Full Counting Statistics Of Stochastic Thermodynamics In A Coupled Quantum Dot Transport System

With the development of semiconductor processing technology,one can successfully fabricate nano-scale artificial structures.In the nano-system,the coherence length of the electron wave function is in an order of magnitude with the characteristic length of the system,and the wave-particle duality of electrons will be pretty obvious.Quantum dots is mesoscopic nanodevice with three dimensions limited below 100 nm.The movement of electrons in all directions within the quantum dot is restricted,then the quantum effect in this structure is immediately observable.Compared with single quantum dot system,coupled double quantum dots have more controllable structural parameters.In this paper,based on the Born-Markov approximation and combined with Full Counting Statistics approach,the General Quantum Master Equation(GQME)of the reduced system with counting field is derived,in the meantime,the counting statistical properties of particle and energy transport in the double quantum dots are studied.The effects of the secular approximation and the non-secular approximation on the transport properties are discussed,and the cumulants of particles and energy were researched.The main contents of this paper are as follows :The basic knowledge about the transport of mesoscopic systems and the development of quantum dots are briefly described in Chapter 1,including the introduction of quantum effects in quantum dot,the preparation process of quantum dots and the application of quantum dots,and the development of related transport theory.The second chapter mainly expounds the theory of Full Counting Statistics.In Chapter 3,we derived the quantum master equation of coupled double quantum dots under the Born-Markov approximation combined with the Full Counting Statistics,and obtain the Generalized Quantum Master Equation combined with the counting field.The matter currents and energy currents from the left and right junctions,as same as noise characteristics of particles and energy,are calculated by using the quantum master equation in the steady state.We find that the matter currents from the left and right junctions are equal,but the energy currents make difference.The net energy current is closely related to non-secular approximation and energy renormalization.Higher-order cumulants have the same result.We compared the situation under the secular approximation and found that the above results are unique to the case of non-secular approximation.In Chapter 4,we make a brief summary of this paper and an outlook for future work.