2022 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 transition / Quantum vacuum / Curved space / Quantum field theory / Zeta function / Effective action / Cold atoms / Spectral geometry |
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| Outline of Annual Research Achievements |
The work carried so far has been focusing on developing a technique to compute quantum vacuum effects in stationary backgrounds and in theories with interactions, as these allow to consider phase transitions and bubble nucleation.
We have developed such a method for a nonlinear quantum field theory for which we could exactly integrate the equation of motion and in turn quantize the theory at full nonlinear level, without resorting to a perturbative approach. Furthermore we have developed an original and very powerful numerical implementation of zeta-function regularization, based on the Weyl spectral theorem. We have tested this approach to compute the vacuum energy in a variety of cases (work published in Physical Review D) and we have just extended the approach to a non-relativistic Schrodinger quantum field theory (a paper is being written up and should be submitted before the summer).
The problem we are currently engaged in has to do with the formation of bubbles, as outlined in the research proposal, in the context of a Bose binary mixture on a spherical surface. This part of the work is in progress: we have developed the necessary formalism to address this problem and we are in the process of developing its numerical implementation. We hope to finish a paper about this also before next summer.
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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
The project is proceeding rather smoothly and my current research that focuses on obtaining bubble solutions in a binary Bose mixture is proven to be very exciting, due to recent experiments in cold atoms. In fact, this is an unexpected positive turn in my research as it can reveal a new path to describe new yet-to-observe physical phenomena and connect certain aspects of quantum field theory in curved space with the physics of ultra-cold atoms as well as indicate new experimental opportunities.
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| Strategy for Future Research Activity |
Over the next 6 months I am planning to complete the work on the bubble formation in binary mixtures, as well as another work on quantum vacuum effects in curved space with defects. I am planning to promote the work at the next JPS meeting and in a research trip next September.
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| Causes of Carryover |
For the next fiscal year, I am planning a research visit to the Centre of Excellence in Future Low-Energy Electronics Technologies at the School of Mathematics and Physics of the University of Queensland in Australia where a very active research group in cold atoms and also one of my collaborators are based. For this trip I am expecting to use about 400,000 yen (flight cost plus 2 weeks stay). In September 2023, I am also planning to attend the JPS meeting to be held at the university of Tohoku, for which I am expecting too use about 100,000 yen (train fare plus one week stay).
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