Dmitry Yampolsky, N. L. Harshman, Vanja Dunjko, Zaijong Hwang, Maxim Olshanii
SciPost Phys. 12, 035 (2022) ·
published 24 January 2022

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We consider a toy model for emergence of chaos in a quantum manybody shortrangeinteracting system: two onedimensional hardcore particles in a box, with a small mass defect as a perturbation over an integrable system, the latter represented by two equal mass particles. To that system, we apply a quantum generalization of Chirikov's criterion for the onset of chaos, i.e.\ the criterion
of overlapping resonances. There, classical nonlinear resonances translate almost verbatim to the quantum language. Quantum mechanics intervenes at a later stage: the resonances occupying less than one Hamiltonian eigenstate are excluded from the chaos criterion.
Resonances appear as contiguous patches of low purity unperturbed eigenstates, separated by the groups of undestroyed statesthe quantum analogues of the classical KAM tori.
M. Olshanii, D. Deshommes, J. Torrents, M. Gonchenko, V. Dunjko, G. E. Astrakharchik
SciPost Phys. 10, 114 (2021) ·
published 26 May 2021

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The recently proposed map [arXiv:2011.01415] between the hydrodynamic equations governing the twodimensional triangular coldbosonic breathers [Phys. Rev. X 9, 021035 (2019)] and the highdensity zerotemperature triangular freefermionic clouds, both trapped harmonically, perfectly explains the former phenomenon but leaves uninterpreted the nature of the initial ($t=0$) singularity. This singularity is a density discontinuity that leads, in the bosonic case, to an infinite force at the cloud edge. The map itself becomes invalid at times $t<0$. A similar singularity appears at $t = T/4$, where $T$ is the period of the harmonic trap, with the FermiBose map becoming invalid at $t > T/4$. Here, we first mapusing the scale invariance of the problemthe trapped motion to an untrapped one. Then we show that in the new representation, the solution [arXiv:2011.01415] becomes, along a ray in the direction normal to one of the three edges of the initial cloud, a freely propagating onedimensional shock wave of a class proposed by Damski in [Phys.~Rev.~A 69, 043610 (2004)]. There, for a broad class of initial conditions, the onedimensional hydrodynamic equations can be mapped to the inviscid Burgers' equation, which is equivalent to a nonlinear transport equation. More specifically, under the Damski map, the $t=0$ singularity of the original problem becomes, verbatim, the initial condition for the wave catastrophe solution found by Chandrasekhar in 1943 [Ballistic Research Laboratory Report No. 423 (1943)]. At $t=T/8$, our interpretation ceases to exist: at this instance, all three effectively onedimensional shock waves emanating from each of the three sides of the initial triangle collide at the origin, and the 2D1D correspondence between the solution of [arXiv:2011.01415] and the DamskiChandrasekhar shock wave becomes invalid.
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in Submissions  report on The origin of the period$2T/7$ quasibreathing in diskshaped GrossPitaevskii breathers