Time-optimal processes for interacting spin systems

Abstract

Reversible adiabatic processes connecting thermal equilibrium states are usually considered to be infinitely slow. Recently, fast reversible adiabatic processes for quantum systems have been discussed. Here we present time-optimal processes for a paradigmatic ensemble of two interacting spin-1 2 systems in an external magnetic field, which previously had been employed as working fluid in a quantum refrigerator. These processes are realized by appropriate bang-bang or quasi-bang-bang controls of the external magnetic field. Explicit control protocols including the necessary times for a transition connecting thermal equilibrium states depending on the limiting conditions on the magnetic field strength are presented.

Quantum Thermodynamics: A Dynamical Viewpoint

“…This possibility, which relies on special dynamical symmetries, has been termed shortcut to adiabaticity [32,[40][41][42][43][44]132]. The idea is to optimize the scheduling function, f (t), of the control,Ĥ C (t) =V C f (t), in such a way that in the shortest time, the frictionless transformation from an initial value of the control function to a final value is achieved.…”

Universal features in the efficiency at maximal work of hot quantum Otto engines

“…In order to have the same population in the beginning and at the end of the adiabatic evolution strokes a certain protocol must be applied. Using the optimal protocol in [19], the minimal time for the adiabatic step is proportional to…”

“…|Ec| (to simplify (24) in [19] we considered the limit ω f, ω i ≪ j). Thus, for the engine to operate at the minimal possible time (e.g to maximize the power) the constraint is…”

Finite-time availability in a quantum system

“…This leads to t P (A P ) which can then readily be inverted to obtain the originally desired result. The advantage of the second approach is that the ensuing control problem is very similar to the one solved in [19] to find the minimal time needed to extract the full reversible availability A P (t P = ∞) = A P (t FEAT ) = A FEAT .…”