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* in principle exists in any system undergoing a continuous transition, but is usually quite small.
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33845673580
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note
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Here, for simplicity we use a highly oversimplified but qualitatively correct FR model in which a coupled multi-channel system is approximated by two (nearly degenerate and therefore dominant) channels.
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21
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33845652115
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note
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The spin-triplet and singlet channels are coupled by the hyperfine interaction corresponding to a singlet-triplet transition via electronic spin flip accompanied by a nuclear spin flip, such that the total spin remains unchanged.
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33845658116
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F) ≪ 1 criterion relevant for the validity of a perturbative treatment of the condensed many-body system, see Section 5.1.2.
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26
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33845649302
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note
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We emphasize the distinction between a resonance, a long lived quasistationary state which eventually decays into the continuum (as used in particle physics where it describes an unstable particle) and the notion of resonant scattering due to an intermediate state coming into resonance (coincident in energy) with a scattering state (a terminology popular in atomic physics). Namely, some resonant scatterings do not exhibit a resonance. For example, as can be seen in Fig. 13, s-wave Feshbach resonance often occurs in the absence of any resonances, quasistationary states (corresponding to a pole of a scattering amplitude with a negative imaginary part with a magnitude much smaller than its positive real part), as is the case in experiments on s-wave wide Feshbach resonances, which take place in the presence of either bound states or virtual bound states, but not a quasistationary state. In contrast, narrow Feshbach resonances studied in this paper do exhibit a resonance. It is somewhat unfortunate that these two distinct notions are referred to with similar names. In the absence of better terminology, we will use these terms but will try to be as clear as possible which usage we mean.
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31
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33845654725
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note
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Recently, a number of interesting studies have appeared. Guided by success in critical phenomena, these introduce a small parameter (ε{lunate} = d - 2, ε{lunate} = 4 - d or 1/N, where d is dimension of space and N a number of fermion flavors) into a generalization of a single-channel model and can thereby treat a full crossover (including interesting unitary point) of even a broad resonance. See for example [81-84].
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Simoni, A.6
Tiesinga, E.7
Williamsa, C.J.8
Julienne, P.S.9
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33845603898
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note
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In the Schrödinger's equation two-particle formulation the vanishing of the s-wave scattering is due to destructive interference (cancellation) between scattering by θ and π - θ. In the many-body language, as can be seen from spin and orbital channel decomposition of Section 3.1, (see e.g., Eq. (3.10)) this happens automatically because identical fermions can be considered to be in the flavor-triplet state {divides}↑,↑〉 which therefore requires the orbital part to be antisymmetric, in particularly forbidding the s-wave channel interaction.
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45
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33845614802
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note
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s the two-body molecular problem is extremely non-trivial but exactly solvable and once solved allows for a controlled treatment of the deep BEC regime where the gas parameter is small [6].
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33845656770
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note
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y-superfluid phase transition was first made in our original manuscript cond-mat/0410620v1. However, in the original version of that paper, for the intermediate regime of dipolar splitting δ only, we made an error that reversed the two phases, a mistake that was subsequently corrected by C.-H. Cheng and S.-K. Yip, cond-mat/0504278, Ref. [43].
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33845618499
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note
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0 → 0, to mimic delta-function, gives a = 0, i.e. no scattering.
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y-superfluid.
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