2021 Fiscal Year Research-status Report
Phase nucleation in curved space
| Project/Area Number |
21K03540
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| Research Institution | Keio University |
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Principal Investigator |
フラキ アントニノ 慶應義塾大学, 商学部(日吉), 准教授 (20444474)
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| Project Period (FY) |
2021-04-01 – 2025-03-31
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| Keywords | phase nucleation / quantum fields / phase transitions / curved surfaces |
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| Outline of Annual Research Achievements |
During the first year of the project I have proceeded development of a numerical scheme to compute the expectation value of the two-point function on a general curved geometry. This is a technical step important for various applications within the project. The analytical part of these calculations has been completed and I am currently developing the numerical part. The second line of research carried out during this fiscal year has been to reproduce some known results regarding phase nucleation in general dimensionality in flat and in maximally symmetric spaces and start looking at the case of general curved surfaces. I have also started to develop a new approach based on heat-kernels to study this problem.
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| Current Status of Research Progress |
Current Status of Research Progress
2: Research has progressed on the whole more than it was originally planned.
Reason
Both the analytical part and the numerical part are being developed smoothly. The numerical part is turning out algebraically more involved than I initially expected, but no major problem has so far arisen.
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| Strategy for Future Research Activity |
During this year, I am planning to complete the numerical part, apply it to specific example, and also develop a more performing version of the numerical code. I hope that this can result into two publications. As for the analysis of nucleation on surfaces, I am confident that the project will be completed within this fiscal year. At the moment I cannot foresee any substantial issue.
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| Causes of Carryover |
Due to covid it has been impossible to travel, participate in conferences, engage in discussions with experts. For this reason, I have deemed useful to postpone the use of the budget to the subsequent fiscal year, in which it seems possible to carry out more effectively international collaborations and interactions.
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