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Foundations of Statistical Mechanics
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Module 8
Ideal Bose Gases and Condensation
1
Ideal Bose Gas Equation of State
Derive the equation of state for an ideal Bose gas at arbitrary temperature.
2
Chemical Potential and BEC in 3D Ideal Bose Gas
Show that a chemical potential μ > 0 is forbidden and derive the criterion for Bose-Einstein condensation (BEC) in a 3D ideal Bose gas.
3
Calculating Critical Temperature (T_c) for BEC
Calculate the critical temperature (T_c) for BEC.
4
Condensate Fraction vs. Temperature Below T_c
Compute the condensate fraction as a function of temperature below T_c.
5
Heat Capacity of Ideal Bose Gas: Temperature Dependence and the Cusp at T_c
Derive the temperature dependence of the heat capacity for an ideal Bose gas and identify the cusp at T_c.
6
No Bose-Einstein Condensation in 1D or 2D
Explain why BEC does not occur in 1D or 2D for a non-interacting, non-relativistic gas.
7
Debye Model for Low-Temperature Specific Heat
Derive the Debye model for the low-temperature specific heat of solids by treating phonons as a gas of bosons.
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Ideal Fermi Gases
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Interacting Systems and Mean-Field Theory