- Introduction. Quenched and configurational disorder. Coarsening. Glassiness and active matter. Models and methods.
- Equilibrium analysis. Free-energy landscapes (extensions of Ginzburg-Landau).
- Out of equilibrium dynamics. Dynamic mean-field theory.
The solar system has a relatively large Lyapunov exponent, and yet has been stable for much longer than the inverse Lyapunov time. Similarly, almost integrable systems like the low energy Fermi-Pasta-Ulam chain take much longer to thermalize than one would expect from their Lyapunov exponent.
This phenomenon has more recently been studied in quantum systems.
El sistema solar tiene un...
In large random systems, certain behaviors are reliably predicted, like the energy density of the ground state. The long-time behavior of many physical and algorithmic dynamics is likewise predictable, through DMFT and related approaches. But can these behaviors be connected to static structures of the problem at hand, like its energy landscape? Recently, development of the Overlap Gap...
Fast thermal equilibration, also known as a shortcut to adiabaticity, is an external control technique employed to expedite operations beyond the system’s natural timescale. In this talk, we will introduce a machine learning technique, specifically automatic differentiation, to identify control protocols that accelerate the equilibration process in stochastic systems modeled by the overdamped...
These three lectures will focus on three manners to fall out of equilibrium, and on the many-body effects that arise from the nonequilibrium nature of the dynamics. We will begin with systems harboring a macroscopic current (leading to long range correlations). Then we shall stop by systems that should be relaxing towards equilibrium, but that fail to do so for reasons that are still under...
A system is called antifragile when damage acts as a constructive element improving the performance of a global function. In this work, we analyze the emergence of antifragility in the movement of random walkers on networks with modular structures or communities. The random walker hops considering the capacity of transport of each link, whereas the links are susceptible to random damage that...
Paper published in 2026: we study two years of access card validation records from Bogotá’s multimodal public transport system, comprising over 2.3 billion trips across bus rapid transit, feeder buses, dual-service buses, and an aerial cable network. From user trajectories constructed exclusively from access records, we derive motifs that reveal recurrent mobility patterns extending beyond...
The model proposed by Default, Neau, Amblard, and Weisbuch (DNAW) is relevant in sociophysics for studying the phenomenon of opinion formation in social systems composed of agents that interact in a binary manner. Its relevance lies in the fact that, through the formulation of an opinion exchange rule between pairs of agents whose opinion differences are smaller than a bounded confidence...
Si bien los LLMs han irrumpido con excepcional fuerza en el campo de la IA con una percepción de un potencial de impacto y cambio enorme, su adopción para resolver problemas en la práctica sigue planteando muchísimos retos. Su naturaleza como modelos estadísticos del lenguaje es la causa principal de estas dificultades y, en ese contexto se han creado muchas técnicas que permiten abordar parte...
In recent years, diffusion generative models have become state-of-the-art for tasks such as image, video, and audio generation, among others. More recently, there has been growing interest in studying the statistical mechanics of these models, driven by the observation of apparent phase transitions during the sampling process. More specifically, a symmetry breaking that resembles the one...
In this work, we study the dynamics of multiple random walkers on networks subject to a simultaneous resetting protocol, whereby all walkers are synchronously returned to their respective initial nodes. For this collective Markovian process, we derive exact analytical expressions for the mean first-encounter time, defined as the average time required for all walkers to meet for the first time...
Collective synchronization is an emergent phenomenon in physical, biological, and
technological systems, where local interactions enable dynamical adjustment among
oscillators. In complex networks, the Kuramoto model provides a fundamental framework to study the transition between incoherent and synchronized states; however, synchronization typically requires sufficiently strong coupling,...
Quantum thermodynamics aims to understand how thermodynamic processes emerge in quantum systems, particularly in relation to information and entanglement. In this work we study the dynamics of correlations of a Werner state composed of two qubits weakly coupled to a thermal bath. The system is described using a Lindblad master equation, modelling the environment as a thermal reservoir that...
In this work, we study the time scale invariance for the heavy tails of the minute log returns time series of the S&P 500 stock index for three different time periods (January 2011 – October 2015, November 2015 – December 2019, January 2020 – October 2023), considering minute, hour, and day time series for each case. Using the symmetric fractional Laskin model, which describes the dissipative...
An econophysical study of datasets on cadastral and commercial values of average prices per property per block in Bogotá leads us to identify the existence of ensemble fluctuation scaling. This scaling, which is a property of complex systems observed in a variety of natural scenarios and is characterized by a power-law relationship between the variance and the mean of the data, is found for...
