We demonstrate that a thermal transistor can be made up with a quantum system of three interacting subsystems, coupled to a thermal reservoir each. This thermal transistor is analogous to an electronic bipolar one with the ability to control the thermal currents at the collector and at the emitter with the imposed thermal current at the base. This is achieved by determining the heat fluxes by means of the strong-coupling formalism. For the case of three interacting spins, in which one of them is coupled to the other two, that are not directly coupled, it is shown that high amplification can be obtained in a wide range of energy parameters and temperatures. The proposed quantum transistor could, in principle, be used to develop devices such as a thermal modulator and a thermal amplifier in nanosystems.Managing and harvesting wasted heat in energy processes is becoming a big issue due to the limited energy resources and to the constraints of global warming. Heat can be transported by fluids and radiation, as well as guided in good conductors or devices, such as heat pipes. However, there exists no device that can manage the switching or heat amplification, as is the case in electricity.In the last century, electricity management and its use for logical operations have been realized through the development of two components: the diode [1] and the transistor [2]. By analogy, one can, of course, envisage developing similar thermal devices that could make the thermal control easier. Thus, one of the goals of recent researches in thermal science has been focused on thermal rectifiers, i.e. components which exhibit an asymmetric flux when the temperatures at their ends are inverted. Thermal rectifiers have been designed for phononic [3][4][5][6][7][8][9][10][11][12][13] and electronic [12,14] thermal transport, which has led to the conception and modeling of thermal transistors [15,16]. In the framework of thermal radiation, rectifiers have been the subject of numerous theoretical works, both in near field [17][18][19] and far field [20][21][22][23][24]. The most efficient of these devices have involved phase change materials, such as thermochrome [25] materials like VO 2 [26,27]. This has led to the design of radiative thermal transistors based on phase change materials too [28,29].The last two decades have also seen the emergence of individual quantum systems, such as classical atoms [30,31] or artificial ones, as is the case of quantum dots [32,33], which have been proposed to develop photon rectifiers [34][35][36], transistors [37,38] or even electrically controlled phonon transistors [39]. Moreover, given that quantum systems are always coupled to their environment, in particular to a thermal bath, the question of how heat is transferred through a set of quantum systems in interaction naturally arises [40][41][42] and has led to several studies reporting thermal rectification [43][44][45][46].The goal of this Letter is to demonstrate that a thermal transistor can be achieved with a quantum system, made of 3 two lev...

Abstract. Understanding and controlling vibrations in condensed matter is emerging as an essential necessity both at fundamental level and for the development of a broad variety of technological applications. Intelligent design of the band structure and transport properties of phonons at the nanoscale and of their interactions with electrons and photons impact the efficiency of nanoelectronic systems and thermoelectric materials, permit the exploration of quantum phenomena with micro-and nanoscale resonators, and provide new tools for spectroscopy and imaging. In this colloquium we assess the state of the art of nanophononics, describing the recent achievements and the open challenges in nanoscale heat transport, coherent phonon generation and exploitation, and in nano-and optomechanics. We also underline the links among the diverse communities involved in the study of nanoscale phonons, pointing out the common goals and opportunities.