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A generalisation of Takens' delay-coordinate embedding theorem to stochastic systems, the Stochastic Embedding Sufficiency Theorem, is an inverse methodology enabling non-parametric recovery of both drift and diffusion fields from scalar…
The semiclassical equations of motion are widely used to describe carrier transport in conducting materials. Nevertheless, the substantial challenge of incorporating disorder systematically into the semiclassical model persists, leading to…
Fractional kinetic equations employ non-integer calculus to model anomalous relaxation and diffusion in many systems. While this approach is well explored, it so far failed to describe an important class of transport in disordered systems.…
Given two probability measures on sequential data, we investigate the transport problem with time-inconsistent preferences in a discrete-time setting. Motivating examples are nonlinear objectives, state-dependent costs, and regularized…
This paper deals with the controllability for a class of non-autonomous neutral differential equations of fractional order with infinite delay in an abstract space. The semi-group theory of bounded linear operators, fractional calculus, and…
In this contribution we present an intrinsic description of time-variant Port Hamiltonian systems as they appear in modeling and control theory. This formulation is based on the splitting of the state bundle and the use of appropriate…
We establish effective versions of Oppenheim's conjecture for generic inhomogeneous quadratic forms. We prove such results for fixed shift vectors and generic quadratic forms. When the shift is rational we prove a counting result which…
A partial differential equation governing the global evolution of the joint probability distribution of an arbitrary number of local flow observations, drawn randomly from a control volume, is derived and applied to examples involving…
We study relative dispersion of passive scalar in non-ideal cases, i.e. in situations in which asymptotic techniques cannot be applied; typically when the characteristic length scale of the Eulerian velocity field is not much smaller than…
The nonequilibrium thermodynamics of interacting quantum many-body systems is investigated within the framework of thermal time-dependent density functional theory using a generalized linear-response formulation for the full quantum work…
Consider the symmetric exclusion process evolving on an interval and weakly interacting at the end-points with reservoirs. Denote by $I_{[0,T]} (\cdot)$ its dynamical large deviations functional and by $V(\cdot)$ the associated…
We discuss our recent study of local quantum mechanical uncertainty relations in quantum many body systems. These lead to fundamental bounds for quantities such as the speed, acceleration, relaxation times, spatial gradients and the…
We develop the kinetic theory of collisionless relaxation for systems with long-range interactions in relation to the statistical theory of Lynden-Bell. We treat the multi-level case. We make the connection between the kinetic equation…
We study uncertainty in the dynamics of time-dependent flows by identifying barriers and enhancers to stochastic transport. This topological segmentation is closely related to the theory of Lagrangian coherent structures and is based on a…
A new model that generalizes the study of quantum Brownian motion (BM) is constructed. We consider disordered environment that may be either static (quenched), noisy or dynamical. The Zwanzig-Caldeira-Leggett BM-model constitutes formally a…
This paper deals with a nonhomogeneous scalar parabolic equation with possibly degenerate diffusion term; the process has only one stationary state. The equation can be interpreted as modeling collective movements (crowd dynamics, for…
In this work we investigate discrete-time transport in a generic U(1)-symmetric disordered model tuned across an array of different dynamical regimes. We develop an aggregate quantity, a circular statistical moment, which is a simple…
We theoretically consider charge transport through two quantum dots coupled in series. The corresponding full counting statistics for noninteracting electrons is investigated in the limits of sequential and coherent tunneling by means of a…
We construct invariant differential operators acting on sections of vector bundles of densities over a smooth manifold without using a Riemannian metric. The spectral invariants of such operators are invariant under both the diffeomorphisms…
The large-time asymptotics of the density matrix solving a drift-diffusion-Poisson model for the spin-polarized electron transport in semiconductors is proved. The equations are analyzed in a bounded domain with initial and Dirichlet…