Physics 510: Statistical Physics (Winter 2004)
Contents
I. Fundamentals of Statistical Mechanics A. Review of Hamiltonian Mechanics B. Ensembles and Averages C. Microcanonical ensemble D. Statistical
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Homework 1 (due September 27)
Problem 1-2 (3 pts.) A useful way of calculating entropy for a known distribution function is: Z S = hlog i = d (q, p) log (q, p) Starting with Liuoville theorem, s
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Physics 510. Final Exam
Problem 1 (5 pts.) Consider a system of N particles whose spin-spin interaction depend on their positions: H= 1X J (|ri rj |) si sj . 2
i6=j
By summarizing over all spin c
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Homework 2 (due October 6)
Problem 2-1 (3 pts.) The classical expression for entropy, S = hlog pk i = X pk log pk
states
is derived under assumption that all microstates of the system have the
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Homework 3 (due October 20)
Problem 3-1 (4 pts.) Consider a dielectric ideal gas in a non-uniform electric eld. The linear polarizability of each molecule is (i.e. d = E). a) Based on the results
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Homework 4 (due November 1)
Problem 4-1 (4 pts.) Find the meansquare uctuation of the number of particles in a volume V , for a system with the given equation of state: P = P (, T ) Apply your resu
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Homework 5 (due November 15)
Problem 5-1 (3 pts.) Let the dispersion relationship for an ideal Bose gas particles be given by the following scaling law: (p) p What should be the dimensionality of
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Homework 8 (due December 16)
Problem 8-1 (5 pts.) Starting with Langevin equation for a 1D Brownian particle, nd the mean square displacement as a function of D E time : (x (t + ) x (t)2 . Negle
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Homework 7 (due December 6)
Problem 7-1 (5 pts.) Find the correlator of a scalar order parameter, below the critical temperature (T < Tc ): G = h (r) (r0 )i Assume the GinzburgLandau functional to
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Homework 6 (due November 24)
Problem 6-1 (5 pts.) Consider an antiferromagnetic Ising system on a cubic lattice: H= J 2z X i j BB X
i
i
i,jnearest. neib
Here J > 0, z = 6 is the number of neare
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Physics 510. Midterm Exam
Problem 1 (5 pts.) Consider a system composed of two coupled spins, s1,2 = 1, subjected to magnetic eld B. Its Hamiltonian is given by H = Js1 s2 B B (s1 + s2 ) . a) Find