Non-Markovian current-current two-time correlation functions and noise spectra in quantum transport systems
Chung-Chin Jian1*, Hsi-Sheng Goan1
1Department of Physics, National Taiwan University, Taipei, Taiwan
* presenting author:Chung-Chin Jian,

Two-time correlation functions (CF’s) of the electric currents through nanostructure devices are important in the study of the transport properties of current fluctuations and noise spectra. The MacDonald’s formula has been widely applied to evaluate the stationary-state current noise spectra in both Markovian and non-Markovian cases [1-4]. The convenience of the MacDonald’s formula is that it contains quantities with only single-time expectation values, and the memory effects prior to the stationary state is obtained from the inhomogeneous term [3,4] which vanish in the Markovian case. But we think the non-Markovian noise spectra calculated by the MacDonald’s formula in the literature may not be valid even when the inhomogeneous term is included and considered. Here, we develop a correct method to calculate the non-Markovian current-current two-time CF's and thus the finite-frequency noise power spectra in the weak system-environment coupling regime. This method of the perturbative quantum master equation approach properly takes into account the cross correlations between two different time regions is based on the similar treatment in our previous work about the non-Markovian two-time CF’s of system operators [5]. We illustrate our results through a simple example of the noise spectrum of electron tunneling through a single quantum dot.
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[3]. D. Marcos, C. Emary, T. Brandes, and R. Aguado, Phys. Rev. B 83, 125426 (2011).
[4]. J.-S. Jin, X.-Q. Li, M. Luo, and Y.-J. Yan, J. Appl. Phys. 109, 053704 (2011).
[5]. H.-S. Goan, P.-W. Chen, and C.-C. Jian , J. Chem. Phys. 134, 124112 (2011).

Keywords: Non-Markovian current-current two-time correlation functions , Noise spectra, MacDonald’s formula, Memory effects , Quantum master equation