Publications Repository - Gdańsk University of Technology

The Hamiltonians of the considered bi-partite systems are of the form $$ H_{S,R} = H_S /times 1_R + Q_{S} /times M_R + 1_S /times H_R $$ Subindex $S$ corresponds to the observed system and $R$ to the reservoir (the enviroment of $S$). Two classes of systems are distinguished: the discrete-continuous (D-C) and the continuous-continuous (C-C) models. In both cases resevoir operators $M_R$ and $H_R$ are of continuous spectrum type. In D-C models the operators $H_S$ and $Q_S$ possess discrete spectra. In C-C models, the operators $H_S$ and $Q_S$ are of continuous spectrum type. In each case of our examples the semigroup property for the reduced dynamics of system $S$ is obtained under particular circumstances, depending on the diagonal of the density matrix of the reference state for $R$. In D-C models, due to discrete spectrum of $Q_S$, the semigroup property of the reduced dynamics of the reservoir $R$ is shown to be impossible, unless the coupling to $S$ is trivial.

Authors

• Małgorzata Bodzioch link open in new tab ,
• dr hab. inż. Joachim Domsta link open in new tab