Abstract
We study the statistics of thermal energy transfer in the nonequilibrium (two-bath) spin-boson model. This quantum many-body impurity system serves as a canonical model for quantum energy transport. Our method makes use of the Majorana fermion representation for the spin operators, in combination with the Keldysh nonequilibrium Green's function approach. We derive an analytical expression for the cumulant generating function of the model in the steady state limit, and show that it satisfies the Gallavotti–Cohen fluctuation symmetry. We obtain analytical expressions for the heat current and its noise, valid beyond the sequential and the co-tunneling regimes. Our results satisfy the quantum mechanical bound for heat current in interacting nanojunctions. Results are compared with other approximate theories, as well as with a non-interacting model, a fully harmonic thermal junction.
Highlights
The spin-boson (SB) model comprises a two-state system interacting with a dissipative thermal environment, a collection of harmonic modes
We focus on the following questions regarding the operation of the nonequilibrium spin-boson (NESB) nanojunction: (i) How are the current and noise influenced by the system-bath coupling strength? (Fig. 1 and 3). (ii) What are the signatures of operation far from equilibrium, as opposed to the linear response regime? (Fig. 1 and 3) (iii) What is the temperature dependence of the heat current? (Fig. 2) (iv) Thermal diode effect: Can we enhance this effect if we go beyond the weak spin-bath coupling? (3) (v) What is the relation between the Majorana-based treatment and other techniques? (Figs. 1-3)
In accord with previous results, we find that Redfield equation dramatically overestimates the current and the noise in comparison to the Majorana and noninteracting blip approximation (NIBA) results
Summary
The spin-boson (SB) model comprises a two-state system (spin) interacting with a dissipative thermal environment, a collection of harmonic modes. The model has found diverse applications in condensed phases physics, chemical dynamics, and quantum optics It offers a rich platform for studying complex physical processes such as dissipative spin-dynamics [1], charge and energy transfer phenomena in condensed phases [1, 3], Kondo physics [2], and decoherence dynamics of superconducting qubits [2, 4]. In such applications, the spin system can represent donor-acceptor charge states, a magnetic impurity [1], or a truncated harmonic spectrum, mimicking an anharmonic oscillator [5, 6]. The bosonic bath may stand for a collection of lattice phonons, electromagnetic modes, bound electron-hole pairs, and other composite bosonic excitations [1, 2]
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