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Extra info for Modern Many Particle Physics
In two dimensions, an analogous model is used to describe the electrons which are confined on the boundary surface of a semiconductor heterostructure (quantum well). In the case of an infinite system the HF equations become particularly simple since it is possible to exploit the translational invariance of the system, which requires pi — pe = const. The constant-density solutions of the HF equations exist and are plane waves ¥>»(r,o-) 1 'LD elk'rXm», where D is the system dimensionality. 81). 34) dk Tlk v k ' ' ^ ~ k 'D' where v(\k - k'|) = 47r/|k - k'| 2 in 3D, and u(|k - k'|) = 27r/|k - k'| in 22?.
C. A. J. G. Hulet, Phys. Rev. Lett. 75, 1687 (1995). F. Dalfovo, S. P. Pitaevskii and S. Stringari, Rev. Mod. Phys. 7 1 , 463 (1999). A. Bohr and B. Mottelson, Nuclear Structure (Benjamin, New York, 1975). K. Huang, Statistical Mechanics, Second Edition (John Wiley and Sons, New York 1987). D. Landau, Sov. Phys. JEPT 3, 920 (1956); 5, 101 (1957). D. Pines and P. Nozieres, The Theory of Quantum Liquids (Benjamin, New York 1966). 1) is included in the theory, the many-Fermion (Boson) wave function is a combination of Slater determinants (symmetric products) that must be determined by means of variational or other more sophisticated techniques.
The resulting beam consists of different aggregates containing different numbers of atoms; it is of interest to measure the relative abundance of clusters of a given type as a function of the number N of constituting atoms. This kind of experiments (see Fig. 1) provides a spectrum of abundance, showing a series of peaks corresponding to some values of N, which are a sort of magic numbers analogous to those observed, for example, in the ionization energies of the atoms and nuclear separation. One of the most well-known results obtained by this technique is the discovery of fullerene (Kroto et al.
Modern Many Particle Physics by Lipparini