This review deals with the nonequilibrium Green's function (NEGF) method applied to the problems of energy transport due to atomic vibrations (phonons), primarily for small junction systems. We present a pedagogical introduction to the subject, deriving some of the well-known results such as the Laudauer-like formula for heat current in ballistic systems. The main aim of the review is to build the machinery of the method so that it can be applied to other situations, which are not directly treated here. In addition to the above, we consider a number of applications of NEGF, not in routine model system calculations, but in a few new aspects showing the power and usefulness of the formalism. In particular, we discuss the problems of multiple leads, coupled left-right-lead system, and system without a center. We also apply the method to the problem of full counting statistics. In the case of nonlinear systems, we make general comments on the thermal expansion effect, phonon relaxation time, and a certain class of mean-field approximations. Lastly, we examine the relationship between NEGF, reduced density matrix, and master equation approaches to thermal transport.

We review studies of vibrational energy transfer in a molecular junction geometry, consisting of a molecule bridging two heat reservoirs, solids or large chemical compounds. This setup is of interest for applications in molecular electronics, thermoelectrics, and nanophononics, and for addressing basic questions in the theory of classical and quantum transport. Calculations show that system size, disorder, structure, dimensionality, internal anharmonicities, contact interaction, and quantum coherent effects are factors that combine to determine the predominant mechanism (ballistic/diffusive), effectiveness (poor/good), and functionality (linear/nonlinear) of thermal conduction at the nanoscale. We review recent experiments and relevant calculations of quantum heat transfer in molecular junctions. We recount the Landauer approach, appropriate for the study of elastic (harmonic) phononic transport, and outline techniques that incorporate molecular anharmonicities. Theoretical methods are described along with examples illustrating the challenge of reaching control over vibrational heat conduction in molecules.

No abstract

We derive an efficiency bound for continuous quantum heat engines absorbing heat from squeezed thermal reservoirs. Our approach relies on a full-counting statistics description of nonequilibrium transport and it is not limited to the framework of irreversible thermodynamics. Our result, a generalized Carnot efficiency bound, is valid beyond the small squeezing and high temperature limit. Our findings are embodied in a prototype three-terminal quantum photoelectric engine where a qubit converts heat absorbed from a squeezed thermal reservoir into electrical power. We demonstrate that in the quantum regime the efficiency can be greatly amplified by squeezing. From the fluctuation relation we further receive other operational measures in linear response, for example, the universal maximum power efficiency bound.

We study the statistical properties of charge and energy transport in electron conducting junctions with electron-phonon interactions, specifically, the thermoelectric efficiency and its fluctuations. The system comprises donor and acceptor electronic states, representing a two-site molecule or a double quantum dot system. Electron transfer between metals through the two molecular sites is coupled to a particular vibrational mode which is taken to be either harmonic or anharmonic-a truncated (twostate) spectrum. Considering these models we derive the cumulant generating function in steady state for charge and energy transfer, correct to second-order in the electron-phonon interaction, but exact to all orders in the metal-molecule coupling strength. This is achieved by using the nonequilibrium Green's function approach (harmonic mode) and a kinetic quantum master equation method (anharmonic mode). From the cumulant generating function we calculate the charge current and its noise and the large deviation function for the thermoelectric efficiency. We demonstrate that at large bias the charge current, differential conductance, and the current noise can identify energetic and structural properties of the junction. We further examine the operation of the junction as a thermoelectric engine and show that while the macroscopic thermoelectric efficiency is indifferent to the nature of the mode (harmonic or anharmonic), efficiency fluctuations do reflect this property.

Universal properties of the statistics of stochastic efficiency for mesoscopic time-reversal symmetry broken energy transducers are revealed in the Gaussian approximation. We also discuss how the second law of thermodynamics restricts the statistics of stochastic efficiency. The tight-coupling limit becomes unfavorable, characterized by an infinitely broad distribution of efficiency at all times, when time-reversal symmetry breaking leads to an asymmetric Onsager response matrix. The underlying physics is demonstrated through the quantum Hall effect and further elaborated in a triple-quantum-dot three-terminal thermoelectric engine.

We use the fundamental nonequilibrium steady state fluctuation symmetry and derive a condition on the validity of the thermodynamic uncertainty relation (TUR) in thermal transport problems, classical or quantum alike. We test this condition and study the breakdown of the TUR in different thermal transport junctions of bosonic and electronic degrees of freedom. First, we prove that the TUR is valid in harmonic oscillator junctions. In contrast, in the nonequilibrium spin-boson model, which realizes many-body effects, it is satisfied in the Markovian limit, but violations arise as we tune (reduce) the cutoff frequency of the thermal baths, thus observing non-Markovian dynamics. Finally, we consider heat transport by noninteracting electrons in a tight-binding chain model. Here we show that the TUR is feasibly violated by tuning e.g. the hybridization energy of the chain to the metal leads. These results manifest that the validity of the TUR relies on the statistics of the participating carriers, their interaction, and the nature of their couplings to the macroscopic contacts (metal electrodes, phonon baths).

We demonstrate that a quantum absorption refrigerator (QAR) can be realized from the smallest quantum system, a qubit, by coupling it in a non-additive (strong) manner to three heat baths. This function is un-attainable for the qubit model under the weak system-bath coupling limit, when the dissipation is additive. In an optimal design, the reservoirs are engineered and characterized by a single frequency component. We then obtain closed expressions for the cooling window and refrigeration efficiency, as well as bounds for the maximal cooling efficiency and the efficiency at maximal power. Our results agree with macroscopic designs and with three-level models for QARs, which are based on the weak system-bath coupling assumption. Beyond the optimal limit, we show with analytical calculations and numerical simulations that the cooling efficiency varies in a non-universal manner with model parameters. Our work demonstrates that strongly-coupled quantum machines can exhibit function that is un-attainable under the weak system-bath coupling assumption.