Triangular Gross-Pitaevskii breathers and Damski-Chandrasekhar shock waves
| Autor: | D. Deshommes, Maxim Olshanii, Grigori E. Astrakharchik, Jordi Torrents, Vanja Dunjko, Marina Gonchenko |
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| Přispěvatelé: | 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 |
| Jazyk: | angličtina |
| Rok vydání: | 2021 |
| Předmět: |
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 |
| Zdroj: | SciPost Physics, Vol 10, Iss 5, p 114 (2021) UPCommons. Portal del coneixement obert de la UPC Universitat Politècnica de Catalunya (UPC) |
| ISSN: | 2542-4653 |
| Popis: | 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 |
| Databáze: | OpenAIRE |
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