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7 Jan 2019: f̃(ω) =. dt f(t)eiωt ; f(t) =1. 2π. dω f̃(ω)eiωt (24). ... G(x,t) = dωdk. (2π2). ei(kxωt). ρω2 iγω Tk2(29). A. (24 January 2002) (TURN OVER.

7 Jan 2019: 2γ(tt′) sin (t t′). (24). We use the Green function to solve for the response to source f(t) by calculating.

7 Jan 2019: " $#&%'() ,---./10 243 24567 849 : 9/24: ;<9 0 :=84/ >9?@9 9 2A BCD4E 9 7 9 E FG0 9 7 FHD@9 I@J J J KLE 9 /: 90

7 Jan 2019: g. aB , ω2B = 12ga. l2(AB). so. ω2B = 12gal2B 24. ... 11. g2. l2ω2B ,. ω4 12gal2ω2 24. 11. g2. l2= 0 ,. and therefore. ω2 = 6ga. l2. 1. 1 2. 33. l2.

7 Jan 2019: 0. ux1du. 1 u= 2πi (24). Identifying the sin πx and dividing through, the required result is obtained.

7 Jan 2019: " $#&%'() ,--. /10 243 24567 849 : 9/24: ;<9 0 :=84/ >9?@9 9 2A BCD4E 9 7 9 E FG0 9 7 FHD@9 I@J J J KLE 9 /: 90 ... kx m n l. q3 J 91JLz|{124IHP B0 I49 0 9 }u4/17 3 B124: v B10<7 849A BHB10 I43 24/17 9 : m n J 849bH3 249 7

7 Jan 2019: z =1 p. 3i. 2+. q. 2. (1 p. 3i)2 4 q = 1 (24).

7 Jan 2019: 22). For P2 we have. P2x. = α/2 (23). P2y. = 0 (24).

30 Jul 2019: Cavendish Laboratory - J.J. Thomson Avenue, Cambridge, CB3 0HE, UK. received 24 October 2018; accepted in final form 18 June 2019published online 22 July 2019. ... and Zwierlein M. W., arXiv:0801.2500. (2008).[23] Chevy F., Phys. Rev. A, 74 (2006) 063628.

30 Jul 2019: in the extrapolation of the training data.24,25 This isconceptually similar to the approach taken to uncertaintyestimation in ensemble models, although here the underlyingmodel is a deep neural network and ... 1. Introduction to Methodology and Encoding

13 Feb 2019: 16. Introduction. radius [24]. There are two reasons why strong-coupling behaviour can be re-alised using localised excitations for which there is no microscopic mo-mentum conservation, despite the condition ... Bose condensation is the result of the

5 Feb 2019: 22. 3.1.3 Exchange and correlation. 23. 3.1.4 The Kohn-Sham equations. 24. ... g) = E (fr. g) : (2.24). This adiabatic principle is crucial because it allows us to separate the nuclear and.

6 Feb 2019: 23. 3.1.3.1 Tomfohr-Sankey method. 24. 3.2 Nuclear Dynamics. 24. 3.2.1 Forces on the nuclei. ... 24. 3.2.2 Atomic positions and velocities. 25. 3.2.2.1 Velocity Verlet algorithm.

5 Feb 2019: 12. 2.3 Bandstructure from the total energy method. 21. 3 Brillouin Zone integrations 24.

5 Feb 2019: 21. 2.4.1 Trial Wavefunctions. 24. v. vi CONTENTS. 2.4.2 Evaluating the Local Energy. ... the variational principle (see section 2.1),. E[(r)] E. 0. : (1.24).