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We study boundary value problems for degenerate elliptic equations and systems with square integrable boundary data. We can allow for degeneracies in the form of an $A_{2}$ weight. We obtain representations and boundary traces for solutions…
We present a new and simple bound for the exponential decay of second order systems using the spectral shift. This result is applied to finite matrices as well as to partial differential equations of Mathematical Physics. The type of the…
Using a Wigner Lorentzian Random Matrix ensemble, we study the fidelity, $F(t)$, of systems at the Anderson metal-insulator transition, subject to small perturbations that preserve the criticality. We find that there are three decay regimes…
In order to assess the accuracy of commonly used approximate exchange-correlation density functionals, we present a comparison of accurate exchange and correlation potentials, exchange energy densities and energy components with the…
We performed molecular dynamics simulations to study relaxation phenomena during vapor-liquid transitions in a single component Lennard-Jones system. Results from two different overall densities are presented; one in the neighborhood of the…
Using event-driven molecular dynamics we study one- and two-dimensional ballistic annihilation. We estimate exponents $\xi$ and $\gamma$ that describe the long-time decay of the number of particles ($n(t)\sim t^{-\xi}$) and of their typical…
We study visibility inside the vacant set of three models in $\mathbb R^d$ with slow decay of spatial correlations: Brownian interlacements, Poisson cylinders and Poisson-Boolean models. Let $Q_x$ be the radius of the largest ball centered…
Causal representation learning promises to extend causal models to hidden causal variables from raw entangled measurements. However, most progress has focused on proving identifiability results in different settings, and we are not aware of…
The dynamics of a two-qubit system is considered with the aim of a general categorization of the different ways in which entanglement can disappear in the course of the evolution, e.g., entanglement sudden death. The dynamics is described…
We study the statistics of the maximum and minimum of a set of $N$ random variables whose dynamical and statistical properties fall within the scope of infinite ergodic theory. These non-stationary yet recurrent systems are described, in…
We study here the random diffusion model. This is a continuum model for a conserved scalar density field $\phi$ driven by diffusive dynamics. The interesting feature of the dynamics is that the {\it bare} diffusion coefficient $D$ is…
We show that the exact exchange-correlation potential of time-dependent density-functional theory displays dynamical step structures that have a spatially non-local and time non-local dependence on the density. Using one-dimensional…
In this work we calculate the dynamical fluctuations at O(1/N) in the low temperature phase of the $p=2$ spherical spin glass model. We study the large-times asymptotic regimes and we find, in a short time-differences regime, a fluctuation…
Two-time correlations are a crucial tool to probe the dynamics of many-body systems. We use these correlation functions to study the dynamics of dissipative quantum systems. Extending the adiabatic elimination method, we show that the…
We study the relation between the spectral gap above the ground state and the decay of the correlations in the ground state in quantum spin and fermion systems with short-range interactions on a wide class of lattices. We prove that, if two…
The behavior of the bulk two-point correlation function $G({\bf r};T|d)$ in $d$-dimensional system with van der Waals type interactions is investigated and its consequences on the finite-size scaling properties of the susceptibility in such…
Value functions are crucial for model-free Reinforcement Learning (RL) to obtain a policy implicitly or guide the policy updates. Value estimation heavily depends on the stochasticity of environmental dynamics and the quality of reward…
Stochastic resetting breaks detailed balance and drives the formation of nonequilibrium steady states . Here, we consider a chain of diffusive processes $x_i(t)$ that interact unilaterally: at random time intervals, the process $x_n$…
Fractal dimensions are tools for probing the structure of quantum states and identifying whether they are localized or delocalized in a given basis. These quantities are commonly extracted through finite-size scaling, which limits the…
We critically examine the role that correlations established between a system and fragments of its environment play in characterising the ensuing dynamics. We employ a class of dephasing models where the state of the initial environment…