Calculating work in adiabatic two-level quantum Markovian master equations: A characteristic function method

We present a characteristic function method to calculate the probability density functions of the inclusive work in adiabatic two-level quantum Markovian master equations. These systems are steered by some slowly varying parameters and the dissipations may depend on time. Our theory is based on the interpretation of the quantum jump for the master equations. In addition to the calculation, we also find that the fluctuation properties of the work can be described by the symmetry of the characteristic functions, which is exactly the same as in the case of isolated systems. A periodically driven two-level model is used to demonstrate the method.

Figure 1

A quantum jump trajectory of the forward adiabatic QMME and its time reversal. The arrows indicate the directions of time. The symbols $\pm$ and 0 represent the $A_{\pm }$ and $A_0$ jumps, respectively.

Figure 2

The PDFs of the inclusive work for the TLS (37). The bars are calculated by simulating the quantum trajectories, while the solid bold lines are obtained by the CF method. The unit of work $W$ is $\omega$. In these panels the thin dashed lines at zero positions are guides for the eyes.