Kinetic approach to the nuclear-spin polaron formation

Under optical cooling of nuclei, a strongly correlated nuclear-spin polaron state can form in semiconductor nanostructures with localized charge carriers due to the strong hyperfine interaction of the localized electron spin with the surrounding nuclear spins. Here we develop a kinetic-equation formalism describing the nuclear-spin polaron formation. We present a derivation of the kinetic equations for an electron-nuclear spin system coupled to reservoirs of different electron and nuclear spin temperatures which generate the exact thermodynamic steady state for equal temperatures independent of the system size. We illustrate our approach using the analytical solution of the central spin model in the limit of an Ising form of the hyperfine coupling. For homogeneous hyperfine coupling constants, i.e., the box model, the model is reduced to an analytically solvable form. Based on the analysis of the nuclear-spin distribution function and the electron-nuclear spin correlators, we derive a relation between the electron and nuclear spin temperatures, where the correlated nuclear-spin polaron state is formed. In the limit of large nuclear baths, this temperature line coincides with the critical temperature of the mean-field theory for polaron formation. The criteria of the polaron formation in a finite-size system are discussed. We demonstrate that the system's behavior at the transition temperature does not depend on details of the hyperfine-coupling distribution function but only on the effective number of coupled bath spins. In addition, the kinetic equations enable the analysis of the temporal formation of the nuclear-polaron state, where we find the build-up process predominated by the nuclear spin-flip dynamics.Comment: 11 pages, 5 figure

Scenario-based modeling in industrial information systems

This manuscript addresses the creation of scenario-based models to reason about the behavior of existing industrial information systems. In our approach the system behavior is modeled in two steps that gradually introduce detail and formality. This manuscript addresses the first step, where text-based descriptions, in the form of structured rules, are used to specify how the system is or should be regulated. Those rules can be used to create behavioral snapshots, which are collections of scenario-based descriptions that represent different instances of the system behavior. Snapshots are specified in an intuitive and graphical notation that considers the elements from the problem domain and permit designers to discuss and validate the externally observable behavior, together with the domain experts. In the second step (not fully covered in this manuscript), the system behavior is formalized with an executable model. This formal model, which in our approach is specified using the Colored Petri Net (CP-nets) language, allows the system internal behavior to be animated, simulated, and optimized. The insights gained by experimenting with the formal model can be subsequently used for reengineering the existing system

The SEA Language for System Engineering and Animation

This paper describes the hierarchical, graphical SEA Language. The SE