We develop a path-integral formulation of first-passage random walks on networks and extend it to fractional transport dynamics. In this framework, the random-walk effective distance is defined from the ensemble of all first-passage trajectories connecting a source to a target, weighted by both their probabilities and their lengths. This construction naturally introduces a trajectory partition...
The stability of matter is often assumed without question. We typically believe that established physical theories can easily predict that atoms and molecules will not collapse or that the total energy of matter scales linearly with the number of particles. However, these questions remained unresolved when quantum theory was first established, and it actually took several decades before any...
Non-extensive statistical mechanics, introduced by Tsallis, provides a robust theoretical framework for describing complex systems characterized by long-range correlations and extreme events. In the context of financial markets, the q-Gaussian distributions that emerge from this formalism constitute a natural generalization of Gaussian approaches, as they are capable of capturing the heavy...
This work presents an analytical Green's function study of one-dimensional topological models aimed at connecting their equilibrium spectral properties to nonequilibrium quantum transport. Working in the continuum limit, we derive exact expressions for the retarded Green's function of the bulk, the semi-infinite chain, and the finite chain, computing the Local Density of States (LDOS) in each...
Bosonisation is a technique to solve one-dimensional fermion models by transforming them to bosonic systems. S. Coleman (1975) showed that the correlators of the massive Thirring model, a one-dimensional Dirac fermion with self-interactions, coincide with those of the Sine-Gordon boson, and later, S. Mandelstam (1975) found the explicit map between these two systems. The identities found by...
Este trabajo analiza cómo las modificaciones topológicas afectan la entropía residual y la degeneración del estado base en sistemas frustrados del modelo de Ising. Tomando como referencia las redes triangular y kagome antiferromagnéticas, se emplea un enfoque computacional basado en simulaciones de Monte Carlo e integración termodinámica.
Se estudian tanto defectos aleatorios como...
Manganites with a $CaMnO_3$-type structure are generally antiferromagnetic and insulating at low temperatures. However, chemical substitution with rare-earth elements induces strong competition between coexisting antiferromagnetic (AFM) and ferromagnetic (FM) phases, often leading to phase separation and field-induced metamagnetic transitions. These transitions can be understood as percolation...
The past decade has witnessed a surge in the development and adoption of machine learning algorithms to solve day-a-day computational tasks. Yet, a solid theoretical understanding of even the most basic tools used in practice is still lacking, as traditional statistical learning methods are unfit to deal with the modern regime in which the number of model parameters are of the same order as...
We investigate the complex interplay of competing phases in bulk La$_{5/8−x}$Pr$_x$Ca$_3/8$MnO$_3$ (LPCMO) to demonstrate the coexistence of volatile and non-volatile multilevel resistive switching (RS) within a single device. In this system, ferromagnetic metallic (FM-M) and chargeordered insulating (COI) phases spatially coexist across a broad ∼160 K temperature window. While volatile RS...
In this work we describe magnetization measurements on lamellar Mn oxides un-doped and dope with Co. They show that the magnetic structure of this oxides system is extremely sensitivity to the (Co/Mn) ratio. Special emphasis is given to the inverse susceptibility and the temperature derivative of the magnetic susceptibility. Interestingly, the magnetic order changes from a typical...
Solid solutions of transition-metal dichalcogenides (TMDs), a family of cuasi-2D van der Waals materials, provide a powerful platform to explore how composition, structural symmetry, and defect chemistry collectively determine electronic and ferroic properties in layered materials. In particular, the ability to independently tune substitutional disorder and intrinsic defect populations offers...
Understanding how frustration and disorder shape relaxation in complex systems is a central challenge in statistical physics and directly relevant to quantum annealing. Spin-glass models provide a natural setting to address this problem, as their energy landscapes are governed by competing interactions and constrained network topologies. In this talk, I explore the non-exponential relaxation...
While the physics of classical active particles—such as bacteria,
synthetic Janus colloids, and bird flocks—is well-established via models like Active Brownian Motion (ABM), the extension of these principles to the quantum regime has only recently gained traction. This talk will first review the fundamental principles of classical self-propulsion, highlighting unique features of individual...
Chess is a board game that demands deep positional understanding from the very first move of the opening to the end of the game. The initial moves, by both White and Black, contain information at the individual level about each player’s strengths, knowledge of the adversary, and personal preferences, as well as broader insights into the state of the art of the game itself. The evolution of...
