To investigate frequency-dependent current noise (FDCN) in open quantum systems at steady states, we present a theory which combines Markovian quantum master equations with a finite time full counting statistics. Our formulation of the FDCN generalizes previous zero-frequency expressions and can be viewed as an application of MacDonald’s formula for electron transport to heat transfer. As a demonstration, we consider the paradigmatic example of quantum heat transfer in the context of a non-equilibrium spin-boson model. We adopt a recently developed polaron-transformed Redfield equation which allows us to accurately investigate heat transfer with arbitrary system-reservoir coupling strength, arbitrary values of spin bias, and temperature differences. We observe a turn-over of FDCN in the intermediate coupling regimes, similar to the zero-frequency case. We find that the FDCN with varying coupling strengths or bias displays a universal Lorentzian-shape scaling form in the weak coupling regime, and a white noise spectrum emerges with zero bias in the strong coupling regime due to distinctive spin dynamics. We also find that the bias can suppress the FDCN in the strong coupling regime, in contrast to its zero-frequency counterpart which is insensitive to bias changes. Furthermore, we utilize the Saito-Utsumi relation as a benchmark to validate our theory and study the impact of temperature differences at finite frequencies. Together, our results provide detailed dissections of the finite time fluctuation of heat current in open quantum systems.
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21 June 2018
Research Article|
June 20 2018
Frequency-dependent current noise in quantum heat transfer: A unified polaron calculation
Junjie Liu
;
Junjie Liu
1
Singapore-MIT Alliance for Research and Technology (SMART) Center
, 1 CREATE Way, Singapore 138602, Singapore
2
Department of Chemistry, Massachusetts Institute of Technology
, 77 Massachusetts Avenue, Cambridge, Massachusetts 02139, USA
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Chang-Yu Hsieh;
Chang-Yu Hsieh
1
Singapore-MIT Alliance for Research and Technology (SMART) Center
, 1 CREATE Way, Singapore 138602, Singapore
2
Department of Chemistry, Massachusetts Institute of Technology
, 77 Massachusetts Avenue, Cambridge, Massachusetts 02139, USA
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Changqin Wu;
Changqin Wu
3
State Key Laboratory of Surface Physics and Department of Physics, Fudan University
, Shanghai 200433, China
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Jianshu Cao
Jianshu Cao
1
Singapore-MIT Alliance for Research and Technology (SMART) Center
, 1 CREATE Way, Singapore 138602, Singapore
2
Department of Chemistry, Massachusetts Institute of Technology
, 77 Massachusetts Avenue, Cambridge, Massachusetts 02139, USA
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J. Chem. Phys. 148, 234104 (2018)
Article history
Received:
February 09 2018
Accepted:
May 28 2018
Citation
Junjie Liu, Chang-Yu Hsieh, Changqin Wu, Jianshu Cao; Frequency-dependent current noise in quantum heat transfer: A unified polaron calculation. J. Chem. Phys. 21 June 2018; 148 (23): 234104. https://doi.org/10.1063/1.5025367
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