PHZ3400 Midterm Solution: Difference between revisions

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-==PHZ 3400 – Phenomena in  Condensed Matter==
-Midterm Exam – March 20, 2009
-.	Give some examples of spontaneous symmetry breaking. How large must the system be to display spontaneous symmetry breaking?
-.	Describe the difference between a first order and a second order phase transition. Give examples of each type.
-.	What determines the Curie temperature of a ferromagnet? How does it depend on the coordination number of the corresponding crystal lattice?
-.	What is the physical principle behind the fact that atoms act as hard spheres, i.e. they have a “core” impenetrable to other atoms?
-.	Consider a one dimensional metal with electronic density n.
-a.	Determine the relation between the Fermi energy and the density in this case.
-b.	Determine the ground state kinetic energy as a function of density.
-.	Consider a one dimensional vibrational system consisting with atoms of mass m connected by harmonic springs with spring constant K.
-a.	Determine the highest possible vibrational frequency of this system.
-b.	Sketch the motion of atoms corresponding to that mode.
-c.	Determine the low frequency speed of sound.
-d.	Determine the Debye temperature for this system.
-e.	Compute the temperature dependence of the specific heat at low temperatures.
-f.	Compute the temperature dependence of the specific heat at high          temperatures.

Latest revision as of 20:42, 17 March 2011