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postgraduate thesis: Investigations of time-dependent quantum transport properties in nanoscale structures

TitleInvestigations of time-dependent quantum transport properties in nanoscale structures
Authors
Advisors
Advisor(s):Wang, J
Issue Date2017
PublisherThe University of Hong Kong (Pokfulam, Hong Kong)
Citation
Yuan, J. [袁江涛]. (2017). Investigations of time-dependent quantum transport properties in nanoscale structures. (Thesis). University of Hong Kong, Pokfulam, Hong Kong SAR.
AbstractIn this thesis, certain aspects of time-dependent quantum transport properties in nanoscale structures are investigated using the non-equilibrium 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 time-dependent thermoelectric effects are evaluated based on this general solution and it is shown that the time-dependent 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 fluctuation-dissipation 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 one-half. For the quantum dot system, at short times, a universal scaling relation among transient peak values of cumulants of entanglement entropy is shown.
DegreeDoctor of Philosophy
SubjectGreen's functions
Quantum theory - Mathematics
Transport theory
Nanostructures
Dept/ProgramPhysics
Persistent Identifierhttp://hdl.handle.net/10722/249826

 

DC FieldValueLanguage
dc.contributor.advisorWang, J-
dc.contributor.authorYuan, Jiangtao-
dc.contributor.author袁江涛-
dc.date.accessioned2017-12-19T09:27:26Z-
dc.date.available2017-12-19T09:27:26Z-
dc.date.issued2017-
dc.identifier.citationYuan, J. [袁江涛]. (2017). Investigations of time-dependent quantum transport properties in nanoscale structures. (Thesis). University of Hong Kong, Pokfulam, Hong Kong SAR.-
dc.identifier.urihttp://hdl.handle.net/10722/249826-
dc.description.abstractIn this thesis, certain aspects of time-dependent quantum transport properties in nanoscale structures are investigated using the non-equilibrium 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 time-dependent thermoelectric effects are evaluated based on this general solution and it is shown that the time-dependent 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 fluctuation-dissipation 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 one-half. For the quantum dot system, at short times, a universal scaling relation among transient peak values of cumulants of entanglement entropy is shown.-
dc.languageeng-
dc.publisherThe University of Hong Kong (Pokfulam, Hong Kong)-
dc.relation.ispartofHKU Theses Online (HKUTO)-
dc.rightsThe author retains all proprietary rights, (such as patent rights) and the right to use in future works.-
dc.rightsThis work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.-
dc.subject.lcshGreen's functions-
dc.subject.lcshQuantum theory - Mathematics-
dc.subject.lcshTransport theory-
dc.subject.lcshNanostructures-
dc.titleInvestigations of time-dependent quantum transport properties in nanoscale structures-
dc.typePG_Thesis-
dc.description.thesisnameDoctor of Philosophy-
dc.description.thesislevelDoctoral-
dc.description.thesisdisciplinePhysics-
dc.description.naturepublished_or_final_version-
dc.date.hkucongregation2017-
dc.identifier.mmsid991043976390603414-

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