# SciPost Thesis Link

Title: | Density fluctuations in the 1D Bose gas | |

Author: | M.K. Panfil | |

As Contributor: | Milosz Panfil | |

Type: | Ph.D. | |

Discipline: | Physics | |

Subject area: | Atomic, Molecular and Optical Physics - Theory | |

Approach: | Theoretical | |

URL: | http://hdl.handle.net/11245/1.398582 | |

Degree granting institution: | University of Amsterdam | |

Supervisor(s): | J.-S. Caux | |

Defense date: | 2013-10-09 |

### Abstract:

The thesis is organized in the following way • Chapter 2: Contains an introduction to the Lieb-Liniger model and to the density- density correlations which we study in various circumstances throughout the rest of the thesis. • Chapter 3: Contains a brief introduction to the method of Algebraic and Ther- modynamic Bethe Ansatz. Focuses on highlighting key concepts, sacrificing the completeness of discussion whenever it seems appropriate. For the complete expo- sure to the method we refer to the bible of the Algebraic Bethe Ansatz [18]. • Chapter 4: This is the first chapter containing the author’s contribution to the field. We show how the Luttinger liquid (macroscopic theory) can be fine-tuned with the microscopic (1D Bose gas) input. We focus on the zero temperature correlation functions. • Chapter 5: Here we present results on finite temperature correlation functions obtained directly from the microscopic description of the 1D Bose gas. • Chapter 6: Finally we describe a metastable super Tonks-Girardeau gas, that is a specific out-of-equilibrium regime in which correlations between particles are specifically strong. In a sense this describes a regime of the 1D Bose gas that is far away from the free gas. • Chapter 7: We conclude by giving an outlook on further interesting directions that could be undertaken in a future and would extend the results presented here. Notations and some extra calculations are placed in Appendices A, B, C.