## Abstract

The detailed understanding of the intricate dynamics of quantum fluids, in particular in the rapidly growing subfield of quantum turbulence which elucidates the evolution of a vortex tangle in a superfluid, requires an in-depth understanding of the role of finite temperature in such systems. The Landau two-fluidmodel is themost successful hydrodynamical theory of superfluid helium, but by the nature of the scale separations it cannot give an adequate description of the processes involving vortex dynamics and interactions. In our contribution we introduce a framework based on a nonlinear classical-field equation that is mathematically identical to the Landau model and provides a mechanism for severing and coalescence of vortex lines, so that the questions related to the behavior of quantized vortices can be addressed self-consistently. The correct equation of state aswell as nonlocality of interactions that leads to the existence of the roton minimum can also be introduced in such description. We review and apply the ideas developed for finite-temperature description of weakly interacting Bose gases as possible extensions and numerical refinements of the proposedmethod. We apply thismethod to elucidate the behavior of the vortices during expansion and contraction following the change in applied pressure.We showthat at low temperatures, during the contraction of the vortex core as the negative pressure grows back to positive values, the vortex line density grows through a mechanism of vortex multiplication. This mechanism is suppressed at high temperatures.

Original language | English |
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Pages (from-to) | 4675-4682 |

Number of pages | 8 |

Journal | Proceedings of the National Academy of Sciences of the United States of America |

Volume | 111 |

Issue number | SUPPL. 1 |

DOIs | |

Publication status | Published - 25 Mar 2014 |

## Keywords

- (truncated) Gross-Pitaevskii equation
- Quantum Boltzmann equation
- Stochastic Ginzburg-Landau equation
- Superfluidity
- ZNG theory