Related papers: Theoretical and Numerical Study of Self-Organizing…
Phase transitions, sharp in the thermodynamic limit, get smeared in finite systems where macroscopic order-parameter fluctuations dominate. Achieving a coherent and complete theoretical description of these fluctuations is a central…
Probabilistic solvers for ordinary differential equations (ODEs) have emerged as an efficient framework for uncertainty quantification and inference on dynamical systems. In this work, we explain the mathematical assumptions and detailed…
Stochastic evolution underpins several approaches to the dynamics of open quantum systems, such as random modulation of Hamiltonian parameters, the stochastic Schrodinger equation (SSE), and the stochastic Liouville equation (SLE). These…
The neural ordinary differential equation (ODE) framework has emerged as a powerful tool for developing accelerated surrogate models of complex physical systems governed by partial differential equations (PDEs). A popular approach for PDE…
We study the dynamics of classical and quantum systems undergoing a continuous measurement of position by schematizing the measurement apparatus with an infinite set of harmonic oscillators at finite temperature linearly coupled to the…
Partial differential equation (PDE)-constrained optimization arises in many scientific and engineering domains, such as energy systems, fluid dynamics and material design. In these problems, the decision variables (e.g., control inputs or…
We investigate a discrete model consisting of self-propelled particles that obey simple interaction rules. We show that this model can self-organize and exhibit coherent localized solutions in one- and in two-dimensions.In one-dimension,…
We discuss the dynamics of classical Dicke-type models, aiming to clarify the mechanisms by which coherent states could develop in potentially non-equilibrium systems such as semiconductor microcavities. We present simulations of an…
Probabilistic ordinary differential equation (ODE) solvers have been introduced over the past decade as uncertainty-aware numerical integrators. They typically proceed by assuming a functional prior to the ODE solution, which is then…
We study the Classical Probability analogue of the dilations of a quantum dynamical semigroup in Quantum Probability. Given a (not necessarily homogeneous) Markov chain in discrete time in a finite state space E, we introduce a second…
The driven double-well Duffing oscillator is a well-studied system that manifests a wide variety of dynamics, from periodic behavior to chaos, and describing a diverse array of physical systems. It has been shown to be relevant in…
Many physical, chemical and biological systems can be modeled by means of random-frequency harmonic oscillator systems. Even though the noise-free evolution of harmonic oscillator systems can be easily implemented, the way to experimentally…
We prove the holding of chaos in the sense of Li-Yorke for a family of four-dimensional discrete dynamical systems that are naturally associated to ODE systems describing coupled oscillators subject to an external non-conservative force,…
The standard quantum mechanical harmonic oscillator has an exact, dual relationship with a completely classical system: a classical particle running along a circle. Duality here means that there is a one-to-one relation between all…
Partial differential equations (PDEs) govern physical phenomena across the full range of scientific scales, yet their computational solution remains one of the defining challenges of modern science. This critical review examines two mature…
In the thermodynamics of nanoscopic systems the relation between classical and quantum mechanical description is of particular importance. To scrutinize this correspondence we study an anharmonic oscillator driven by a periodic external…
There is a rising interest in Spatio-temporal systems described by Partial Differential Equations (PDEs) among the control community. Not only are these systems challenging to control, but the sizing and placement of their actuation is an…
Spatial reaction-diffusion models have been employed to describe many emergent phenomena in biological systems. The modelling technique most commonly adopted in the literature implements systems of partial differential equations (PDEs),…
We consider stochastic dynamical systems defined by differential equations with a uniform random time delay. The latter equations are shown to be equivalent to deterministic higher-order differential equations: for an $n$-th order equation…
We provide a fully quantum description of a mechanical oscillator in the presence of thermal environmental noise by means of a quantum Langevin formulation based on quantum stochastic calculus. The system dynamics is determined by symmetry…