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Effective thermodynamics of reduced density matices

研究課題

研究課題/領域番号 22K14007
研究種目

若手研究

配分区分基金
審査区分 小区分13030:磁性、超伝導および強相関系関連
研究機関近畿大学

研究代表者

Mikkelsen Mathias  近畿大学, 理工学部, 博士研究員 (30938907)

研究期間 (年度) 2022-04-01 – 2024-03-31
研究課題ステータス 中途終了 (2023年度)
配分額 *注記
3,120千円 (直接経費: 2,400千円、間接経費: 720千円)
2023年度: 1,040千円 (直接経費: 800千円、間接経費: 240千円)
2022年度: 2,080千円 (直接経費: 1,600千円、間接経費: 480千円)
キーワードThermodynamics / Dynamics / Quantum Chaos / Tensor network / Noise correlations / Hubbard model / Quantum chaos / Bose gases / Non-equilibrium Dynamics / Irreversibility / Quantum quench
研究開始時の研究の概要

The unitary non-equilibrium dynamics of closed many-body systems will be investigated. The thermodynamics of the full system is described solely by the work distribution, but as the system energy is described by a sum of few-body operators, the effective thermodynamics of reduced density matrices (RDMs), where effective heat and work terms can be defined with the remaining system acting as the environment, is a natural way to gain further insight. These concepts will be investigated using the Bose-Hubbard model which can be tuned between integrable and chaotic regimes through the interaction.

研究実績の概要

In the 4 months after my last report, I continued investigating the reduced thermodynamics (RT) of the Bose-Hubbard model using exact diagonalization techniques. These results suggest that the physical interpretation is trickier than initially hoped, but that it would be useful to connect the RT in terms of the reduced density matrices to ergotropy, which relates extractable work to the difference between Hamiltonian eigenstates and local density matrix eigenstates.

I also worked on the publication of a paper on chaos and integrability in few-body continuum Bose-mixtures, which also investigates reduced system dynamics and the relation to thermodynamic quantities. This paper has now been published in SciPost physics.

Due to finishing the project early, I did not fully implement the original proposal, but I obtained the following results: Last year I implemented the calculation of real-space two-body reduced density matrices for Hubbard models using Tensor Networks, essential for further studies of reduced thermodynamics. I published a paper on noise correlations in SU(N) Hubbard models in PRA which used these techniques. I also worked on reduced system dynamics in two-component Bose mixtures and published a paper on this in SciPost physics. Further study of the energy exchange between the two components is a good direction for gaining physical intuition about reduced state thermodynamics. I also implemented the effective thermodynamics in one-component BH models using ED, but realized that further work is required to get a meaningful physical interpretation.

報告書

(2件)
  • 2023 実績報告書
  • 2022 実施状況報告書
  • 研究成果

    (4件)

すべて 2023 2022

すべて 雑誌論文 (2件) (うち国際共著 2件、 査読あり 2件、 オープンアクセス 2件) 学会発表 (2件) (うち国際学会 1件)

  • [雑誌論文] Quantum chaos in interacting Bose-Bose mixtures2023

    • 著者名/発表者名
      Duong Anh-Tai Tran、Mikkelsen Mathias、Busch Thomas、Fogarty Thomas
    • 雑誌名

      SciPost Physics

      巻: 15 号: 2 ページ: 048-048

    • DOI

      10.21468/scipostphys.15.2.048

    • 関連する報告書
      2023 実績報告書
    • 査読あり / オープンアクセス / 国際共著
  • [雑誌論文] Relation between the noise correlations and the spin structure factor for Mott-insulating states in SU(N) Hubbard models2023

    • 著者名/発表者名
      Mathias Mikkelsen and Ippei Danshita
    • 雑誌名

      Physical Review A

      巻: 107 号: 4 ページ: 043313-043313

    • DOI

      10.1103/physreva.107.043313

    • 関連する報告書
      2022 実施状況報告書
    • 査読あり / オープンアクセス / 国際共著
  • [学会発表] Resonant superfluidity in the Rabi-coupled spin-dependent Fermi-Hubbard model2022

    • 著者名/発表者名
      Mathias Mikkelsen
    • 学会等名
      Atomtronics@Benasque2022
    • 関連する報告書
      2022 実施状況報告書
    • 国際学会
  • [学会発表] Comparison between noise correlations and the spin-structure factor in SU(N) Hubbard models2022

    • 著者名/発表者名
      Mathias Mikkelsen
    • 学会等名
      JPS 2022 Autumn Meeting
    • 関連する報告書
      2022 実施状況報告書

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公開日: 2022-04-19   更新日: 2024-12-25  

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