Quantum thermal transistors: Operation characteristics in steady state versus transient regimes

We show that a quantum thermal transistor can also cause the transistor effect - where one out of three terminals can control the flow of heat current in the other two - with good amplification properties in the transient regime for certain paradigmatic initial states. We find three broad classes of transient quantum thermal transistors - the first having a smaller amplification than the steady state quantum thermal transistor, the second with better amplification but a smaller operating region in terms of temperature, and the third that gives higher amplification with a larger operating region. The last type is of particular interest as it also operates in the region where the steady state thermal transistors lose the transistor effect. We discuss in some detail certain initial states for which the cases of necessarily transient transistors arise. We analyze the time variation of the amplification factor of transient thermal transistors and estimate the preferable time and duration for which they can work efficiently. Cumulative studies of the differences in magnitudes of the amplifications of heat currents at the non-base terminals of the quantum thermal transistor, first with respect to the base-terminal temperature and next with time, are also presented.