We investigate the time evolution of the thermopower in a vibrating quantum dot suddenly shifted into the Kondo regime via a gate voltage by adopting the time-dependent non-crossing approximation and linear response Onsager relations. Behaviour of the instantaneous thermopower is studied for a range of temperatures both in zero and strong electron-phonon coupling. We argue that inverse of the saturation value of decay time of thermopower to its steady state value might be an alternative tool in determination of the Kondo temperature and the value of the electron-phonon coupling strength. Keywords: A. Quantum dots; D. TunnelingInvestigation of time-dependent electron transport in single electron transistors has gained considerable traction lately as a result of tremendous advances in the burgeoning field of nanotechnology and their perceived potential to replace MOSFET transistors 1 one day. Development of quantum computers 2 and single electron guns 3 are expected to benefit from advances in detection of electrons in real time too 4 .Transient current ensuing after sudden shifting of the gate or bias voltage 5,6,8 displays different time scales 9,10 . For an asymmetrically coupled system, interference between the Kondo resonance and the sharp features in the contacts' density of states gives rise to oscillations in the long time scale 11 . Modeling the contacts' density of states in a realistic fashion via ab initio calculations yielded accurate predictions about transient current 12,13 .Measurement of thermopower (Seebeck coefficient) S can provide additional insight into transport experiments because its sign is a valuable tool to determine the alignment of orbitals of the impurity with respect to the Fermi levels of the contacts. To this end, significant progress has been achieved in performing thermoelectric measurements in molecular junctions [14][15][16][17] .Theoretical studies focused on incorporating strong correlation effects into this prototype. Kondo effect, arising from a hybridization between the net spin localized within the impurity and the electrons in the contacts, is a prime example of strong electronic correlations. Schemes employing Ng's ansatz 18 and Wilson's numerical renormalization group 19 both found that the sign of the thermopower can be adjusted by tuning the energy level of the quantum dot in the presence of Kondo correlations. When the electrodes are ferromagnetic, it was found that the thermopower is suppressed at low temperatures in parallel configuration and asymmetrically coupled antiparallel configuration 20 .Nevertheless, all of the aforementioned studies only took into account the steady state behaviour of thermoelectric transport and there was very little understanding of the temporal evolution of thermopower until now. Indeed, a recent work made the first attempt to elucidate the time-dependent behaviour of the Seebeck coefficient for a noninteracting system 21 . In this paper, we will take a step forward and study the transient response of thermopower for an interacting q...
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