Mathematical physics of one-dimensional Bose-Einstein condensate control

2023 Fiscal Year Final Research Report

• Project/Area Number: 21K03409
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Review Section: Basic Section 13010:Mathematical physics and fundamental theory of condensed matter physics-related
• Research Institution: Kochi University of Technology
• Principal Investigator: Zen Takuju 高知工科大学, 理工学群, 教授 (60227353)
• Project Period (FY): 2021-04-01 – 2024-03-31
• Keywords: 異種混合系 / 相転移 / 量子力学 / 社会物理学

Outline of Final Research Achievements

In order to control of the Bose-Einstein condensates, as a preliminary study, we examined the multi-agent model of aggregation and separation on two-dimensional lattice grid space, using numerical simulations. Assuming the existence of attraction between homogeneous agents and repulsion between heterogeneous agents, 2-parameter model. We observe that the mixed habitation pattern of heterogeneous agents, seen in the case of week repulsion and attraction, transitions to droplet-like aggregation of homogeneous agents, if the attraction is strong. Also, when the repulsion between heterogeneous agents is strong, as the agent density is changed as a control parameter, we find that the mixed pattern changes to a "habitat separation" pattern with amorphous boundary through a second-order phase transition. Furthermore, when the repulsion is very strong, we observe a first-order phase transition to a "chaotic unstable state."

Free Research Field

量子力学、数理物理学、社会物理学

Academic Significance and Societal Importance of the Research Achievements

本研究は、巨視的なスケールで得意な量子的性質を示すことが予想される、複数元素からなるボーズ・アインシュタイン凝縮の状態制御の、簡単ではあるが十分に現実的な理論的モデルを提供する。そこに見出された異種混在状態と同種液滴状集結状態、また異種分離状態の間の相転移、また不安定なカオス状態の出現は、数理生態学的また社会物理学的設定での二種のアクティヴ・エージェントの混住及び分離の多彩なパターンの出現と数学的に同等であって、これは分野を超えた全く異なった対象で同じ動力学が実現される例としても興味深いであろう。