Related papers: Memory effects in measure transport equations
We reexamine the problem of having nonconservative equations of motion arise from the use of a variational principle. In particular, a formalism is developed that allows the inclusion of fractional derivatives. This is done within the…
A space fractional diffusion-like equation is introduced, which embodies the nonlocality in time, represented by the memory kernel and the non-locality in space. A specific example of the nonlocal term is considered in combination with…
We are witnessing the birth of a new variety of pharmacokinetics where non-integer-order differential equations are employed to study the time course of drugs in the body: this is dubbed "fractional pharmacokinetics." The presence of…
An elementary system leading to the notions of fractional integrals and derivatives is considered. Various physical situations whose description is associated with fractional differential equations of motion are discussed.
We study a nonlinear transport equation defined on an oriented network where the velocity field depends not only on the state variable, but also on the solution itself. We prove existence, uniqueness and continuous dependence results for…
The effects of the propagation of particles which have a finite life-time and an according width in their mass spectrum are discussed in the context of transport descriptions. In the first part the coupling of soft photon modes to a source…
We propose that memory effects in the conductivity of metallic systems can be produced by the same two levels systems that are responsible for the 1/f noise. Memory effects are extremely long-lived responses of the conductivity to changes…
We present a conundrum that results from the imprecise use of notation for partial derivatives. Taking an example from mechanics, we show that lack of proper care in representing partial derivatives in Lagrangian and Hamiltonian…
Traditional nonparametric estimation methods often lead to a slow convergence rate in large dimensions and require unrealistically enormous sizes of datasets for reliable conclusions. We develop an approach based on partial derivatives,…
A Langevin equation is proposed to describe the transport of overdamped Brownian particles in a periodic rough potential and driven by an unbiased periodic force. The equation can be transformed into the Fokker-Planck equation by using the…
Quantum memory effects can be induced even when the degrees of freedom associated to the environment are not affected at all during the system evolution. In this paper, based on a bipartite representation of the system-environment dynamics,…
In many biological systems, the movement of individual agents is commonly characterized as having multiple qualitatively distinct behaviors that arise from various biophysical states. This is true for vesicles in intracellular transport,…
Fractionally integrated time series, exhibiting long memory with slowly decaying autocorrelations, are frequently encountered in economics, finance, and related fields. Since the seminal work of Robinson (1995), a variety of semiparametric…
An analytical expression is derived for the transition path time distribution for a one-dimensional particle crossing of a parabolic barrier. Two cases are analyzed: (i) A non-Markovian process described by a generalized Langevin equation…
In relativistic quantum field theory with local interactions, charge is locally conserved. This implies local conservation of probability for the Dirac and Klein-Gordon wavefunctions, as special cases; and then in turn for non-relativistic…
Memory effects play a key role in the dynamics of strongly correlated systems driven out of equilibrium. In the present study, we explore the nature of memory in the nonequilibrium Anderson impurity model. The Nakajima--Zwanzig--Mori…
Recently, a series of different measures quantifying memory effects in the quantum dynamics of open systems has been proposed. Here, we derive a mathematical representation for the non-Markovianity measure based on the exchange of…
In this paper the generalisation of previous author's formulation of fractional continuum mechanics to the case of anisotropic non-locality is presented. The considerations include the review of competitive formulations available in…
We establish some quantitative concentration estimates for the empirical measure of many independent variables, in transportation distances. As an application, we provide some error bounds for particle simulations in a model mean field…
We investigate memory effects and quantum transport in two-dimensional lattice systems within the framework of non-equilibrium Green's functions and Schwinger-Keldysh non-equilibrium quantum field theory. Starting from a 2D tight-binding…