Related papers: Quantum graphs with mixed dynamics: the transport/…
Quantum teleportation plays a key role in modern quantum technologies. Thus, it is of much interest to generate alternative approaches or representations aimed at allowing us a better understanding of the physics involved in the process…
We introduce a fractional Klein-Kramers equation which describes sub-ballistic superdiffusion in phase space in the presence of a space-dependent external force field. This equation defines the differential L{\'e}vy walk model whose…
Detailed calculations of the transport coefficients of a recently introduced particle-based model for fluid dynamics with a non-ideal equation of state are presented. Excluded volume interactions are modeled by means of biased stochastic…
In this paper, we consider a class of stochastic delay fractional evolution equations driven by fractional Brownian motion in a Hilbert space. Sufficient conditions for the existence and uniqueness of mild solutions are obtained. An…
We provide a new perturbation theorem for substochastic semigroups on abstract AL spaces extending Kato's perturbation theorem to non-densely defined operators. We show how it can be applied to piecewise deterministic Markov processes and…
We discuss a method by which quantum fluctuations can be included in microscopic transport models based on wave packets that are not energy eigenstates. By including the next-to-leading order term in the cumulant expansion of the…
We study transport processes on infinite metric graphs with non-constant velocities and matrix boundary conditions in the $\\mathrm{L}^{\infty}$-setting. We apply the theory of bi-continuous operator semigroups to obtain well-posedness of…
In this article, we give a unified theory for constructing boundary layer expansions for dis-cretized transport equations with homogeneous Dirichlet boundary conditions. We exhibit a natural assumption on the discretization under which the…
A new approach to quantum walks is presented. Considering a quantum system undergoing some unitary discrete-time evolution in a directed graph G, we think of the vertices of G as sites that are occupied by the quantum system, whose internal…
We discuss the semiclassical approximation to transport problems in quantum chaotic systems. The figures of merit are moments of the transmission matrix and of the time delay matrix. After reviewing a few results obtained by treating these…
Mathematical models of motility are often based on random-walk descriptions of discrete individuals that can move according to certain rules. It is usually the case that large masses concentrated in small regions of space have a great…
The Fast Fourier Transform is extended to functions on finite graphs whose edges are identified with intervals of finite length. Spectral and pseudospectral methods are developed to solve a wide variety of time dependent partial…
For a quantum walk on a graph, there exist many kinds of operators for the discrete-time evolution. We give a general relation between the characteristic polynomial of the evolution matrix of a quantum walk on edges and that of a kind of…
The elements of the quantum mechanical diffusion matrix, leading to a Gibbs equilibrium state for a set of $N$ coupled quantum harmonic oscillators are derived within Lindblad's axiomatic approach. Consequences of the fundamental…
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…
We study the entanglement dynamics of discrete time quantum walks acting on bounded finite sized graphs. We demonstrate that, depending on system parameters, the dynamics may be monotonic, oscillatory but highly regular, or quasi-periodic.…
We study dynamical semigroups of positive, but not completely positive maps on finite-dimensional bipartite systems and analyze properties of their generators in relation to non-decomposability and bound-entanglement. An example of…
The development and time evolution of a transport barrier in a magnetically confined plasma with non-monotonic, nonlinear dependence of the anomalous flux on mean gradients is analyzed. Upon consideration of both the spatial inhomogeneity…
We consider a diffusion process on an evolving surface with a piecewise Lipschitz-continuous boundary from an energetic point of view. We employ an energetic variational approach with both surface divergence and transport theorems to derive…
We show that a class of background independent models of quantum spacetime have local excitations that can be mapped to the first generation fermions of the standard model of particle physics. These states propagate coherently as they can…