors, and capacitors) and nonlinear memory elements called memristors. We provide analytic results regarding the feasibility of these reservoirs, and give a systematic characterization of their computational properties by examining the types of input-output relationships that they can approximate. This allows us to design reservoirs with optimal properties. By introducing measures of the total linear and nonlinear computational capacities of the reservoir, we are able to design electronic circuits whose total computational capacity scales extensively with the system size. Our electronic reservoirs can match or exceed the performance of conventional "echo state network" reservoirs in a form that may be directly implemented in hardware.

cs.NE↗

arXiv2022

From Vertices to Vortices in magnetic nanoislands

Recent studies in magnetic nanolithography show that a variety of complex magnetic states emerge as a function of a single magnetic island's aspect ratio. We propose a model which, in addition to fitting experiments, predicts magnetic states with continuous symmetry at particular aspect ratios and reveals a duality between vortex and vertex states. Our model then opens new means of engineering novel types of artificial spin systems, and their application to complex magnetic textures in devices and computing.

cond-mat.mes-hall↗

arXiv2022

Anisotropic MagnetoMemristance

In the last decade, nanoscale resistive devices with memory have been the subject of intense study because of their possible use in brain-inspired computing. However, operational endurance is one of the limiting factors in the adoption of such technology. For this reason, we discuss the emergence of current-induced memristance in magnetic materials, known for their durability. We show analytically and numerically that a single ferromagnetic layer can possess GHz memristance, due to a combination of two factors: a current-induced transfer of angular momentum (Zhang-Li torque) and the anisotropic magnetoresistance (AMR). We term the resulting effect the anisotropic magneto-memristance (AMM). We connect the AMM to the topology of the magnetization state, within a simple model of a 1-dimensional annulus-shaped magnetic layer, confirming the analytical results with micromagnetic simulations for permalloy. Our results open a new path towards the realization of single-layer magnetic memristive devices operating at GHz frequencies.

cond-mat.mes-hall↗

arXiv2022

The Bellman equation and optimal local flipping strategies for kinetic Ising models

There is a deep connection between thermodynamics, information and work extraction. Ever since the birth of thermodynamics, various types of Maxwell demons have been introduced in order to deepen our understanding of the second law. Thanks to them it has been shown that there is a deep connection between thermodynamics and information, and between information and work in a thermal system. In this paper, we study the problem of energy extraction from a thermodynamic system satisfying detailed balance, from an agent with perfect information, e.g. that has an optimal strategy, given by the solution of the Bellman equation, in the context of Ising models. We call these agents kobolds, in contrast to Maxwell's demons which do not necessarily need to satisfy detailed balance. This is in stark contrast with typical Monte Carlo algorithms, which choose an action at random at each time step. It is thus natural to compare the behavior of these kobolds to a Metropolis algorithm. For various Ising models, we study numerically and analytically the properties of the optimal strategies, showing that there is a transition in the behavior of the kobold as a function of the parameter characterizing its strategy.

cond-mat.stat-mech↗

arXiv2022

Random Quantum Batteries

Quantum nano-devices are fundamental systems in quantum thermodynamics that have been the subject of profound interest in recent years. Among these, quantum batteries play a very important role. In this paper we lay down a theory of random quantum batteries and provide a systematic way of computing the average work and work fluctuations in such devices by investigating their typical behavior. We show that the performance of random quantum batteries exhibits typicality and depends only on the spectral properties of the time evolving operator, the initial state and the measuring Hamiltonian. At given revival times a random quantum battery features a quantum advantage over classical random batteries. Our method is particularly apt to be used both for exactly solvable models like the Jaynes-Cummings model or in perturbation theory, e.g., systems subject to harmonic perturbations. We also study the setting of quantum adiabatic random batteries.

quant-ph↗

arXiv2022

Direct observation of a dynamical glass transition in a nanomagnetic artificial Hopfield network

Spin glasses, generally defined as disordered systems with randomized competing interactions, are a widely investigated complex system. Theoretical models describing spin glasses are broadly used in other complex systems, such as those describing brain function, error-correcting codes, or stock-market dynamics. This wide interest in spin glasses provides strong motivation to generate an artificial spin glass within the framework of artificial spin ice systems. Here, we present the experimental realization of an artificial spin glass consisting of dipolar coupled single-domain Ising-type nanomagnets arranged onto an interaction network that replicates the aspects of a Hopfield neural network. Using cryogenic x-ray photoemission electron microscopy (XPEEM), we performed temperature-dependent imaging of thermally driven moment fluctuations within these networks and observed characteristic features of a two-dimensional Ising spin glass. Specifically, the temperature dependence of the spin glass correlation function follows a power law trend predicted from theoretical models on two-dimensional spin glasses. Furthermore, we observe clear signatures of the hard to observe rugged spin glass free energy in the form of sub-aging, out of equilibrium autocorrelations and a transition from stable to unstable dynamics.

cond-mat.dis-nn↗

arXiv2022

Reconfigurable Training and Reservoir Computing in an Artificial Spin-Vortex Ice via Spin-Wave Fingerprinting

