Density matrix theory — a retrospective

J. W. Clark

Manfred Ristig was a leading contributor to the advancement of microscopic theory of strongly interacting quantum many-body systems for over four decades. This retrospective on his life and scientific career pays tribute to his pivotal role in the development of correlated wavefunction approaches to quantitative ab initio description of quantum fluids, nuclear systems and condensed matter more generally. Highlights include his contributions to the formulation of Fermi hypernetted chain theory and correlated density matrix theory. Special attention is given to Ristig's seminal work of recent years, which has yielded rich insights into the interplay of exchange effects (arising from quantum statistics) and the strong interactions between constituent bosons or fermions.

Bernd Esser

Mark E. Casida

Karl Blum

Jhon Manuel Portella Delgado, Ankit Goel

This paper presents an online learning-based adaptive control framework for density-matrix tracking in a two-level Lindblad-Gorini-Kossakowski-Sudarshan (LGKS) quantum system, in which the feedback control law does not require prior knowledge of the system Hamiltonian or dissipative operators. The adaptive controller is based on a continuous-time formulation of retrospective cost adaptive control (RCAC). To preserve the geometric structure of the quantum-state evolution, an adaptive PID controller driven by Uhlmann's fidelity is employed. The proposed approach is validated in numerical simulations for both low-entropy and high-entropy density-tracking tasks, and robustness to measurement noise in the feedback path is investigated.

Karl Blum