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First we introduce a field theoretical technique known as 2 Particle Irreducible (2PI) effective action and review derivation of equation of motion for mean fields and fluctuations, then derive KadanoffBaym equation in scalar and gauge theories. In order to analyze thermalization processes we introduce relativistic entropy current based on the first order gradient expansion of KadanoffBaym equation. Then we show that in taking into account nexttoleading order (NLO) selfenergy of the coupling expansion in \u03c64 theory (in symmetric phase \u003c\u03c6^\u003e = 0), it is possible to prove the Htheorem within the 1st order gradient expansion. We also show that it is possible to prove the Htheorem for KB equation with NLO selfenergy of 1/N expansion in O(N) theory (in symmetric phase). Furthermore we suggest a possibility for Htheorem to be satisfied in KB equation with leadingorder (LO) selfenergy of the coupling expansion in nonAbelian gauge theory. In d+1 dimensions (d\uff1e2) LO particle number changing processes, such as 0to3, 1to2 and 2to1, which are prohibited in the normal Boltzmann approach with onshell particles, may contribute to entropy production in KB approach although we must deal with gauge dependence and infrared divergence to complete the proof. Next we perform numerical simulations in spatially homogeneous configurations to investigate thermalization properties of the system in 1+1 and 2+1 dimensions for \u03c64 theory with NLO selfenergy of the coupling expansion and 1+1 dimensions for O(N) theory with NLO selfenergy of 1/N expansion. We also estimate the time evolution of the kinetic entropy in the case of scalar \u03c64 and O(N) theory. Then we find that at later times X0\u226b1/m, where m represents mass of particles, the kinetic entropy increases monotonically and approaches the equilibrium value, although the limited time interval at the earlier times X0\uff5e1/m invalidates the use of it. No thermalization occurs in the simulations with the normal Boltzmann equation with 2to2 collision term in 1+1 dimensions, while it occurs in the simulations with KB equation in 1+1 dimensions. 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KadanoffBaym Theory for Thermalization of Quantum Fields
https://doi.org/10.15083/00002503
20778bde4f304f038892b8c81760400b
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nishiyama_1.pdf (124.8 kB)



nishiyama_2.pdf (2.0 MB)


item type  学位論文 / Thesis or Dissertation(1)  

公開日  20120301  
タイトル  
タイトル  KadanoffBaym Theory for Thermalization of Quantum Fields  
言語  
言語  eng  
資源タイプ  
資源  http://purl.org/coar/resource_type/c_46ec  
タイプ  thesis  
ID登録  
ID登録  10.15083/00002503  
ID登録タイプ  JaLC  
その他のタイトル  
その他のタイトル  量子場の熱化課程のカダノフ・ベイム理論  
著者 
Nishiyama, Akihiro
× Nishiyama, Akihiro 

著者別名  
姓名  
姓名  西山, 陽大  
著者所属  
東京大学総合文化研究科広域科学専攻  
Abstract  
内容記述タイプ  Abstract  
内容記述  We present a theoretical study of thermalization of quantum fields with KadanoffBaym (KB) equation. First we introduce a field theoretical technique known as 2 Particle Irreducible (2PI) effective action and review derivation of equation of motion for mean fields and fluctuations, then derive KadanoffBaym equation in scalar and gauge theories. In order to analyze thermalization processes we introduce relativistic entropy current based on the first order gradient expansion of KadanoffBaym equation. Then we show that in taking into account nexttoleading order (NLO) selfenergy of the coupling expansion in φ4 theory (in symmetric phase <φ^> = 0), it is possible to prove the Htheorem within the 1st order gradient expansion. We also show that it is possible to prove the Htheorem for KB equation with NLO selfenergy of 1/N expansion in O(N) theory (in symmetric phase). Furthermore we suggest a possibility for Htheorem to be satisfied in KB equation with leadingorder (LO) selfenergy of the coupling expansion in nonAbelian gauge theory. In d+1 dimensions (d＞2) LO particle number changing processes, such as 0to3, 1to2 and 2to1, which are prohibited in the normal Boltzmann approach with onshell particles, may contribute to entropy production in KB approach although we must deal with gauge dependence and infrared divergence to complete the proof. Next we perform numerical simulations in spatially homogeneous configurations to investigate thermalization properties of the system in 1+1 and 2+1 dimensions for φ4 theory with NLO selfenergy of the coupling expansion and 1+1 dimensions for O(N) theory with NLO selfenergy of 1/N expansion. We also estimate the time evolution of the kinetic entropy in the case of scalar φ4 and O(N) theory. Then we find that at later times X0≫1/m, where m represents mass of particles, the kinetic entropy increases monotonically and approaches the equilibrium value, although the limited time interval at the earlier times X0～1/m invalidates the use of it. No thermalization occurs in the simulations with the normal Boltzmann equation with 2to2 collision term in 1+1 dimensions, while it occurs in the simulations with KB equation in 1+1 dimensions. It is due to two types of offshell effects: memory effects and spectral functions with the decay width.  
書誌情報  発行日 20100324  
日本十進分類法  
主題Scheme  NDC  
主題  421  
学位名  
学位名  博士(学術)  
学位  
値  doctoral  
学位分野  
Humanities and Social Sciences (学術)  
学位授与機関  
学位授与機関名  
学位授与機関名  University of Tokyo (東京大学)  
研究科・専攻  
Department of MultiDisciplinary Sciences, Graduate School of Arts and Sciences (総合文化研究科広域科学専攻)  
学位授与年月日  
学位授与年月日  20100324  
学位授与番号  
学位授与番号  甲第25541号  
学位記番号  
博総合第990号 