Short-time dynamics of molecular junctions after projective measurement

Abstract

In this work, we study the short time dynamics of a molecular junction described by AndersonHolstein model using full-counting statistics after projective measurement. The coupling between the central quantum dot (QD) and two leads was turned on at remote past and the system is evolved to steady state at time t = 0, when we perform the projective measurement in one of the lead. Generating function for the charge transfer is expressed as a Fredholm determinant in terms of Keldysh nonequilibrium Green's function in the time domain. It is found that the current is not constant at short times indicating that the measurement does perturb the system. We numerically compare the current behaviors after the projective measurement with those in the transient regime where the subsystems are connected at t = 0. The universal scaling for high-order cumulants is observed for the case with zero QD occupation due to the unidirectional transport at short times. The influences of electron-phonon interaction on short time dynamics of electric current, shot noise and differential conductance are analyzed.

Numerically exact full counting statistics of the nonequilibrium Anderson impurity model

“…Despite this flurry of theoretical activity, computing the FCS for generic interacting fermionic systems has so far proven to be challenging. In noninteracting systems, there now exist robust approaches to the study of both steady state and transient FCS, including an appealing coherent state path integral nonequilibrium Green's function formalism (PI-NEGF) [45,[77][78][79] which can be perturbatively extended to interacting cases [79][80][81]. Exact results are available for steady state FCS and noise characteristics of the AIM in the Fermi liquid regime and at the Toulouse point [22,23,[82][83][84][85].…”

Full counting statistics of phonon transport in disordered systems

“…Since the phonon current along is not enough to fully characterize phonon transport properties, we need higher order cumulants or moments of the phonon current operator and the average value is simply the first order cumulant. Full counting statistics (FCS), which has been widely used in transport study such as energy current 27,28 and transient dynamics 29,30 , is suitable for evaluating high-order cumulants and moments. Different from the previous work 19 which focused on the transmission coefficient cumulants, we will show that the transmission moments will give more precise results.…”

Transient dynamics in interacting nanojunctions within self-consistent perturbation theory

“…The most interesting and general coherentinteracting regime constitutes a great theoretical challenge. This regime has been addressed using several complementary approaches: diagrammatic techniques [33][34][35][36][37][38][39][40][41][42][43][44][45][46][47], quantum Monte-Carlo (MC) [48][49][50][51][52][53][54][55], timedependent NRG [56][57][58][59][60][61][62][63], time-dependent DFT [64][65][66][67][68][69][70] among others [71][72][73][74][75].However, all of these techniques as they are actually implemented have some limitations. For instance, numerically exact methods like quantum MC are strongly time-consuming, require finite temperature and typically do not allow to reach long time scales.…”