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Added by
Claude-Alain Pillet
Publication date
2014
fields
Physics
and research's language is
English
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In the independent electron approximation, the average (energy/charge/entropy) current flowing through a finite sample S connected to two electronic reservoirs can be computed by scattering theoretic arguments which lead to the famous Landauer-Buttiker formula. Another well known formula has been proposed by Thouless on the basis of a scaling argument. The Thouless formula relates the conductance of the sample to the width of the spectral bands of the infinite crystal obtained by periodic juxtaposition of S. In this spirit, we define Landauer-Buttiker crystalline currents by extending the Landauer-Buttiker formula to a setup where the sample S is replaced by a periodic structure whose unit cell is S. We argue that these crystalline currents are closely related to the Thouless currents. For example, the crystalline heat current is bounded above by the Thouless heat current, and this bound saturates iff the coupling between the reservoirs and the sample is reflectionless. Our analysis leads to a rigorous derivation of the Thouless formula from the first principles of quantum statistical mechanics.
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In this work, we model the zero-bias conductance for the four different DNA strands that were used in conductance measurement experiment [A. K. Mahapatro, K. J. Jeong, G. U. Lee, and D. B. Janes, Nanotechnology 18, 195202 (2007)]. Our approach consists of three elements: (i) ab initio calculations of DNA, (ii) Greens function approach for transport calculations, and (iii) the use of two parameters to determine the decoherence rates. We first study the role of the backbone. We find that the backbone can alter the coherent transmission significantly at some energy points by interacting with the bases, though the overall shape of the transmission stays similar for the two cases. More importantly, we find that the coherent electrical conductance is tremendously smaller than what the experiments measure. We consider DNA strands under a variety of different experimental conditions and show that even in the most ideal cases, the calculated coherent conductance is much smaller than the experimental conductance. To understand the reasons for this, we carefully look at the effect of decoherence. By including decoherence, we show that our model can rationalize the measured conductance of the four strands, both qualitatively and quantitatively. We find that the effect of decoherence on G:C base pairs is crucial in getting agreement with the experiments. However, the decoherence on G:C base pairs alone does not explain the experimental conductance in strands containing a number of A:T base pairs. Including decoherence on A:T base pairs is also essential. By fitting the experimental trends and magnitudes in the conductance of the four different DNA molecules, we estimate for the first time that the deocherence rate is 6 meV for G:C and 1.5 meV for A:T base pairs.
The quantum fluctuations of the entropy production for fermionic systems in the Landauer-Buttiker non-equilibrium steady state are investigated. The probability distribution, governing these fluctuations, is explicitly derived by means of quantum field theory methods and analysed in the zero frequency limit. It turns out that microscopic processes with positive, vanishing and negative entropy production occur in the system with non-vanishing probability. In spite of this fact, we show that all odd moments (in particular, the mean value of the entropy production) of the above distribution are non-negative. This result extends the second principle of thermodynamics to the quantum fluctuations of the entropy production in the Landauer-Buttiker state. The impact of the time reversal is also discussed.
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