Triangular Gross-Pitaevskii breathers and Damski-Chandrasekhar shock waves
| العنوان: | Triangular Gross-Pitaevskii breathers and Damski-Chandrasekhar shock waves |
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| المؤلفون: | D. Deshommes, Maxim Olshanii, Grigori E. Astrakharchik, Jordi Torrents, Vanja Dunjko, Marina Gonchenko |
| المساهمون: | Universitat Politècnica de Catalunya. Departament de Matemàtiques, Universitat Politècnica de Catalunya. Departament de Física, Universitat Politècnica de Catalunya. EGSA - Equacions Diferencials, Geometria, Sistemes Dinàmics i de Control, i Aplicacions, Universitat Politècnica de Catalunya. SIMCON - First-principles approaches to condensed matter physics: quantum effects and complexity |
| المصدر: | SciPost Physics, Vol 10, Iss 5, p 114 (2021) UPCommons. Portal del coneixement obert de la UPC Universitat Politècnica de Catalunya (UPC) |
| بيانات النشر: | SciPost, 2021. |
| سنة النشر: | 2021 |
| مصطلحات موضوعية: | Shock wave, Physics, Breather, Física matemàtica, QC1-999, FOS: Physical sciences, Matemàtiques i estadística [Àrees temàtiques de la UPC], General Physics and Astronomy, Scale invariance, Nonlinear system, Singularity, Quantum Gases (cond-mat.quant-gas), Mathematical physics, Initial value problem, Convection–diffusion equation, Condensed Matter - Quantum Gases, Chandrasekhar limit |
| الوصف: | The recently proposed map [arXiv:2011.01415] between the hydrodynamic equations governing the two-dimensional triangular cold-bosonic breathers [Phys. Rev. X 9, 021035 (2019)] and the high-density zero-temperature triangular free-fermionic 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 $t T/4$. Here, we first map -- using the scale invariance of the problem -- the 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 one-dimensional shock wave of a class proposed by Damski in [Phys.~Rev.~A 69, 043610 (2004)]. There, for a broad class of initial conditions, the one-dimensional 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 one-dimensional shock waves emanating from each of the three sides of the initial triangle collide at the origin, and the 2D-1D correspondence between the solution of [arXiv:2011.01415] and the Damski-Chandrasekhar shock wave becomes invalid. 14 pages, 2 figures. Submission to SciPost |
| وصف الملف: | application/pdf |
| اللغة: | English |
| تدمد: | 2542-4653 |
| URL الوصول: | https://explore.openaire.eu/search/publication?articleId=doi_dedup___::f6e3ebe37e3147aa219458b041f9a5f1 https://scipost.org/SciPostPhys.10.5.114 |
| Rights: | OPEN |
| رقم الانضمام: | edsair.doi.dedup.....f6e3ebe37e3147aa219458b041f9a5f1 |
| قاعدة البيانات: | OpenAIRE |
| تدمد: | 25424653 |
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