Stochastic model of noise for a quantum thermal transistor

Our focus in this investigation lies in developing a noise model for a quantum thermal transistor model inspired by its electronic counterpart, with the primary aim of establishing a platform for constructing analogous models. Previous studies on coupled two-level systems-based thermal transistors were focused on their average energy exchange. In this paper, we shift our attention to exploring the stochastic behavior of such thermal transistors due to the disturbances caused to their environment, such as continuous measurements. In the literature, the master equation for the transistor model is derived using the reduced dynamics method. This way, it masks the study of the stochastic nature of the energy flows in the system due to disturbances to the environment. In this paper, we describe a quantum trajectory under measurement theory whose ensemble average unravels the master equation for a quantum thermal transistor. This allows us to analyze the fluctuations and noise levels in the transistor model with greater detail. Then, we produce a numerical solution for the transistor dynamics based on Euler-Maruyama approximation. This helps to establish a model for the thermal transistor, drawing parallels to the small-signal/noise model in an electronic transistor. We define two parameters, thermal conductance and output thermal resistance, to describe the small signal-like model for the thermal transistor. Through these investigations, we seek to gain insights that can help design advanced heat management devices at the quantum level.