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Exact correlations in the Lieb-Liniger model and detailed balance out-of-equilibrium
by Jacopo De Nardis, Miłosz Panfil
- Published as SciPost Phys. 1, 015 (2016)
|As Contributors:||Milosz Panfil|
|Submitted by:||Panfil, Milosz|
|Submitted to:||SciPost Physics|
|Subject area:||Condensed Matter Physics - Theory|
We study the density-density correlation function of the 1D Lieb-Liniger model and obtain an exact expression for the small momentum limit of the static correlator in the thermodynamic limit. We achieve this by summing exactly over the relevant form factors of the density operator in the small momentum limit. The result is valid for any eigenstate, including thermal and non-thermal states. We also show that the small momentum limit of the dynamic structure factors obeys a generalized detailed balance relation valid for any equilibrium state.
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List of changes
We thank the referee for carefully reading our manuscript and kindly proposing important improvements to it.
1.1 We added a short discussion on this result at the end of section 4.3 and we added fig. 4 highlighting the dependence of S(0) on the rapidity distribution. The figure shows that at the intuitive level what controls S(0) is not the interatomic repulsion per se, but the amount of the entropy in the rapidity distribution. In practice what matters is the compressibility and for the BEC quench it takes a very simple form reported in eqs. (87) and (88). The remarkable phenomena is that in this limit S(0) is independent of the post-quench value of the interaction. At the level of equations the reason for this is clear. At the level of intuitions we have only a limited explanation presented at the end of section 4.3.
2.1 We added a bar for S(x,t) in order to not confuse it with its Fourier transform S(k,omega).
2.2 We implemented the suggested change.
2.3 We would like to point out that footnote 3 explains this only apparent discrepancy in detail.
2.4 We added equation (9) that explains what is detailed balance for a quantum gas in a thermal state.
2.5 We now refer to it.
2.7 We thank the referee for spotting this mistake, it's now corrected.
2.8 We now define m as the number of particle-hole.
2.9 We remark that this is indeed the shift due to particle-hole excitations on the rapidity distribution.