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Title
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Collective excitation branch in the continuum of pair-condensed Fermi gases : analytical study et scaling laws = Branche d’excitation collective du continuum dans les gaz de fermions condensés par paires : étude analytique et lois d’échelle
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Author
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Abstract
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| The pair-condensed unpolarized spin-1/2 Fermi gases have a collective excitation branch in their pair-breaking continuum (V.A. Andrianov, V.N. Popov, 1976). We study it at zero temperature, with the eigenenergy equation deduced from the linearized time-dependent BCS theory and extended analytically to the lower half complex plane through its branch cut, calculating both the dispersion relation and the spectral weights (quasiparticle residues) of the branch. In the case of BCS superconductors, so called because the effect of the ion lattice is replaced by a short-range electron-electron interaction, we also include the Coulomb interaction and we restrict ourselves to the weak coupling limit Delta/mu -> 0(+) (Delta is the order parameter, mu the chemical potential) and to wavenumbers q = O(1/xi) where xi is the size of a pair; when the complex energy z(q) is expressed in units of Delta and q in units of 1/xi, the branch follows a universal law insensitive to the Coulomb interaction. In the case of cold atoms in the BEC-BCS crossover, only a contact interaction remains, but the coupling strength Delta/mu can take arbitrary values, and we study the branch at any wave number. At weak coupling, we predict three scales, that already mentioned q approximate to 1/xi, that q approximate to (Delta/mu)(-1/3)/xi where the real part of the dispersion relation has a minimum and that q approximate to (mu/Delta) / xi approximate to k(F) (k(F) is the Fermi wave number) where the branch reaches the edge of its existence domain. Near the point where the chemical potential vanishes on the BCS side, mu/Delta -> 0(+), where xi approximate to k(F), we find two scales q (mu/Delta)(1/2) / xi and q approximate to 1/xi. In all cases, the branch has a limit 2 Delta and a quadratic start at q = 0. These results were obtained for mu > 0, where the eigenenergy equation admits at least two branching points epsilon(a) (q) and epsilon(b) (q) on the positive real axis, and for an analytic continuation through the interval [epsilon(a) (q), epsilon(b)(q)]. We find new continuum branches by performing the analytic continuation through [epsilon(b )(q), +infinity[ or even, for q low enough, where there is a third real positive branching point epsilon(c) (q), through [epsilon(b) (q),epsilon(c)(q)] and [epsilon(c) (q), +infinity[. On the BEC side mu < 0 not previously studied, where there is only one real positive branching point epsilon(a) (q), we also find new collective excitation branches under the branch cut [epsilon(a) (q),+infinity[. For mu > 0, some of these new branches have a low-wavenumber exotic hypoacoustic z(q )approximate to q(3/2) or hyperacoustic z(q) approximate to q(4/5) behavior. For mu < 0, we find a hyperacoustic branch and a nonhypoacoustic branch, with a limit 2 Delta and a purely real quadratic start at q = 0 for Delta/vertical bar mu vertical bar < 0.222. |
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Language
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English
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Source (journal)
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Comptes rendus : physique / Académie des sciences. - Paris, 2002, currens
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Publication
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Paris
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Elsevier
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2020
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ISSN
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1631-0705
[print]
1878-1535
[online]
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DOI
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10.5802/CRPHYS.1
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Volume/pages
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21
:3
(2020)
, p. 253-310
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ISI
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000590790100004
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Full text (Publisher's DOI)
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Full text (open access)
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