Using the Diagrammatic Technique to Study Beliaev Damping in Bose Einstein Condensation

Semester: 
Summer

Using the Diagrammatic Technique to Study Beliaev Damping in Bose Einstein Condensation

Candidate: Khloud Ahmed Saad.

(Summer 2020)

Abstract: 

At a very low temperature, bosons and fermions show two different phenomena. Bosons show Bose-Einstein Condensation (BEC), while fermions show degenerate Fermi gas, or under certain conditions, we can form Cooper pair, which is the building block for superconductivity. Concerning mixtures, we may obtain three different ones, each of them shows interesting phenomena at a low temperature; for e.g. in the case of F-F mixture, we can form Cooper pair, while in the case of F-B mixture we can obtain BEC on a Fermi sphere, where the Fermionic atoms act as the electrons (responsible for the superconducting current) and the attractive interactions between the electrons required for Cooper pairing is provided by the presence of the bosonic atoms like phonon in a crystal. The last mixture is B-B, where the phase transition at a low T, lead to BEC.

       In this study, the candidate learned how to derive Dyson-Beliaev equation, and Hugenholtz-Pines equation, which describes the relation between chemical potential and the self-energy, for single and two-component Bose gas. Also, she knew how to use the diagrammatic technique to calculate the Beliaev damping for single component bose gas.


Ref: 

  • Wolfgang Ketterle. Rev. Mod. Phys. 74, 1131.
  • S.T. Beliaev, Soviet Phys. JETP 7 (1958) 289. 
  • Finite-temperature excitations in a dilute Bose-condensed gas, A.A. Maradudin, Physics Reports 304 (1998) 1—87.


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