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東京確率論セミナー
過去の記録 ～05/17｜次回の予定｜今後の予定 05/18～
| 開催情報 | 月曜日 16:00～17:30 数理科学研究科棟(駒場) 126号室 |
|---|---|
| 担当者 | 佐々田槙子、中島秀太（慶應義塾大学）、星野壮登（東京科学大学）、蛯名真久（東京科学大学） |
| セミナーURL | https://sites.google.com/view/tokyo-probability-seminar23/ |
2026年06月15日(月)
16:00-17:30 数理科学研究科棟(駒場) 126号室
15:15〜 ２階のコモンルームでTea timeを行います。ぜひこちらにもご参加ください。
一場 知之 氏 (University of California Santa Barbara)
Feynman formula for discrete-time quantum walk and its applications
15:15〜 ２階のコモンルームでTea timeを行います。ぜひこちらにもご参加ください。
一場 知之 氏 (University of California Santa Barbara)
Feynman formula for discrete-time quantum walk and its applications
[ 講演概要 ]
We explicitly connect (discrete-time) quantum walks on Z with a four-state Markov additive process via a Feynman-type formula. Using this representation, we derive a relation between the spectral decomposition of the Markov additive process and the limiting density of the homogeneous quantum walk. In addition, we consider a space-time rescaling of quantum walks, which leads to a system of quantum transport PDEs of Dirac type in continuous time and space with phase interaction and potential terms. Our probabilistic representation for this type of PDE offers its stochastic extension as well as an efficient Monte Carlo computational technique. This is joint work with Jean-Pierre Fouque and Ka Lok Lam.
We explicitly connect (discrete-time) quantum walks on Z with a four-state Markov additive process via a Feynman-type formula. Using this representation, we derive a relation between the spectral decomposition of the Markov additive process and the limiting density of the homogeneous quantum walk. In addition, we consider a space-time rescaling of quantum walks, which leads to a system of quantum transport PDEs of Dirac type in continuous time and space with phase interaction and potential terms. Our probabilistic representation for this type of PDE offers its stochastic extension as well as an efficient Monte Carlo computational technique. This is joint work with Jean-Pierre Fouque and Ka Lok Lam.