Strongly-interacting artificial spin systems are moving beyond mimicking naturally-occurring materials to emerge as versatile functional platforms, from reconfigurable magnonics to neuromorphic computing. Typically artificial spin systems comprise nanomagnets with a single magnetisation texture: collinear macrospins or chiral vortices. By tuning nanoarray dimensions we achieve macrospin/vortex bistability and demonstrate a four-state metamaterial spin-system 'Artificial Spin-Vortex Ice' (ASVI). ASVI can host Ising-like macrospins with strong ice-like vertex interactions, and weakly-coupled vortices with low stray dipolar-field. Vortices and macrospins exhibit starkly-differing spin-wave spectra with analogue-style mode-amplitude control and mode-frequency shifts of df = 3.8 GHz. The enhanced bi-textural microstate space gives rise to emergent physical memory phenomena, with ratchet-like vortex training and history-dependent nonlinear fading memory when driven through global field cycles. We employ spin-wave microstate fingerprinting for rapid, scaleable readout of vortex and macrospin populations and leverage this for spin-wave reservoir computation. ASVI performs linear and non-linear mapping transformations of diverse input signals as well as chaotic time-series forecasting. Energy costs of machine learning are spiralling unsustainably, developing low-energy neuromorphic computation hardware such as ASVI is crucial to achieving a zero-carbon computational future.

cond-mat.mes-hall↗

arXiv2022

Some exactly solvable and tunable frustrated spin models

We discuss three exactly solvable spin models of geometric frustration. First, we discuss a 1-parameter subfamily of the 16 vertex model, which can be mapped to a planar Ising model and solved via Fisher-Dubedát decorations. We then consider a 1-parameter family generalization of the Villain's fully frustrated model, which interpolates between Onsager's 2D Ising model and the Villain one. We then discuss spin ice models on a tree, which can be solved exactly using recursions \textit{a lá Bethe}.

cond-mat.stat-mech↗

arXiv2022

Memristive effects in nanopatterned permalloy Kagomé array

We study memristive effects in Kagomé nanopatterned permalloy. We observe that at low frequencies a thermistor effect is present, a phenomenon arising due to the lithography and absent in similar experiments for thin films. However, we also show via an independent anisotropic magnetoresistive study that a small hysteresis accounting for 1% of the effect is not attributable to a thermistive effect. Such effect is also confirmed by a careful subtraction scheme between nearby thermal hysteresis. In the millihertz regime, an effective model is provided to describe the experimental results for the thermistor, showing that there should be a crossover from the millihertz to the gigahertz, from a thermistor to an memresistive effect for nanopatterned permalloy.

cond-mat.stat-mech↗

arXiv2022

Projective Embedding of Dynamical Systems: uniform mean field equations

We study embeddings of continuous dynamical systems in larger dimensions via projector operators. We call this technique PEDS, projective embedding of dynamical systems, as the stable fixed point of the dynamics are recovered via projection from the higher dimensional space. In this paper we provide a general definition and prove that for a particular type of projector operator of rank-1, the uniform mean field projector, the equations of motion become a mean field approximation of the dynamical system. While in general the embedding depends on a specified variable ordering, the same is not true for the uniform mean field projector. In addition, we prove that the original stable fixed points remain stable fixed points of the dynamics, saddle points remain saddle, but unstable fixed points become saddles.

math.DS↗

arXiv2022

Global minimization via classical tunneling assisted by collective force field formation

Simple dynamical models can produce intricate behaviors in large networks. These behaviors can often be observed in a wide variety of physical systems captured by the network of interactions. Here we describe a phenomenon where the increase of dimensions self-consistently generates a force field due to dynamical instabilities. This can be understood as an unstable ("rumbling") tunneling mechanism between minima in an effective potential. We dub this collective and nonperturbative effect a "Lyapunov force" which steers the system towards the global minimum of the potential function, even if the full system has a constellation of equilibrium points growing exponentially with the system size. The system we study has a simple mapping to a flow network, equivalent to current-driven memristors. The mechanism is appealing for its physical relevance in nanoscale physics, and to possible applications in optimization, novel Monte Carlo schemes and machine learning.

cond-mat.mes-hall↗

arXiv2021

Macroscopic Magnetic Monopoles in a 3D-Printed Mechano-Magnet

The notion of magnetic monopoles has puzzled physicists since the introduction of Maxwell's Equations and famously Dirac had hypothesized them in the context of quantum mechanics. While they have proved experimentally elusive as elementary particles, the concept has come to describe excitations or topological defects in various material systems, from liquid crystals, to Hall systems, skyrmion lattices, and Bose-Einstein condensate. Perhaps the most versatile manifestation of magnetic monopoles as quasiparticles in matter has been in so-called spin ice materials. There, they represent violations of the ice rule, carry a magnetic charge, and can move freely unbound. Spin ice emergent magnetic monopoles appear at the atomic scale in rare earth pyrochlores or at the nano-scale in artificial spin ices systems. Here we demonstrate for the first time that the notion of magnetic monopoles can be transported at the macroscopic scale. We have built a mechano-magnet realized via 3D-printing, that consists of mechanical rotors on which macroscopic magnets can pivot. By controlling the relative height of the rotors we can achieve different regimes for magnetic monopoles, including the free monopole state. We then explore their driven dynamics under field. In the future, integration of our proof of principle in an elastic matrix can lead to novel macroscopic mechano-magnetic materials, to explore unusual piezomagnetism and magnetostriction, with applications to actuators and soft-robotics.

cond-mat.stat-mech↗

arXiv2021

How production networks amplify economic growth

Technological improvement is the most important cause of long-term economic growth. We study the effects of technology improvement in the setting of a production network, in which each producer buys input goods and converts them to other goods, selling the product to households or other producers. We show how this network amplifies the effects of technological improvements as they propagate along chains of production. Longer production chains for an industry bias it towards faster price reduction, and longer production chains for a country bias it towards faster GDP growth. These predictions are in good agreement with data and improve with the passage of time, demonstrating a key influence of production chains in price change and output growth over the long term.

q-fin.GN↗