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By Allan Griffin
This quantity supplies an up to date, systematic account of the microscopic concept of Bose-condensed fluids built because the overdue Nineteen Fifties. The center of the current booklet is the advance of the field-theoretic research had to take care of a Bose-condensed fluid. notwithstanding, the writer additionally brings out the fundamental physics at the back of the formal Green's functionality innovations and provides believable eventualities to appreciate contemporary excessive solution neutron and Raman scattering facts. the 1st 3 chapters supply an invaluable assessment and introductory fabric whereas the concluding bankruptcy supplies an overview and recommendations for additional study.
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Sample text
B) A realization of the qualitative differences between the spectrum exhibited by a Bose-condensed gas at T = 0, in which almost all the atoms are in the condensate, and at finite temperatures where the dynamics of the non-condensate atoms play a crucial role. This led to simple models which were more appropriate to compare with 20 Theory of excitations in superfluid 4He: an introduction superfluid 4 He than the traditional weakly interacting dilute Bose gas at T = 0 with n0 ^ n. (c) Understanding how the excitations of the superfluid merge with those of the normal phase as the liquid passes through the transition temperature.
This suggests an approximation in which the potential energy of a struck atom does not change appreciably during this scattering time. 37) where COR = Q2/2m is the kinetic energy of the recoiling 4 He atom. 27 K 8. 10 3. 00 Fig. 9. The atomic momentum distribution in the normal and superfluid phases of liquid 4 He. 3 [Source: Sears, Svensson, Martel and Woods, 1982]. 39) where rc(p) is normalized to unity. This result is the impulse or independent-particle approximation (IA). In this limit, 5(Q,co) is seen to depend only on the equilibrium atomic momentum distribution.
If \i is fixed and the temperature decreases, {hk)o decreases and hence the total number of atoms decreases. Indeed, for any finite \i, the value of N must decrease to zero as T —• 0. 3) where n is the density of atoms. The scenario is therefore as follows: to keep N fixed as the temperature decreases, the chemical potential approaches zero until, at TBE, it reaches zero. For temperatures below TBE, Einstein (1925) first pointed out that extra atoms can go into the k = 0 state, which then becomes macroscopically occupied.