AUTHOR=Khan Ayan , Debnath Argha 

TITLE=Quantum Droplet in Lower Dimensions

JOURNAL=Frontiers in Physics

VOLUME=Volume 10 - 2022

YEAR=2022

URL=https://www.frontiersin.org/journals/physics/articles/10.3389/fphy.2022.887338

DOI=10.3389/fphy.2022.887338

ISSN=2296-424X

ABSTRACT=The study of Bose-Einstein condensation (BEC) in lower dimensions plays an important role in understanding the fundamentals of many-body physics as they can be treated theoretically with relative ease and can be verified experimentally. Very recently, observation of a liquid-like state in a BEC mixture has been reported along with theoretical prescription for its observation in lower dimension. This observation is unique and has serious ramification in our prevailing conception of the liquid state which has deep influence of Van der Waals theory. In explaining the self-bound nature of these state, quantum fluctuations and it's fine balance with mean-field (MF) interaction turns out to be playing a key role. Though the experiments are performed predominantly in three-dimension however, theoretical studies extend to the lower dimensions as well. In this brief review, we plan to summarise the recent theoretical advances in droplet research in lower dimension along with an elaborate description of our contributions. We will mainly focus on analytical results related to this self- bound state in one-dimension and quasi one-dimension environment. We intent to cover few results starting from the family of cnoidal solutions to droplet solutions with smooth transitions between each other and finishing it by carrying a modest discussion out  about supersolid phase.