In this article we consider the Hamiltonian dynamics of systems of fermions and derive the time-dependent Hartree-Fock equation in the mean field limit. We follow the approach of Spohn, who derived a… (More)

We propose to quantify the correlation inherent in a many-electron (or many-fermion) wave function psi by comparing it to the unique uncorrelated state that has the same 1-particle density operator… (More)

This note introduces some examples of quantum random walks in R and proves the weak convergence of their rescaled n-step densities. One of the examples is called the Plancherel quantum walk because… (More)

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 chaos means that… (More)

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 transformation which is… (More)

According to the Quantum de Finetti Theorem, locally normal infinite particle states with Bose-Einstein symmetry can be represented as mixtures of infinite tensor powers of vector states. This note… (More)

We show that that the jackknife variance estimator vjack and the the infinitesimal jackknife variance estimator are asymptotically equivalent if the functional of interest is a smooth function of the… (More)

We propose to quantify the “correlation” inherent in a many-electron (or manyfermion) wavefunction ψ by comparing it to the unique uncorrelated state that has the same 1-particle density operator as… (More)

This article concerns the time-dependent Hartree-Fock (TDHF) approximation of single-particle dynamics in systems of interacting fermions. We find that the TDHF approximation is accurate when there… (More)

Bosonic Josephson junctions can be realized by confining ultracold gases of bosons in multiwell traps and studied theoretically with the M-site Bose-Hubbard model. We show that canonical equilibrium… (More)