SU(N)費米流體理論

Theory of SU(N) Fermi Liquids

高榮伸(Jung-shen Kao)

指導教授 ： 葉崇傑

國立臺灣大學/理學院/物理學研究所/碩士(2018年)

https://doi.org/10.6342/NTU201803566

摘要

藍道費米流體理論在強相關系統中扮演基礎的角色, 他處理了在費米系統的交互作用下如何用某種粒子圖像精準的描述系統行為. 在交互作用存在之下, 此粒子圖像稱為準粒子. 除了點出準粒子的存在, 藍道費米流體理論進一步介紹了準粒子之間的交互作用, 並以此得出費米流體的各種靜態與動態性質, 例如有效質量,磁化率,壓縮率,比熱與聲速等等.
傳統的藍道費米流體是描述具有兩個自旋狀態的費米子, 即自旋二分之一粒子, 我們將之推廣到自旋二分之任意奇數的具有N個自旋狀態的粒子, 並討論其在自旋空間的全對稱之下, 即SU(N)下的形式. 我們將這形式應用到目前已經實現的SU(N)費米氣體, 並利用微擾方法將此系統在零溫時的有效質量,磁化率與壓縮率算至第二階. 發現了在第二階修正下, N大於2時磁化率有了本質上的修正

關鍵字

藍道費米流體 ； 準粒子 ； SU(2) ； SU(N) ； 微擾 ； 磁化率 ； 壓縮率 ； 費米氣體

並列摘要

Landau Fermi Liquid theory describes the repulsively interacting Fermi system by quasiparticles near Fermi surface. It is valid as long as temperature T ≪ TF which is common for electrons in metal. The cold atomic gas brings atom to this regime, and is more flexible. Lots of parameters inaccessible in condensed matter system are released in those low temperature atomic systems. One of the parameters is the enlargement of spin symmetry.
We generalize SU(2) Landau Fermi liquid theory to N-component with SU(N) symmetry and apply it to atomic Fermi gas with SU(N) repulsive interaction at zero temperature. The thermodynamic quantities such as effective mass, compressibility and magnetic susceptibility are derived to second order in kFas. The results depend on N and we see how it deviates from ideal Fermi gas and SU(2) Fermi liquid within and beyond mean field level. We find a drastic modification in second order in kFas for magnetic susceptibility and the Stoner instability of the SU(N) case is discussed.

並列關鍵字

Landau Fermi Liquid ； SU(2) ； SU(N) ； susceptibility ； compressibility ； Fermi gas

參考文獻

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