The cycle model of a regenerative quantum heat engine working with many noninteracting harmonic oscillators is established. The cycle consists of two isothermal and two constant-frequency processes. The performance of the cycle is investigated, based on the quantum master equation and semigroup approach. The inherent regenerative losses in the two constant-frequency processes are calculated. The expressions of several important performance parameters such as the efficiency, power output, and rate of the entropy production are derived for several interesting cases. Especially, the optimal performance of the cycle in high-temperature limit is discussed in detail. The maximum power output and the corresponding parameters are calculated. The optimal region of the efficiency and the optimal ranges of the temperatures of the working substance in the two isothermal processes are determined.

We model a Brownian heat engine as a Brownian particle that hops in a periodic ratchet potential where the ratchet potential is coupled with a linearly decreasing background temperature. It is shown that the efficiency of such Brownian heat engine is far from Carnot efficiency even at quaistatic limit. At quasistatic limit, the efficiency of the heat engine approaches the efficiency of endoreversible engine η = 1 − Tc/T h [23]. On the other hand, the maximum power efficiency of the engine approaches η M AX = 1 − (Tc/T h) 1 4. Moreover, the dependence of the current as well as the efficiency on the model parameters is explored analytically by omitting the heat exchange via the kinetic energy. In this case we show that the optimized efficiency always lies between the efficiently at quaistatic limit and the efficiency at maximum power. On the other hand, the efficiency at maximum power is always less than the optimized efficiency since the fast motion of the particle comes at the expense of the energy cost. If one includes the heat exchange at the boundary of the heat baths, the efficiency of the engine becomes much smaller than the Carnot efficiency. In addition, the dependence for the coefficient of performance of the refrigerator on the model parameters is explored by including the heat exchange via the potential and kinetic energy. We show that such a Brownian heat engine has a higher performance when acting as a refrigerator than when operating as a device subjected to a piecewise constant temperature. The role of time on the performance of the motor is also explored via numerical simulations. Our numerical results depict that the time t as well as the external load dictate the direction of the particle velocity. Moreover the performance of the heat engine improves with time. At large t (steady state),the velocity, the efficiency and the coefficient of performance of the refrigerator attain their maximum value.

A quantum-dot thermal transistor consisting of three Coulomb-coupled quantum dots coupled to respective electronic reservoirs by tunnel contacts is established. The heat flows through the collector and emitter can be controlled by the temperature of the base. It is found that a small change in the base heat flow can induce a large heat flow change in the collector and emitter. The huge amplification factor can be obtained by optimizing the Coulomb interaction between the collector and the emitter or by decreasing the energy-dependent tunneling rate at the base. The proposed quantum-dot thermal transistor may open up potential applications in low-temperature solid-state thermal circuits at the nanoscale. I. INTRODUCTIONControlling heat flow at the nanoscale has attracted significant attention because of its fundamental and potential applications. 1-3 The thermal diode effect and negative differential thermal resistance (NDTR) are two most important features for building the basic components of functional thermal devices, which are the key tools for the implementation of solid-state thermal circuits. 3,4 The first model of a thermal rectifier/diode was proposed by controlling the heat conduction in one dimensional nonlinear lattice. 5 Based on different microscopic mechanisms, a very significant rectifying effect was exhibited and the concept of NDTR was also proposed in the subsequent works. 6,7 In recent years, the thermal diode effect and NDTR have been extensively studied in the different systems including quantum-dot systems, [8][9][10][11] metal-dielectric interfaces, 12 metal or superconductor systems, [13][14][15][16] quantum Hall conductors, 17 a) Electronic mail: jcchen@xmu.edu.cn 2 / 14 and spin quantum systems. 18 One of the particularly interesting tasks is to further build and implement a thermal transistor, which is analogous to an electronic transistor and can control the heat flows at the collector and emitter by small changes in the temperature or the heat flow at the base. Since Li et al. put forward the first theoretical proposal for a thermal transistor, 7,19 several proposals have been given to design other types of thermal transistors, such as superconductor-normal-metal thermal transistors, 20 near-field thermal transistors, 21 far-field thermal transistors, 22-24 and quantum thermal transistors. 25 Moreover, new concepts for thermal devices such as thermal logical gates 26 and thermal memories 27-29 have also been proposed and demonstrated. In recent years, the electron and heat transport properties of Coulomb-coupled quantum-dot system have been investigated in detail in the thermoelectric generators 30,31 and refrigerators. 32 Moreover, recent experiments have shown that many new applications for Coulomb-coupled quantum-dot system including rectification, 33-35 logical stochastic resonance, 36 and thermal gating 37 can be realized by the voltage fluctuation or thermal fluctuation to control and manage the charge current. Ruokola et al. introduced a single-electron thermal diode consisting...