Los sistemas complejos presentan diferentes tipos de escalamiento, tales como el escalamiento de la fluctuación temporal caracterizada por el hecho de que la dispersión de los datos en una serie de tiempo no estacionaria (cuantificada mediante la variancia) satisface una relación de ley de potencia con respecto al promedio de los datos, o el escalamiento del Theil temporal en el que la...
We perform an econophysics study of the gross domestic product per capita (GDPP) data from $N=105$ countries worldwide, which have annual records in the World Bank database for every year between 1960 and 2023.
Starting from the time series of annual values of the average GDPP per country and the variance of the GDPP for the period 1960-2023, we find that the variance presents a power law...
Neural scaling laws underlie many of the recent advances in deep learning, yet their theoretical understanding remains largely confined to linear models. In this work, we present a systematic analysis of scaling laws for quadratic and diagonal neural networks in the feature learning regime. Leveraging connections with matrix compressed sensing and LASSO, we derive a detailed phase diagram for...
La Relación de Crooks [1], uno de los teoremas de fluctuación, es hoy en día un método estándar para calcular diferencias de energía libre entre dos estados de un sistema utilizando procesos fuera del equilibro. En el presente trabajo construimos un sistema de dos osciladores armónicos de masa y resorte en un baño térmico acoplados por un tercer resorte, y simulamos mediante dinámica...
We simulate a realization of Maxwell’s demon based on the experimental setup developed in \textit{Bayesian Information Engine that Optimally Exploits Noisy Measurements}, in which a heavy bead, immersed in water at room temperature, is trapped by an optical tweezer and lifted through rapid feedback control without net work expenditure. This system functions as an information engine, harnessing...
This study investigates the evolution of asphalt pavement surface damage caused by studded-tire traffic using a combined experimental and stochastic modeling approach. Laboratory tests on six asphalt mixtures were integrated into a Monte Carlo simulation framework that models rutting as the cumulative effect of random stud impacts. The model incorporates parameters describing cumulative...
The production of concentrated emulsions involves high-shear flows and it is well known that at a critical volume fraction the emulsion loses stability, undergoing an extremely rapid process where the continuous and dispersed phases in the emulsion exchange roles. This process, called catastrophic phase inversion, which resembles in several respects a dynamical phase transition, has remained...
The accurate formulation of ion correlations in charged solutions is a critical task for the control of various biological and industrial processes ranging from ion transport through cells to water purification procedures. The theoretical tools enabling the comprehension of these systems is based on the Debye-Hückel (DH) theory suffering from major limitations [1]. Namely, the validity of the...
We study the dynamics of a Log-Coulomb gas consisting of N charged particles confined to a unitary circle and coupled to a thermal bath characterized by a dimensionless effective parameter $\beta = q_0^2/(k_BT)$ with $q_0$ the charge per particle, $T$ the bath temperature, and $k_B$ the Boltzmann’s constant. The use of a circular domain eliminates boundary effects and ensures exact rotational...
In equilibrium fluids, wetting is controlled by the competition of three surface tensions between the three phases (liquid, gas, solid). When the particles comprising the fluid become self-propelled, the question of wetting begins with a proper definition of surface tension (which may not be unique out of equilibrium). I will present a robust mechanics-based definition for surface tension. I...
Entanglement and magic (non-stabilizerness) are widely regarded as necessary for quantum universality and potential advantage. Yet the form in which they must appear within a quantum state remains unclear. We introduce an operational diagnostic of their interplay: \emph{magic-protected entanglement}, defined as entanglement remaining after optimal stabilizer (Clifford) processing. This...
In the development of quantum technologies, the interaction between a quantum system and its environment, that leads to decoherence, is traditionally viewed as a fundamental obstacle. In Quantum Key Distribution (QKD) protocols like BB84, environmental noise inevitably degrades state purity, increases the Quantum Bit Error Rate (QBER), and ultimately compromises the security of the...
The intrinsic transmembrane protein known as sodium iodide symporter (NIS) facilitates the active transport of iodide across the basolateral membrane of thyroid follicular cells. Iodine is an essential molecule that is used to produce the classical thyroid hormones.
To perform a molecular dynamics (MD) simulation, we used structures of apo-NIS and NIS with I− and an oxyanion (ReO4−) bound to...
The Schramm–Loewner Evolution (SLE) provides a rigorous framework for characterizing the scaling limits of fractal curves, encoding their geometric properties through the diffusion parameter of a Brownian motion and enabling a universal classification of stochastic growth processes. In this talk, we introduce the basic ideas behind SLE and discuss its role in understanding conformally...
