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postgraduate thesis: Investigations of timedependent quantum transport properties in nanoscale structures
Title  Investigations of timedependent quantum transport properties in nanoscale structures 

Authors  
Advisors  Advisor(s):Wang, J 
Issue Date  2017 
Publisher  The University of Hong Kong (Pokfulam, Hong Kong) 
Citation  Yuan, J. [袁江涛]. (2017). Investigations of timedependent quantum transport properties in nanoscale structures. (Thesis). University of Hong Kong, Pokfulam, Hong Kong SAR. 
Abstract  In this thesis, certain aspects of timedependent quantum transport properties in nanoscale structures are investigated using the nonequilibrium Green’s function(NEGF). For the transient behaviors of the electric current and heat current after a quantum quench, the exact analytical solution beyond the wide band limit (WBL) is obtained for the first time which paves a way to simulate realistic physical systems. The timedependent thermoelectric effects are evaluated based on this general solution and it is shown that the timedependent thermopower is significantly enhanced in the transient regime. By taking initial correlation into account, the combined Caroli and Cini scheme in quantum transport is proposed and its exact solution beyond WBL is derived for the first time as well. Furthermore, besides the average electric current, a current conserving and gauge invariant formalism for the total electric current operator is established at equilibrium state with the help of the electric displacement current operator formulated by taking the Coulomb interaction into account at the operator level. By means of the NEGF and the scattering matrix theory (SMT), a current conserving theory for equilibrium noise power at finite frequencies is obtained which solves one of the fundamental problems in quantum transport. A generalized equilibrium fluctuationdissipation theorem is presented. Moreover, the entanglement entropy
fluctuation and its distribution are investigated by introducing the entanglement entropy operator. The essential feature of the entanglement entropy generated by quantum transport is that it is a stochastic quantity whose fluctuation and distribution can be obtained from the generating function (GF). Combining the NEGF with the Grassmann algebras, it is found that the GF of entanglement
entropy can be expressed in terms of the lesser Green’s function of the subsystem. The general relation connecting the full counting statistics (FCS) of charge transfer with the GF of entanglement entropy is found which indicates that, from the experimental point of view, the entanglement entropy fluctuation can be measured indirectly. As an illustration of the general theoretical framework of entanglement entropy fluctuation, the quantum point contact (QPC) system as well as the quantum dot (QD) system are studied. It is shown that for a QPC under dc bias, the entanglement entropy is maximized and fluctuationless when the transmission coefficient T is onehalf. For the quantum dot system, at short times, a universal scaling relation among transient peak values of cumulants of entanglement entropy is shown. 
Degree  Doctor of Philosophy 
Subject  Green's functions Quantum theory  Mathematics Transport theory Nanostructures 
Dept/Program  Physics 
Persistent Identifier  http://hdl.handle.net/10722/249826 
DC Field  Value  Language 

dc.contributor.advisor  Wang, J   
dc.contributor.author  Yuan, Jiangtao   
dc.contributor.author  袁江涛   
dc.date.accessioned  20171219T09:27:26Z   
dc.date.available  20171219T09:27:26Z   
dc.date.issued  2017   
dc.identifier.citation  Yuan, J. [袁江涛]. (2017). Investigations of timedependent quantum transport properties in nanoscale structures. (Thesis). University of Hong Kong, Pokfulam, Hong Kong SAR.   
dc.identifier.uri  http://hdl.handle.net/10722/249826   
dc.description.abstract  In this thesis, certain aspects of timedependent quantum transport properties in nanoscale structures are investigated using the nonequilibrium Green’s function(NEGF). For the transient behaviors of the electric current and heat current after a quantum quench, the exact analytical solution beyond the wide band limit (WBL) is obtained for the first time which paves a way to simulate realistic physical systems. The timedependent thermoelectric effects are evaluated based on this general solution and it is shown that the timedependent thermopower is significantly enhanced in the transient regime. By taking initial correlation into account, the combined Caroli and Cini scheme in quantum transport is proposed and its exact solution beyond WBL is derived for the first time as well. Furthermore, besides the average electric current, a current conserving and gauge invariant formalism for the total electric current operator is established at equilibrium state with the help of the electric displacement current operator formulated by taking the Coulomb interaction into account at the operator level. By means of the NEGF and the scattering matrix theory (SMT), a current conserving theory for equilibrium noise power at finite frequencies is obtained which solves one of the fundamental problems in quantum transport. A generalized equilibrium fluctuationdissipation theorem is presented. Moreover, the entanglement entropy fluctuation and its distribution are investigated by introducing the entanglement entropy operator. The essential feature of the entanglement entropy generated by quantum transport is that it is a stochastic quantity whose fluctuation and distribution can be obtained from the generating function (GF). Combining the NEGF with the Grassmann algebras, it is found that the GF of entanglement entropy can be expressed in terms of the lesser Green’s function of the subsystem. The general relation connecting the full counting statistics (FCS) of charge transfer with the GF of entanglement entropy is found which indicates that, from the experimental point of view, the entanglement entropy fluctuation can be measured indirectly. As an illustration of the general theoretical framework of entanglement entropy fluctuation, the quantum point contact (QPC) system as well as the quantum dot (QD) system are studied. It is shown that for a QPC under dc bias, the entanglement entropy is maximized and fluctuationless when the transmission coefficient T is onehalf. For the quantum dot system, at short times, a universal scaling relation among transient peak values of cumulants of entanglement entropy is shown.   
dc.language  eng   
dc.publisher  The University of Hong Kong (Pokfulam, Hong Kong)   
dc.relation.ispartof  HKU Theses Online (HKUTO)   
dc.rights  The author retains all proprietary rights, (such as patent rights) and the right to use in future works.   
dc.rights  This work is licensed under a Creative Commons AttributionNonCommercialNoDerivatives 4.0 International License.   
dc.subject.lcsh  Green's functions   
dc.subject.lcsh  Quantum theory  Mathematics   
dc.subject.lcsh  Transport theory   
dc.subject.lcsh  Nanostructures   
dc.title  Investigations of timedependent quantum transport properties in nanoscale structures   
dc.type  PG_Thesis   
dc.description.thesisname  Doctor of Philosophy   
dc.description.thesislevel  Doctoral   
dc.description.thesisdiscipline  Physics   
dc.description.nature  published_or_final_version   
dc.date.hkucongregation  2017   
dc.identifier.mmsid  991043976390603414   