Ergodic properties in athermal diffusion processes and its applications

• Project/Area Number: 26800204
• Research Category: Grant-in-Aid for Young Scientists (B)
• Allocation Type: Multi-year Fund
• Research Field: Mathematical physics/Fundamental condensed matter physics
• Research Institution: Keio University
• Principal Investigator: Akimoto Takuma 慶應義塾大学, 理工学研究科(矢上), 特任准教授 (30454044)
• Project Period (FY): 2014-04-01 – 2017-03-31
• Project Status: Completed (Fiscal Year 2016)
• Budget Amount: ¥3,510,000 (Direct Cost: ¥2,700,000、Indirect Cost: ¥810,000); Fiscal Year 2016: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000); Fiscal Year 2015: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000); Fiscal Year 2014: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
• Keywords: 異常拡散 / エルゴード特性 / 非熱的な拡散 / 不均一環境 / 非熱的拡散 / エルゴード性 / 非平衡現象 / 非線形現象 / 細胞内輸送

Outline of Final Research Achievements

Purpose of our research project is to clarify ergodic properties of time-averaged mean square displacement characterizing diffusivity of systems in non-thermally driven diffusion processes, where fluctuation-dissipation relation is broken. We consider a random walk model where the jump length is coupled to the waiting time and a Brownian motion where the diffusion coefficient changes randomly with time. We analytical showed the ensemble average and the relative standard deviation of time-averaged mean square displacement as a function of the measurement time and its initial ensemble dependency.
Our works have been published in Phys. Rev. E and J. Stat. Mech. and I gave presentations on this issue in international conferences.

