1. Compare the difference between the two-body problem in a vacuum and on top of the Fermi sea. 2. Introduce the BCS mean-field theory and the BCS ground state wave function and its excitation. 3. Introduce the physical picture of BCS pairing. 4. Introduce the concept of contact using the BCS state as an example. 5. Discuss how the BCS state responds to the Zeeman field. 6. Discuss different pairing symmetries. 7. Discuss how the BCS-BEC crossover mean-field equation recovers features in both the BCS and the BEC limit. 8. Discuss different behaviors of the excitation spectrum in the BCS and the BEC regimes and determine superfluid critical velocity from the excitation spectrum. 9. Discuss how the superfluid transition temperature changes from the BCS regime to the BEC regime. 10. Introduce a list of experimental observations on the BCS-BEC crossover. 11. Discuss the challenging issues in studying the unitary Fermi gas. 12. Introduce the concept of holographic duality and the prediction of the $\eta/s$ bound.1. Compare the difference between the two-body problem in a vacuum and on top of the Fermi sea. 2. Introduce the BCS mean-field theory and the BCS ground state wave function and its excitation. 3. Introduce the physical picture of BCS pairing. 4. Introduce the concept of contact using the BCS state as an example. 5. Discuss how the BCS state responds to the Zeeman field. 6. Discuss different pairing symmetries. 7. Discuss how the BCS-BEC crossover mean-field equation recovers features in both the BCS and the BEC limit. 8. Discuss different behaviors of the excitation spectrum in the BCS and the BEC regimes and determine superfluid critical velocity from the excitation spectrum. 9. Discuss how the superfluid transition temperature changes from the BCS regime to the BEC regime. 10. Introduce a list of experimental observations on the BCS-BEC crossover. 11. Discuss the challenging issues in studying the unitary Fermi gas. 12. Introduce the concept of holographic duality and the prediction of the $\eta/s$ bound.

Cambridge University Press eBooksJan 30, 20210 citations

フェルミ粒子系超流動の物理 : BCS-BECクロスオーバーと新しい物質科学(講義ノート)

洋士大橋

物性研究Nov 20, 20050 citations

Superconductivity and the BCS-Bogoliubov Theory

Shuji Watanabe

First, we reformulate the BCS-Bogoliubov theory of superconductivity from the viewpoint of linear algebra. We define the BCS Hamiltonian on $\mathbb{C}^{2^{2M}}$ , where $M$ is a positive integer. We discuss selfadjointness and symmetry of the BCS Hamiltonian as well as spontaneous symmetry breaking. Beginning with the gap equation, we give the well-known expression for the BCS state and find the existence of an energy gap. We also show that the BCS state has a lower energy than the normal state. Second, we introduce a new superconducting state explicitly and show from the viewpoint of linear algebra that this new state has a lower energy than the BCS state. Third, beginning with our new gap equation, we show from the viewpoint of linear algebra that we arrive at the results similar to those in the BCS-Bogoliubov theory.First, we reformulate the BCS-Bogoliubov theory of superconductivity from the viewpoint of linear algebra. We define the BCS Hamiltonian on $\mathbb{C}^{2^{2M}}$, where $M$ is a positive integer. We discuss selfadjointness and symmetry of the BCS Hamiltonian as well as spontaneous symmetry breaking. Beginning with the gap equation, we give the well-known expression for the BCS state and find the existence of an energy gap. We also show that the BCS state has a lower energy than the normal state. Second, we introduce a new superconducting state explicitly and show from the viewpoint of linear algebra that this new state has a lower energy than the BCS state. Third, beginning with our new gap equation, we show from the viewpoint of linear algebra that we arrive at the results similar to those in the BCS-Bogoliubov theory.

arXiv:1006.1157Jun 7, 20104 citations

Anomalous BCS equation for a Luttinger superconductor

Vieri Mastropietro

In the context of the Anderson theory of high T c cuprates, we develop a BCS theory for Luttinger liquids. If the Luttinger interaction is much stronger than the BCS potential we find that the BCS equation is quite modified compared to usual BCS equation for Fermi liquids. In particular T c predicted by the BCS equation for Luttinger liquids is quite higher than the usual T c for Fermi liquids. 1 The anomalous BCS equation The equivalent of BCS theory for a Luttinger liquid has not formally worked out, despite the relevance of such theory for the problem of superconductivity in the high-T c cuprates, see [1] or the discussion in the following section. Such theory should describe superconductors which in their normal state are Luttinger liquids. In this paper we develop such theory using constructive quantum field theory techniques, applied in many other Luttinger liquid problems, see [2], [3]. In particular, we compute in a rigorous way the BCS self-consistence equation for a spinni...In the context of the Anderson theory of high T c cuprates, we develop a BCS theory for Luttinger liquids. If the Luttinger interaction is much stronger than the BCS potential we find that the BCS equation is quite modified compared to usual BCS equation for Fermi liquids. In particular T c predicted by the BCS equation for Luttinger liquids is quite higher than the usual T c for Fermi liquids. 1 The anomalous BCS equation The equivalent of BCS theory for a Luttinger liquid has not formally worked out, despite the relevance of such theory for the problem of superconductivity in the high-T c cuprates, see [1] or the discussion in the following section. Such theory should describe superconductors which in their normal state are Luttinger liquids. In this paper we develop such theory using constructive quantum field theory techniques, applied in many other Luttinger liquid problems, see [2], [3]. In particular, we compute in a rigorous way the BCS self-consistence equation for a spinni...

Jan 1, 19994 citations

冷却原子で探る量子物理の最前線 BCS-BECクロスオーバー

大橋洋士

数理科学Jan 1, 20200 citations

\eta/s

bound.

First, we reformulate the BCS-Bogoliubov theory of superconductivity from the viewpoint of linear algebra. We define the BCS Hamiltonian on

\mathbb{C}^{2^{2M}}

, where

M

is a positive integer. We discuss selfadjointness and symmetry of the BCS Hamiltonian as well as spontaneous symmetry breaking. Beginning with the gap equation, we give the well-known expression for the BCS state and find the existence of an energy gap. We also show that the BCS state has a lower energy than the normal state. Second, we introduce a new superconducting state explicitly and show from the viewpoint of linear algebra that this new state has a lower energy than the BCS state. Third, beginning with our new gap equation, we show from the viewpoint of linear algebra that we arrive at the results similar to those in the BCS-Bogoliubov theory.