Open-System Many-Body Approaches

No quantum system is isolated. For example, the interplay between an electronic transition and surrounding phononic modes results in scattering phenoma that broaden, decohere, and ultimately thermalize any excitation. It is now far from trivial to describe a complex many-body system that is subject to interaction with such a bath. We tackle this challenge by stacking density matrix hierachies. The Hierarchical Equations of Motion (HEOM), typically described the entire system at once, are traced onto the few-body domain of individual electrons or excitations and approximations for this reduced density matrix hiearchy, known as BBGKY, are enforced. This approach is extremely flexible and powerful. It captures correlation and entanglement between emitters and photons reasonably good while being often barely more expensive to calculate than classical mean-field approaches. Finally, our approach can be used to simulate many-body electronic systems, such as Hubbard or molecular systems, subject to structured baths in a rigorous fashion.

Starting point for the interested reader: (Müller et al., 2024)