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postgraduate thesis: Fullcounting statistics of charge and spin transport
Title  Fullcounting statistics of charge and spin transport 

Authors  
Issue Date  2016 
Publisher  The University of Hong Kong (Pokfulam, Hong Kong) 
Citation  Tang, G. [唐高民]. (2016). Fullcounting statistics of charge and spin transport. (Thesis). University of Hong Kong, Pokfulam, Hong Kong SAR. 
Abstract  This thesis investigates the fullcounting statistics (FCS) of charge and spin transport using nonequilibrium Green's function (NEGF) in noninteracting systems.
Generating function (GF) encodes all the distribution information and is the key of FCS. For the charge statistics, GF is expressed with respect to the modified evolution operator on the complex contour using the two time measurement scheme, the modified evolution operator is expressed in terms of the modified Hamiltonian. Using Keldysh NEGF technique, GF has the form of Fredholm determinant in terms of Greens functions and selfenergies in the time domain. In the long time limit, the celebrated LevitovLesovik's formula and the fluctuation relation are derived from this formalism. GF of charge statistics for the quantum point contact system in the transient regime is obtained as well. The transient dynamics in leaddotlead transport system, including the cumulants of transferred charges and waiting time distribution defined under the transient regime for different temperatures is investigated numerically. A detailed description on how to calculate the GF in the time domain is presented. Generalizations of the formalism to the ferromagnetnormalferromagnet system to investigate the FCS of charge current, spin current and spin transfer torque (STT) are presented. GFs in time domain are Fredholm determinants expressed by NEGF as well. As an application of FCS, a formalism using FCS of STT in the long time limit to calculate the switching probability of a nanomagnet system is proposed. The formalism enables us to calculate the switching probability for nonequilibrium systems which are nonGaussian. From the stochastic LandauLifshitzGilbert (LLG) equation, the contributions to the change of the anisotropic energy, one is from the power gain due to Gilbert damping and the other is from power dissipation due to the spin transfer torque, were derived. Optimal path approximation which requires the nanomagnet a modestly large volume is presented and the approximation greatly reduces the numerical complexities. This formalism could be used to predict the switching probability numerically for real systems in combination with the first principle calculation. 
Degree  Doctor of Philosophy 
Subject  Transport theory Green's functions Quantum statistics 
Dept/Program  Physics 
Persistent Identifier  http://hdl.handle.net/10722/233943 
DC Field  Value  Language 

dc.contributor.author  Tang, Gaomin   
dc.contributor.author  唐高民   
dc.date.accessioned  20161007T01:44:37Z   
dc.date.available  20161007T01:44:37Z   
dc.date.issued  2016   
dc.identifier.citation  Tang, G. [唐高民]. (2016). Fullcounting statistics of charge and spin transport. (Thesis). University of Hong Kong, Pokfulam, Hong Kong SAR.   
dc.identifier.uri  http://hdl.handle.net/10722/233943   
dc.description.abstract  This thesis investigates the fullcounting statistics (FCS) of charge and spin transport using nonequilibrium Green's function (NEGF) in noninteracting systems. Generating function (GF) encodes all the distribution information and is the key of FCS. For the charge statistics, GF is expressed with respect to the modified evolution operator on the complex contour using the two time measurement scheme, the modified evolution operator is expressed in terms of the modified Hamiltonian. Using Keldysh NEGF technique, GF has the form of Fredholm determinant in terms of Greens functions and selfenergies in the time domain. In the long time limit, the celebrated LevitovLesovik's formula and the fluctuation relation are derived from this formalism. GF of charge statistics for the quantum point contact system in the transient regime is obtained as well. The transient dynamics in leaddotlead transport system, including the cumulants of transferred charges and waiting time distribution defined under the transient regime for different temperatures is investigated numerically. A detailed description on how to calculate the GF in the time domain is presented. Generalizations of the formalism to the ferromagnetnormalferromagnet system to investigate the FCS of charge current, spin current and spin transfer torque (STT) are presented. GFs in time domain are Fredholm determinants expressed by NEGF as well. As an application of FCS, a formalism using FCS of STT in the long time limit to calculate the switching probability of a nanomagnet system is proposed. The formalism enables us to calculate the switching probability for nonequilibrium systems which are nonGaussian. From the stochastic LandauLifshitzGilbert (LLG) equation, the contributions to the change of the anisotropic energy, one is from the power gain due to Gilbert damping and the other is from power dissipation due to the spin transfer torque, were derived. Optimal path approximation which requires the nanomagnet a modestly large volume is presented and the approximation greatly reduces the numerical complexities. This formalism could be used to predict the switching probability numerically for real systems in combination with the first principle calculation.   
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  Creative Commons: Attribution 3.0 Hong Kong License   
dc.subject.lcsh  Transport theory   
dc.subject.lcsh  Green's functions   
dc.subject.lcsh  Quantum statistics   
dc.title  Fullcounting statistics of charge and spin transport   
dc.type  PG_Thesis   
dc.identifier.hkul  b5793636   
dc.description.thesisname  Doctor of Philosophy   
dc.description.thesislevel  Doctoral   
dc.description.thesisdiscipline  Physics   
dc.description.nature  published_or_final_version   