Effective thermodynamics of reduced density matices
| Project/Area Number |
22K14007
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| Research Category |
Grant-in-Aid for Early-Career Scientists
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| Allocation Type | Multi-year Fund |
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| Review Section |
Basic Section 13030:Magnetism, superconductivity and strongly correlated systems-related
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| Research Institution | Kindai University |
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Principal Investigator |
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| Project Period (FY) |
2022-04-01 – 2024-03-31
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| Project Status |
Discontinued (Fiscal Year 2023)
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| 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)
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| Keywords | Thermodynamics / Dynamics / Quantum Chaos / Tensor network / Noise correlations / Hubbard model / Quantum chaos / Bose gases / Non-equilibrium Dynamics / Irreversibility / Quantum quench |
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| 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.
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| 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.
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Report
(2 results)
Research Products
(4 results)
