Ebers–Moll model inspired equivalent circuit for quantum thermal transistors

Abstract

The widespread success of electronic transistors is partly due to their ability to be modeled using equivalent circuits, which not only enables detailed analysis and efficient design but also provides greater insight for designers, facilitating the development of complex electronic systems. The Ebers–Moll model, for example, is a widely used large-signal equivalent circuit that replicates the operational characteristics of bipolar junction transistors. Similar to electronic transistors, research on quantum thermal transistors has gained considerable attention in recent years; however, minimal focus has been placed on developing equivalent circuit representations. Drawing inspiration from equivalent models of electronic transistors, our study proposes an equivalent model for a quantum thermal transistor built on a strongly coupled qubit–qutrit–qubit architecture. This configuration allows replication of its transistor behavior using a diode-based equivalent model, leveraging its property of splitting the qutrit into two individual qubits. The proposed quantum thermal diode-based equivalent model closely mirrors the diode-based representation of an electronic transistor. Using frameworks of open quantum systems and the quantum Markovian master equation, along with the Born approximation and rotating wave approximation, we conduct a comprehensive analysis and comparison of our quantum thermal diode-based equivalent model with an established quantum thermal transistor model. Furthermore, we discuss the intrinsic internal coupling between the two diodes and determine the optimum coupling strength necessary for efficient heat amplification. This equivalent model provides greater insight into the analysis of quantum thermal transistors and significantly contributes to the advancement of nanoscale thermal circuit designs.