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20 Jan 2016: 2mṙθ̇ mrθ̈ = ka sin(θ θB). d. dt. L. ṙ=L. ... r= mr̈ = mrθ̇2 kr ka cos(θ θB). d. dt. L.

10 Oct 2012: Ĥ = JN S2 B.Z.Xk! ka†kak O(S0) (2.16). where! k = 2JS(1 cos k) = 4JS sin2(k/2) represents the dispersion relation of the spinexcitations.

10 Oct 2012: cos ka. ——————————————–. Quantum Condensed Matter Field Theory.

10 Nov 2013: ka†k. )] O(N. 1/20 ). cf. quantum AF in spin-wave approximation. ... 2. (akak a. †ka†k. )]As with quantum AF, Ĥ diagonalised by Bogoluibov transformation:(.

4 Apr 2010: The first indication of unusual behaviour in the two-dimensional XY -model (n = 2)appeared in an analysis of the high temperature series expansion by Stanley and Ka-plan (1971).

22 Nov 2009: and verify that the scattering is isotropic when the energy of the incidentparticle or the size of the scatterer is sufficiently low, so that Ka 1.Obtain an expression for the

21 Oct 2009: κa =. {ka tan(ka) evenka cot(ka) odd. κa =. (2ma2V0! 2 (ka)2. ... leads to the condition,. k [An1 cos(ka) Bn1 sin(ka) An] =2maV0!

12 Oct 2009: κa =. {ka tan(ka) evenka cot(ka) odd. κa =. (2ma2V0! 2 (ka)2. ... leads to the condition,. k [An1 cos(ka) Bn1 sin(ka) An] =2maV0!

17 Nov 2009: eikna = ks (eika eika). 1N. eikna2ks cos(ka). We therefore find that. ... Classical chain: normal modes. ωk = 2. ksm| sin(ka/2)|. At low energies, k 0, (i.e.

17 Nov 2009: Substituted into the equations of motion, we obtain. (mω2 2ks ) = 2ks cos(ka). ... ksm| sin(ka/2)|. Classical chain: normal modes. ωk = 2. ksm| sin(ka/2)|.