By Kirk W Madison, Kai Bongs, Visit Amazon's Lincoln D Carr Page, search results, Learn about Author Central, Lincoln D Carr, , Ana Maria Rey, Hui Zhai
The purpose of this e-book is to comprise overview articles describing the newest theoretical and experimental advancements within the box of chilly atoms and molecules. Our desire is this sequence will advertise learn by means of either highlighting fresh breakthroughs and through outlining essentially the most promising examine instructions within the field.
Readership: examine scientists together with graduate scholars and top point undergraduate scholars.
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4. 55 The QMC result for the energy per particle is displayed in Fig. k As expected, the energy matches the known results in the BCS and BEC limits (taking the QMC value for A in Eq. (55)). Indeed, by interpolating between the known weakcoupling results in the BCS and BEC regimes, we can obtain a reasonable k Note that we have used a different definition of a 2D compared with the original QMC paper — see the discussion in Sec. 2. 5 2 3 4 0 2 0 2 4 6 5 0 2 (a) 4 6 (b) Fig. 11. (a) Energy per particle in units of ε F /2 (the energy per particle in the noninteracting gas) as a function of interaction strength.
In the many-body system, it is convenient to work in the basis of the individual atoms rather than only considering the relative pair motion as in the two-body problem. However, since the interaction only depends on ˆ 3 n 4 are best the relative motion, the interaction matrix elements n 1 n 2 |g|n determined by switching to relative and center of mass harmonic oscillator quantum numbers, ν and N respectively. This yields ˆ 3n4 = g n 1 n 2 |g|n f ν n 1n 2 |N ν fν N ν |n 3 n 4 Nνν VNn1 n2 VNn3 n4 , ≡g (44) N ˜ ˜ where f ν = kz φν (k z ), and φν is the Fourier transform of the ν-th harmonic oscillator eigenfunction.
11. (a) Energy per particle in units of ε F /2 (the energy per particle in the noninteracting gas) as a function of interaction strength. The trivial two-body binding energy has been subtracted. The data points are the results of the QMC calculation,55 while the solid line is an interpolation between the known weak coupling results in the BCS and BEC limits. (b) Chemical potential in units of the Fermi energy. The solid (black) line is an interpolation between the known limiting behaviors, while the dashed (blue) line is the mean-field result µ = ε F − εb /2.