(A) REDUCED DENSITY MATRIX GENERATION ALGORITHMS IN SINGLE-PARTICLE-EXACT DENSITY FUNCTIONAL THEORY, (B) QUANTUM DYNAMICAL SIMULATION OF A TRANSVERSAL STERN-GERLACH INTERFEROMETER, (C) OPEN QUANTUM SYSTEM PROCESS TOMOGRAPHY

Abstract

(A)

A central problem arising in single-particle-exact density functional theory is the generation of reduced single-particle density matrices from a suitable class. We present one solution to this problem, prove its correctness and discuss its applications.

(B)

We revisit the question of the reversibility of the Stern--Gerlach apparatus. In the original proposal, evolution of an atomic beam split by the Stern--Gerlach apparatus was to be reversed by placing suitably oriented magnets, generating a reverse magnetic field. Previous theoretical works showed that this is difficult to accomplish experimentally. We supplement theoretical insights with an exact wave function simulation of the transversal Stern--Gerlach interferometer dynamics, presenting firm evidence in favor of its fundamental irreversibility.

(C)

We study the problem of characterizing the dynamics of an open quantum system. We model the system-environment dynamics with a time-discretized, joint evolution channel, developing an extension of quantum state tomography to characterize relevant parts of the environment influencing the system, in a simplified scenario where the joint evolution channel is known. In the general case, when nothing is known about the system-environment interaction, we develop a numerical scheme to characterize the effective evolution of the system under the influence of noise.