Statistical Mechanics
The excitability property of spiking neurons describes their capability to output an action potential as a real-time response to an input synaptic excitation current and is central to the event-based neuromorphic computing paradigm. The…
In this paper, we introduce a general framework to quantify dissimilarities between generalized Lotka-Volterra dynamical processes, ranging from classical predator-prey systems to multispecies communities interacting on networks. The…
One of the major advances of quantum technology is the engineering of complex quantum channels in lattice systems that paves the way for a variety of novel non-equilibrium phenomena. For a boundary driven lattice with such engineered…
We compute the full probability distribution of the moment of inertia $I \propto \sum_{i=1}^N \vec{r}_i^{\,2}$ of a gas of $N$ noninteracting bosons trapped in a harmonic potential $V(r) = (1/2)\, m\, \omega^2 r^2$, in all dimensions and at…
In this work, we present evidence for the spontaneous breaking of a continuous symmetry in a nearest-neighbour interacting spin-1 chain tuned to a quantum critical point at $T=0$ between two XY quasi-long-range order phases differing by the…
A fairly brief and complete presentation of the Zwanzig-Mori projection operator technique is given.
We endow the elements of a random matrix drawn from the Gaussian Unitary Ensemble with a Dyson Brownian motion dynamics. We initialize the dynamics of the eigenvalues with all of them lumped at the origin, but one outlier. We solve the…
A century after Ising introduced the Ising measure to study equilibrium systems, its relevance has expanded well beyond equilibrium contexts, notably appearing in non-equilibrium frameworks such as the Katz--Lebowitz--Spohn (KLS) model. In…
Synchronization phenomena in complex systems are fundamental to understanding collective behavior across disciplines. While classical approaches model such systems by using scalar-weighted networks and simple diffusive couplings, many…
We study the entropy production rate (EPR) of aligning self-propelled particles which undergo a flocking transition towards a polarized collective motion. In our thermodynamically consistent lattice model, individual self-propulsion is the…
Content-addressable memory, i.e. stored information that can be retrieved from content-based cues, is key to computation. Besides natural and artificial neural networks, physical learning systems have recently been shown to have remarkable…
Experiments, in particular on biological systems, typically probe lower-dimensional observables which are projections of high-dimensional dynamics. In order to infer consistent models capturing the relevant dynamics of the system, it is…
Generative models have advanced significantly in sampling material systems with continuous variables, such as atomistic structures. However, their application to discrete variables, like atom types or spin states, remains underexplored. In…
Rare-earth orthonickelates RNiO3 are Jahn-Teller magnets, unstable with respect to the anti-Jahn-Teller disproportionation reaction with the formation of a system equivalent to a system of effective spin-triplet composite bosons moving in a…
This short book is an elementary course on entropy, leading up to a calculation of the entropy of hydrogen gas at standard temperature and pressure. Topics covered include information, Shannon entropy and Gibbs entropy, the principle of…
We consider a system formed by two different segments of particles, coupled to thermal baths, one at each end, modeled by Langevin thermostats. The particles in each segment interact harmonically and are subject to an on-site potential, for…
We consider the Hindmarsh-Rose neuron model modified by taking into account the effect of electromagnetic induction on membrane potential. We study the impact of the magnetic flux on the neuron dynamics, through the analysis of the…
We investigate the ergodic properties of Brownian motion in heterogeneous media through the statistics of occupation times. Using the Feynman-Kac formalism, we derive analytical expressions for the distributions, moments, and ergodicity…
We study the fluctuation properties of the local time density, ${\rho _T} = \frac{1}{T}\int_0^T {\delta ( {r(t) - 1} )} dt$, spent by a $d$-dimensional Brownian particle at a spherical shell of unit radius, where $r(t)$ denotes the radial…
We introduce a boundary condition twisted by time translation as a novel probe to characterize dynamical phases in periodically driven (Floquet) quantum systems. Inspired by twisted boundary conditions in equilibrium systems, this approach…