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AQP Seminar: A non-equilibrium Green's function approach to energy transfer in many-body quantum systems

Aalto Quantum Physics Seminar (Nanotalo). Speaker: Dr. N. Lo Gullo (QTF Centre of Excellence, Turku)

The non-equilibrium Green's function (NEGF) formalism is a powerful microscopic theory which allows to account for many-body interactions and coupling to external reservoirs on the same footing and in a consistent way. A major drawback of this approach is that the equation of motion in real time are computationally very demanding. This is the reason which prevented the extensive application of this approach up until the appearance of supercomputers.

I will shortly present the general ideas behind this approach and I will then move to discuss the main features of the numerical techniques we employ to circumvent the heavy computational requirements .

After this introduction on the NEGFs I will show how, in the context of this approach, it is possible to derive an expression for the energy current flowing through an interacting many-body system.

This expression can be seen as the time-dependent version of the Meir-Wingreen formula for the steady state charge current through an interacting system.

I will show that this expression for the energy current is consistent with the conservation of the total energy at any time of the evolution of the system, even in the transient. This allows to compute the energy flowing through an interacting region away from stationarity and thus opens the door to the exploration of energy transfer in driven systems. I will show an application of our expression to the single-impurity Anderson model (SIAM) in the Kondo regime.