2 research outputs found
Quantum Pontryagin Principle under Continuous Measurements and Feedback
In this note we develop the theory of the quantum Pontryagin principle for
continuous measurements and feedback. The analysis is carried out under the
assumption of compatible events in the output channel. The plant is a quantum
system, which generally is in a mixed state, coupled to a continuous
measurement channel. The Pontryagin Maximum Principle is derived in both the
Schr\"{o}dinger picture and Heisenberg picture, in particular in statistical
moment coordinates. To avoid solving stochastic equations we derive a LQG
scheme which is more suitable for control purposes.Comment: This paper has been accepted in Journal of Mathematical Physic
Introduction to Quantum Thermodynamics: History and Prospects
Quantum Thermodynamics is a continuous dialogue between two independent
theories: Thermodynamics and Quantum Mechanics. Whenever the two theories
addressed the same phenomena new insight has emerged. We follow the dialogue
from equilibrium Quantum Thermodynamics and the notion of entropy and entropy
inequalities which are the base of the II-law. Dynamical considerations lead to
non-equilibrium thermodynamics of quantum Open Systems. The central part played
by completely positive maps is discussed leading to the
Gorini-Kossakowski-Lindblad-Sudarshan GKLS equation. We address the connection
to thermodynamics through the system-bath weak-coupling-limit WCL leading to
dynamical versions of the I-law. The dialogue has developed through the
analysis of quantum engines and refrigerators. Reciprocating and continuous
engines are discussed. The autonomous quantum absorption refrigerator is
employed to illustrate the III-law. Finally, we describe some open questions
and perspectives