Maggie's Quantum Odyssey

The true sign of intelligence is not knowledge but imagination.

Condense many body physics

Condense matter field theory

Posted by Maggie on April 14, 2024

Fermion Doubling in Condensed Matter Physics

Fermion doubling problem Here, I will post some useful literatures. Absence of neutrinos on a lattice:(I). Proof by homotopy theory". Absence of neutrinos on a lattice:(II). Intuitive topo...

Posted by Maggie on April 9, 2024

Tight binding model on square lattice with stagger flux

Tight binding model on square lattice with stagger flux Introduction: The Staggered Flux Model Electrons moving in a two-dimensional crystal lattice subject to a magnetic field exhibit fascinatin...

Posted by Maggie on April 8, 2024

Condense matter theory

Condense matter theory note

Condense matter physics notes Fermi liquid Superconductivity Green function KT transition Some useful links ...

Posted by Maggie on April 7, 2024

Isomorphism Theorem

The Third Isomorphism Theorem

The Third Isomorphism Theorem 在 Lattice Isomorphism Theorem 中，可以看到很多本來在群中有的關係，在同時取 quotient group 之後，仍然會在取出來的 quotient group 之間保持。這時，突然有個大膽的想法：==quotient group 的關係在取 quotient group 之後，會不會維持？== 定理...

Posted by Maggie on July 11, 2022

Isomorphism Theorem

Lattice Isomorphism Theorem

Lattice Isomorphism Theorem (Part 1) 這邊要討論子群之間一起取 quotient group 後，他們的某些關係是否能維持。取 quotient group 是個把群「濃縮」的過程，所以一些群之間的關係，在拿兩者共同的不變子群下去作 quotient group 之後，這個關係也會一併「繼承」給做出來的那兩個 quotient group。而有哪些關...

Posted by Maggie on July 11, 2022

Isomorphism Theorem

Diamond Isomorphism Theorem

Diamond Isomorphism Theorem Diamond Isomorphism Theorem 又叫 second isomorphism theorem，算是 isomorphism theorem 系列的第二個定理。之所以會稱作 Diamond，是因為他描述的同構關係就像一個鑽石嗎？。平行的邊所代表的 quotient group 之間，會有同構關係：前置準備 ...

Posted by Maggie on July 9, 2022

Isomorphism Theorem

The First Isomorphism Theorem

The First Isomorphism Theorem 給定一個 homomorphism $\phi$ 之後，他的 kernel $K$ 也會是 normal subgroup。拿這個 kernel 去做 quotient group 其實就是把母集合分割成許多互斥的 coset，而且這些 coset 自己還能形成群。而如果是拿 kernel 做，那麼處在同一個 coset 的元...

Posted by Maggie on July 8, 2022