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7 Jan 2019: m. (a, ,b ). z. M. (r, ,z). B B. (a) Show that, up to irrelevant constants and ignoring gravity, the Lagrangian forthe system is: [6]. ... 2. (b) Find the corresponding equations of motion for the particle and the bead.

7 Jan 2019: rr$"B<1&u="B1"%=r.6r'[ l8?<7=([="F Q1=&1¡&u<="')?'="%:r'C1|1"%&h). ... 2:')?'="%: $"%' % ri"%$h)0A:mr|=<1&¡&,-8 "%' % ri"B<7@ <1@(h[=<1/. (

13 Feb 2019: a†a b†b = 1. (1.18). The Hamiltonian describing cavity polaritons for localised excitationsis then. ... H = Eg(n). 2. (. b†b a†a). ωcψ†ψ H′, (1.19). H′ =1N. (.

7 Jan 2019: d. dt(γmv) = e(E v B). ——————. (b) [unseen calculation] Suppose that B = 0, that E is constant and that att = 0 the particle has velocity v0. ... d2v. dt2=. e. mγ. dv. dtB =. (e. mγ. )2(v B) B =. (e. mγ. )2(vB2 B(v B)). In terms of the

7 Jan 2019: a uniform static magneticfield perpendicular to the plane, B = Bẑ (E > 0, B > 0). ... 6]. (b) Compute the behaviour of the zero-field magnetic susceptibilityχ = (φ/B)|B=0 close to the transition (both above and below).

5 Feb 2019: B.4 Finding out about the singularities. 112. B.5 Vertex singularities. 112. ... 114. B.9 The volume singularity. 115. B.10 Evaluation of the tangents.

7 Jan 2019: 40 3 u4C7 849wde3 : 9 0 B: B. A B: r l y q y [ l q 849t: 7 /?4E 9tDMB: 3 7 3 B12N84/:e7 B?M9 rsu424E 9 : :A ... 9 2 ;9 2 3 ;.: 3 ;#6 9 3 4 ;.9 4 B>? ;:

7 Jan 2019: 2aχ 6m2χ = 1. where χ = m/B|B=0. Above the transition (a > 0), m(B = 0) = 0 andχ = 1/2a. ... Below the transition (a < 0), m(B = 0) =. a and χ = 1/4a.

5 Feb 2019: B Conjugate gradients 131. Bibliography 137. x. List of Figures. 2.1 Indistinguishable particles in quantum mechanics. ... 9.8 Variation of computational eort with system-size. 122. B.1 Steepest descents method.

27 Jul 2019: B active subset of ptsp cities. Bn expected optimal number of costs paid at level n. ... half-winding num. ber)B. alance. General Form. alism. Approxim. ate SolutionsE. xact Solutions.