SLIDE 14 14
Calculating : remarks
F[ρ]
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- A. Using typicality of eigenstates (‘Generalized ETH’), one might replace the double sum by a single sum
- ver post-loss states. For a given ‘representative eigenstate’ :
However, numerically, this does not work well: we find that, to evaluate numerically, it is better to sum also over pre-loss states. But, analytically, this would be the way to go.
- B. Analytical progress on summation of form factors crucially needed!
- C. What about the quasi-condensate regime, ? How to calculate there?
Connection to theoretical and experimental works in that regime? [Rauer-Grisins-Mazets-Schweigler-Rohringer—
Langen-Schmiedmayer, PRL 116, 2016; Grisins-Rauer-Langen-Schmiedmayer-Mazets, PRA 93, 2016; Bouchoule-Schemmer-Henkel, SciPost 5, 2018; Johnson, Szigeti, Schemmer, Bouchoule, PRA 96, 2017; Schemmer-Bouchoule, PRL121, 2018]
- D. In recent related works, various approximations have been proposed to tackle effects of integrability
- breaking. Is it possible to use one of these to describe atom losses?
[Caux-Doyon-JD-Konik-Yoshimura, SciPost 6, 2019; Mallayya-Rigol-de Roeck, PRX 9, 2019; Friedman-Gopalakrishnan-Vasseur, PRB 101, 2020; Bastianello-De Nardis-De Luca, arXiv:2003.01702; Durnin-Bhaseen-Doyon, arXiv:2004.11030; Lopez-Piqueres-Ware-Gopalakrishnan- Vasseur, arXiv:2005.13546]
This is not obvious. In particular, for losses, the sum over particle-hole excitations does not truncate.
- E. In the hard-core limit, the equation turns out to be exactly solvable. A special
role is played by the (non-hermitian) charges: Why is that so?
sum over post- loss states
|{vi}i
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F[ρ]
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F[ρ](v) / X
|{wj}i
2 4
N
X
i=1
δσ(v vi)
NK
X
j=1
δσ(w wj) 3 5
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energy per atom scattering energy repulsion energy
e ' gn mg2/~2
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F[ρ]
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dρ(v)/dt = −ΓF[ρ](v)
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Q(z; {vi}) =
N
X
i=1
1 z − vi , z ∈ C.
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