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Effective thermodynamics of reduced density matices

Research Project

Project/Area Number 22K14007
Research Category

Grant-in-Aid for Early-Career Scientists

Allocation TypeMulti-year Fund
Review Section Basic Section 13030:Magnetism, superconductivity and strongly correlated systems-related
Research InstitutionKindai University

Principal Investigator

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

Project Period (FY) 2022-04-01 – 2024-03-31
Project Status Discontinued (Fiscal Year 2023)
Budget Amount *help
¥3,120,000 (Direct Cost: ¥2,400,000、Indirect Cost: ¥720,000)
Fiscal Year 2023: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2022: ¥2,080,000 (Direct Cost: ¥1,600,000、Indirect Cost: ¥480,000)
KeywordsThermodynamics / Dynamics / Quantum Chaos / Tensor network / Noise correlations / Hubbard model / Quantum chaos / Bose gases / Non-equilibrium Dynamics / Irreversibility / Quantum quench
Outline of Research at the Start

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.

Outline of Annual Research Achievements

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.

Report

(2 results)
  • 2023 Annual Research Report
  • 2022 Research-status Report
  • Research Products

    (4 results)

All 2023 2022

All Journal Article (2 results) (of which Int'l Joint Research: 2 results,  Peer Reviewed: 2 results,  Open Access: 2 results) Presentation (2 results) (of which Int'l Joint Research: 1 results)

  • [Journal Article] Quantum chaos in interacting Bose-Bose mixtures2023

    • Author(s)
      Duong Anh-Tai Tran、Mikkelsen Mathias、Busch Thomas、Fogarty Thomas
    • Journal Title

      SciPost Physics

      Volume: 15 Issue: 2 Pages: 048-048

    • DOI

      10.21468/scipostphys.15.2.048

    • Related Report
      2023 Annual Research Report
    • Peer Reviewed / Open Access / Int'l Joint Research
  • [Journal Article] Relation between the noise correlations and the spin structure factor for Mott-insulating states in SU(N) Hubbard models2023

    • Author(s)
      Mathias Mikkelsen and Ippei Danshita
    • Journal Title

      Physical Review A

      Volume: 107 Issue: 4 Pages: 043313-043313

    • DOI

      10.1103/physreva.107.043313

    • Related Report
      2022 Research-status Report
    • Peer Reviewed / Open Access / Int'l Joint Research
  • [Presentation] Resonant superfluidity in the Rabi-coupled spin-dependent Fermi-Hubbard model2022

    • Author(s)
      Mathias Mikkelsen
    • Organizer
      Atomtronics@Benasque2022
    • Related Report
      2022 Research-status Report
    • Int'l Joint Research
  • [Presentation] Comparison between noise correlations and the spin-structure factor in SU(N) Hubbard models2022

    • Author(s)
      Mathias Mikkelsen
    • Organizer
      JPS 2022 Autumn Meeting
    • Related Report
      2022 Research-status Report

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Published: 2022-04-19   Modified: 2024-12-25  

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