Distinctive subdynamic features of bipartite systems

TL;DR

This paper explores the relationship between Green function and Kraus representation methods for analyzing bipartite systems, illustrating their application to the Jaynes-Cummings model and highlighting their unique insights into subdynamics and entanglement.

Contribution

It establishes a connection between two distinct techniques for studying bipartite systems and compares their effectiveness in revealing subdynamic features.

Findings

Relationship between Green function and Kraus methods established

Illustrative examples demonstrate effects of interaction and entanglement

Comparison highlights the strengths of each approach in subdynamics analysis

Abstract

There are several important bipartite systems of great interest in condensed matter physics and in quantum information science. In condensed matter systems, the subsystems are examined traditionally by using the Green function and mean-field-like methods based on the Heisenberg representation. In quantum information science, the subsystems are handled by composite density matrix, its marginals describing the subsystems, and the Kraus representation to elucidate the subsystem properties. In this work, a relationship is first established between the two techniques which appear to be distinct at first sight. This will be illustrated in detail by presenting the two methods in the case of the celebrated exactly soluable Jaynes - Cummings model (1963) of a two-state atom interacting with a one-mode quantized electromagnetic field. The dynamics of this system was treated in the Heisenberg representation by Ackerhalt and Rzazewski (1975). We present here the corresponding subdynamics using Kraus representation. A relationship between the two approaches is established and the relative merits of the two techniques are discussed in elucidating the distinctive features of the subdynamics. The striking effects of interaction and entanglement are made transparent in two illustrative examples: the transformations that manifest in non-interacting number and spin representations due to interactions in their respective subspaces.