Dispersive and classical shock waves in Bose-Einstein condensates and gas dynamics

Abstract

A Bose-Einstein condensate ͑BEC͒ is a quantum fluid that gives rise to interesting shock-wave nonlinear dynamics. Experiments depict a BEC that exhibits behavior similar to that of a shock wave in a compressible gas, e.g., traveling fronts with steep gradients. However, the governing Gross-Pitaevskii ͑GP͒ equation that describes the mean field of a BEC admits no dissipation, hence classical dissipative shock solutions do not explain the phenomena. Instead, wave dynamics with small dispersion is considered and it is shown that this provides a mechanism for the generation of a dispersive shock wave ͑DSW͒. Computations with the GP equation are compared to experiment with excellent agreement. A comparison between a canonical onedimensional ͑1D͒ dissipative and dispersive shock problem shows significant differences in shock structure and shock-front speed. Numerical results associated with the three-dimensional experiment show that three-and two-dimensional approximations are in excellent agreement and 1D approximations are in good qualitative agreement. Using 1D DSW theory, it is argued that the experimentally observed blast waves may be viewed as dispersive shock waves.

Riemann surface and quantization

“…It also works in reverse, that is, the use of classical hydro-dynamic solutions in quantum mechanics. From here we can see the possibility of the existence of quantum shock wave systems, to which many studies are devoted to [34][35][36][37][38][39][40][41].…”

Nonlinear waves in Bose–Einstein condensates: physical relevance and mathematical techniques

“…Finally, shock waves were studied experimentally and theoretically in Ref. [397]; in the experiments reported in this work, repulsive laser beams were used (as in Ref. [395], but with a nonrotating condensate) to push atoms from the BEC center, thus forming "blast-wave" patterns.…”

“…On the theoretical side, shock waves in repulsive BECs were mainly studied in the framework of mean-field theory and the GP equation for weakly-interacting Bose gases [397][398][399][400][401][402][403][404][405], but also for strongly interacting ones [406] and in the BEC-Tonks crossover [407]; additionally, the effect of temperature (see Sec. 5.7) on shock wave formation and dynamics and the effect of depleted atoms were respectively discussed in Refs.…”

Observation of Dispersive Shock Waves, Solitons, and Their Interactions in Viscous Fluid Conduits

“…Dispersive shock waves and solitons are ubiquitous excitations in dispersive hydrodynamics, having been observed in many environments such as quantum shocks in quantum systems (ultra-cold atoms [2,3], semiconductor cavities [4], electron beams [5]), optical shocks in nonlinear photonics [6], undular bores in geophysical fluids [7,8], and collisionless shocks in rarefied plasma [9]. However, all DSW studies to date have been severely constrained by expensive laboratory setups [2,3,5,7] or challenging field studies [8], difficulties in capturing dynamical information [2,3,6], complex physical modeling [8], or a loss of coherence due to multi-dimensional instabilities [2,4] or dissipation [5,9].…”

“…However, all DSW studies to date have been severely constrained by expensive laboratory setups [2,3,5,7] or challenging field studies [8], difficulties in capturing dynamical information [2,3,6], complex physical modeling [8], or a loss of coherence due to multi-dimensional instabilities [2,4] or dissipation [5,9]. Here we report on a novel dispersive hydrodynamics testbed that circumvents all of these difficulties: the effective superflow of interfacial waves between two high viscosity contrast, low Reynolds number Stokes fluids.…”