6 papers
Convergence of coined quantum walks on d-dimensional Euclidean space
Alex D. Gottlieb, Svante Janson, Petra F. Scudo
Coined quantum walks may be interpreted as the motion in position space of a quantum particle with a spin degree of freedom; the dynamics are determined by iterating a unitary tran…
Two examples of discrete-time quantum walks taking continuous steps
Alex D. Gottlieb
This note introduces some examples of quantum random walks in d-dimensional Eucilidean space and proves the weak convergence of their rescaled n-step densities. One of the examples…
Accuracy of the time-dependent Hartree-Fock approximation
Claude Bardos, Francois Golse, Alex D. Gottlieb +1
This article examines the time-dependent Hartree-Fock (TDHF) approximation of single-particle dynamics in systems of interacting fermions. We find the TDHF approximation to be accu…
Classical and Quantum Propagation of Chaos
Alex D Gottlieb
This article examines the relationship between classical and quantum propagation of chaos. (In this context, "chaos" refers to the Boltzmann's Ansatz of molecular disorder, not to…
Markov Transitions and the Propagation of Chaos
Alexander David Gottlieb
The propagation of chaos is a central concept of kinetic theory that serves to relate the equations of Boltzmann and Vlasov to the dynamics of many-particle systems. Propagation of…
The Propagation of Molecular Chaos by Markov Transitions
Alexander David Gottlieb
We establish a necessary and sufficient condition for the propagation of chaos by a family of many-particle Markov processes, if the particles live in a Polish space: a sequence of…