Introduction to Physics Of Ultra Cold Gases

Baranov M.

Table of contents :
Introduction……Page 7
Traps……Page 8
Many particles……Page 9
Bosons……Page 11
Single particle operator……Page 13
Two particle operator……Page 14
General properties……Page 17
Superfluidity in Free Bose Gas condensate……Page 20
BEC in lower dimensions……Page 21
Box……Page 22
Parabolic trap……Page 23
Weakly interacting Bose gas……Page 25
Mean field approximation……Page 30
Comparison of terms in GP……Page 36
Thomas-Fermi-Regime……Page 38
General properties……Page 47
Pressure of degenerated Fermi gas……Page 51
Excitations of Fermions at T=0……Page 53
Trapped non-interacting Fermi gas at T=0……Page 55
Ground state……Page 58
Decay of excitations……Page 62
Landau-Fermi-Liquid……Page 64
Zero Sound……Page 68
General treatment……Page 70
BCS Hamiltonian……Page 74
Andreev reflection……Page 88
General energy-momentum relation……Page 90
Calculation for section 3.3.1……Page 91
Lifetime and Fermis Golden Rule……Page 92
Bibliography……Page 93