pset3 - 1 Physics 219 - Problem Set 3 Due Date: February...

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1 Physics 219 - Problem Set 3 Due Date: February 19, 2008 Please note: there was a typo in problem 3 in the definition of the compressibility, κ T . It has now been corrected. Please see below. 1. When electrons are confined to move in a two-dimensional plane (e.g. in a semiconductor quantum well or heterostructure), they will form a triangular lattice if their density is too low. Such a state is called a Wigner crystal . The transverse vibrations of such a crystal are similar to those of the ionic lattice, but the longitudinal vibrations satisfy ω ~ k = a k as a result of the unscreened long-ranged Coulomb interaction between electrons. What is the contribution to the low-temperature specific heat of a Wigner crystal coming from longitudinal vibrations. 2. Consider a gas obeying the van der Waals equation of state: p = Nk B T V - b - a V 2 where a , b are constants. Suppose the specific heat at constant volume is a constant, inde- pendent of temperature: C V = cNk B What are the entropy and energy of the gas as a function of
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pset3 - 1 Physics 219 - Problem Set 3 Due Date: February...

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