Related papers: Sensitivity Analysis of Separation Time Along Weak…
Many measurements on soft condensed matter (e.g., biological and materials) systems track low-dimensional observables projected from the full system phase space as a function of time. Examples are dynamic structure factors, spectroscopic…
Time-dependent potentials are common in galactic systems that undergo significant evolution, interactions, or encounters with other galaxies, or when there are dynamic processes like star formation and merging events. Recent studies show…
Evaluating robustness under temporal distribution shift remains an open challenge. Existing metrics quantify the average decline in performance, but fail to capture how models adapt to evolving data. As a result, temporal degradation is…
This paper considers the robustness of an uncertain nonlinear system along a finite-horizon trajectory. The uncertain system is modeled as a connection of a nonlinear system and a perturbation. The analysis relies on three ingredients.…
The geometry of the weak stability boundary region for the planar restricted three-body problem about the secondary mass point has been an open problem. Previous studies have conjectured that it may have a fractal structure. In this paper,…
The unitarity of quantum evolutions implies that the overlap between two initial states does not change in time. This property is commonly believed to explain the lack of state sensitivity in quantum theory, a feature that is prevailing in…
We introduce novel characterizations for many-body phase transitions between delocalized and localized phases based on the system's sensitivity to boundary conditions. In particular, we change boundary conditions from periodic to…
We study the weak localization correction (WLC) to transport coefficients of a system of electrons in a static long-range potential (e.g. an antidot array or ballistic cavity). We found that the weak localization correction to the current…
Stochastic parabolic equations are widely used to model many random phenomena in natural sciences, such as the temperature distribution in a noisy medium, the dynamics of a chemical reaction in a noisy environment, or the evolution of the…
The spectral theory for weakly stationary processes valued in a separable Hilbert space has known renewed interest in the past decade. Here we follow earlier approaches which fully exploit the normal Hilbert module property of the time…
We study the thermal conductivity in disordered $s$-wave superconductors. Expanding on previous works for normal metals, we develop a formalism that tackles particle diffusion as well as the weak localization (WL) and weak anti-localization…
We consider bounded extremum seeking controls for time-varying linear systems with uncertain coefficient matrices and measurement uncertainty. Using a new change of variables, Lyapunov functions, and a comparison principle, we provide…
We study transport in a model perturbed integrable Hamiltonian system by calculating the volume, V(t), of elementary phase space cells visited by a trajectory, as a function of time. We use this function in order to "measure" the fractality…
Due to the widespread deployment of Global Navigation Satellite Systems (GNSSs) for critical road or urban applications, one of the major challenges to be solved is the provision of integrity to terrestrial environments, so that GNSS may be…
We study a disordered weakly-coupled superconductor around the Anderson transition by solving numerically the Bogoliubov-de Gennes (BdG) equations in a three dimensional lattice of size up to $20\times20\times20$ in the presence of a random…
Two dimensional stochastic time model of scrape-off layer (SOL) turbulent transport is studied. Instability arisen in the system with respect to the stochastic perturbations of both either density or vorticity reveals itself in the strong…
In this work, we explore the critical behaviors of fidelity susceptibility and trace distance susceptibility associated to the steady states of dissipative systems at continuous phase transitions. We investigate on two typical models, one…
The discovery of interstellar interlopers such as 1I/`Oumuamua, 2I/Borisov, and 3I/ATLAS have highlighted the necessity of understanding the dynamical pathways that eject small bodies from planetary systems into hyperbolic trajectories. In…
Recent molecular dynamics simulations show that a dilute relativistic gas equilibrates to a Juettner velocity distribution if ensemble velocities are measured simultaneously in the observer frame. The analysis of relativistic Brownian…
In a dissipative system the time to reach an attractor is often influenced by the peculiarities of the model and in particular by the strength of the dissipation. In particular, as a dissipative model we consider the spin-orbit problem…