Energia, calor e trabalho em sistemas quânticos abertos com dinâmica markoviana

Abstract

We consider the accurate investigation of the energy current and its components, heat and work, in some boundary driven quantum spin systems. The expressions for the currents, as well as the associated Lindblad master equation, are obtained via a repeated interaction scheme. For the XXZ chain we present cases in which different compositions of heat and work currents, obtained via the repeated interaction protocol, lead to the same energy current, which may be obtained via the Lindblad master equation, i.e., to obtain information about the heat flow in the system and about the work done on the system we must go beyond the Lindblad equation. In addition, we exhibit situations in which the XXZ chain presents rectification and situations in which it can operate in different thermodynamic regimes: refrigerator, thermal engine and heater. We also consider alternative definitions of the internal energy of open quantum systems that lead to different definitions of heat and work inserted in the system. We show that, for a certain class of definitions, the information about the energy flow obtained by the Lindblad equation is the same information obtained by the repeated interactions protocol regardless of which definition of internal energy is used. Despite this, only through the Lindblad equation it is not possible to distinguish heat and work inserted in the system. Our findings make clear that to talk about heat in these boundary driven spin quantum systems we must go beyond an investigation involving only the Lindblad master equation.