Research Products

• [Int'l Joint Research] Bar-Ilan大学(イスラエル)
• [Journal Article] Instability of buried hydration sites increases protein subdomains fluctuations in the human prion protein by the pathogenic mutation T188R (2016)
  • Author(s): K. Tomobe, E. Yamamoto, T. Akimoto, M. Yasui, and K. Yasuoka
  • Journal Title: AIP Adv. Volume: 6 Issue: 5 Pages: 055324-055324
  • DOI: 10.1063/1.4953061
  • Peer Reviewed
• [Journal Article] Distributional behaviors of time-averaged observables in Langevin equation with fluctuating diffusivity: Normal diffusion yet anomalous fluctuations (2016)
  • Author(s): T. Akimoto and E. Yamamoto
  • Journal Title: Phys. Rev. E Volume: 93 Issue: 6 Pages: 062109-062109
  • DOI: 10.1103/physreve.93.062109
  • Peer Reviewed / Acknowledgement Compliant
• [Journal Article] Langevin equation with fluctuating diffusivity: a two-state model (2016)
  • Author(s): T. Miyaguchi, T. Akimoto, and E. Yamamoto
  • Journal Title: Phys. Rev. E Volume: 94 Issue: 1 Pages: 012109-012109
  • DOI: 10.1103/physreve.94.012109
  • Peer Reviewed / Acknowledgement Compliant
• [Journal Article] Characteristic Sign Renewals of Kardar-Parisi-Zhang Fluctuations, (2016)
  • Author(s): *Kazumasa A. Takeuchi and Takuma Akimoto,
  • Journal Title: Journal of Statistical Physics Volume: 164 Issue: 5 Pages: 1167-1182
  • DOI: 10.1007/s10955-016-1582-0
  • Peer Reviewed / Acknowledgement Compliant
• [Journal Article] Universal Fluctuations of Single-Particle Diffusivity in Quenched Environment (2016)
  • Author(s): Takuma Akimoto, Eli Barkai, Keiji Saito
  • Journal Title: Physical Review Letters Volume: 117 Issue: 18 Pages: 180602-180602
  • DOI: 10.1103/physrevlett.117.180602
  • Peer Reviewed / Int'l Joint Research / Acknowledgement Compliant
• [Journal Article] Distributional behavior of diffusion coefficients obtained by single trajectories in annealed transit time model (2016)
  • Author(s): T. Akimoto and E. Yamamoto
  • Journal Title: J. Stat. Mech. Volume: 2016 Issue: 12 Pages: 123201-123201
  • DOI: 10.1088/1742-5468/2016/12/123201
  • Peer Reviewed / Acknowledgement Compliant
• [Journal Article] Transition from distributional to ergodic behavior in an inhomogeneous diffusion process: Method revealing an unknown surface diffusivity (2015)
  • Author(s): Takuma Akimoto and Kazuhiko Seki
  • Journal Title: Physical Review E Volume: 92 Issue: 2 Pages: 022114-022114
  • DOI: 10.1103/physreve.92.022114
  • Peer Reviewed
• [Journal Article] Fluctuation analysis of time-averaged mean-square displacement for the Langevin equation with time-dependent and fluctuating diffusivity (2015)
  • Author(s): Takashi Uneyama, Tomoshige Miyaguchi, and Takuma Akimoto
  • Journal Title: Physical Review E Volume: 92 Issue: 3 Pages: 032140-032140
  • DOI: 10.1103/physreve.92.032140
  • Peer Reviewed / Acknowledgement Compliant
• [Journal Article] Anomalous Dynamics of a Lipid Recognition Protein on a Membrane Surface (2015)
  • Author(s): Eiji Yamamoto, Antreas C. Kalli, Takuma Akimoto, Kenji Yasuoka and Mark S. P. Sansom
  • Journal Title: Scientific Reports Volume: 5 Issue: 1 Pages: 18245-18245
  • DOI: 10.1038/srep18245
  • Peer Reviewed / Open Access / Int'l Joint Research
• [Journal Article] Distributional behavior of time averages of non-L1 observables in one-dimensional intermittent maps with infinite invariant measures (2015)
  • Author(s): Takuma Akimoto, Soya Shinkai, Yoji Aizawa
  • Journal Title: Journal of Statistical Physics Volume: 158 Issue: 2 Pages: 476-493
  • DOI: 10.1007/s10955-014-1138-0
  • Peer Reviewed / Open Access / Acknowledgement Compliant
• [Journal Article] Generalized Lyapunov exponent as a unified characterization of dynamical instabilities (2015)
  • Author(s): Takuma Akimoto, Masaki Nakagawa, Soya Shinkai, Yoji Aizawa
  • Journal Title: Physical Review E Volume: 91 Issue: 1 Pages: 012926-012926
  • DOI: 10.1103/physreve.91.012926
  • Peer Reviewed / Open Access / Acknowledgement Compliant
• [Journal Article] Phase diagram in stored-energy-driven Levy flight (2014)
  • Author(s): T. Akimoto and T. Miyaguchi
  • Journal Title: J. Stat. Phys. Volume: 157 Issue: 3 Pages: 515-530
  • DOI: 10.1007/s10955-014-1084-x
  • Peer Reviewed / Open Access / Acknowledgement Compliant
• [Presentation] トラップモデルにおける不均一性に由来する拡散係数の大きな揺 らぎ (2017)
  • Author(s): 秋元琢磨、Eli Barkai、齊藤圭司
  • Organizer: 日本物理学会・第７２回年次大会
  • Place of Presentation: 大阪大学（大阪府・豊中市）
  • Year and Date: 2017-03-20
• [Presentation] 大数の法則の破れと異常拡散 (2017)
  • Author(s): 秋元琢磨
  • Organizer: 量子と古典の物理と幾何
  • Place of Presentation: 名古屋大学（愛知県・名古屋市）
  • Year and Date: 2017-02-11
  • Invited
• [Presentation] 異常拡散におけるエルゴード性の破れとサンプル依存性 (2016)
  • Author(s): 秋元琢磨
  • Organizer: 東京確率論セミナー
  • Place of Presentation: 東京大学（東京都・目黒区）
  • Year and Date: 2016-12-12
  • Invited
• [Presentation] Fluctuation analysis of time-averaged mean square displacements (2016)
  • Author(s): Takuma Akimoto
  • Organizer: Workshop on Stochasticity and Fluctuations in Small Systems
  • Place of Presentation: POSTECH (Korea)
  • Year and Date: 2016-11-30
  • Int'l Joint Research / Invited
• [Presentation] 局所的な拡散係数の本質的な揺らぎの検出理論 (2016)
  • Author(s): 秋元琢磨
  • Organizer: 「理論と実験」2016
  • Place of Presentation: 広島大学（広島県・東広島市）
  • Year and Date: 2016-10-07
  • Invited
• [Presentation] 不均質な環境下において自己駆動するゲルの拡散 (2016)
  • Author(s): 秋元琢磨、前田慎吾
  • Organizer: 第９回自然知能セミナー
  • Place of Presentation: 慶應義塾大学（神奈川県・横浜市）
  • Year and Date: 2016-09-21
  • Invited
• [Presentation] 不均一な環境により駆動されるゲルのランダムウォーク (2016)
  • Author(s): 秋元琢磨、前田慎吾
  • Organizer: 日本物理学会・秋季大会
  • Place of Presentation: 金沢大学（石川県・金沢市）
  • Year and Date: 2016-09-15
• [Presentation] Infinite invariant density in laser cooling (2016)
  • Author(s): Takuma Akimoto
  • Organizer: Ergodicity breaking and anomalous dynamics
  • Place of Presentation: Warwick (UK)
  • Year and Date: 2016-08-10
  • Int'l Joint Research / Invited
• [Presentation] Non-self-averaging transport coefficients in single-particle tracking: Beyond annealed approach (2016)
  • Author(s): Takuma Akimoto, Eli Barkai, Keiji Saito
  • Organizer: STATPHYS26
  • Place of Presentation: Lyon (France)
  • Year and Date: 2016-07-22
  • Int'l Joint Research
• [Presentation] General Framework for the Propagator in Heterogeneous Diffusion Processes (2016)
  • Author(s): Takuma Akimoto
  • Organizer: WE-Heraeus-Seminar on ``Quantifying Complex Transport with L\'evy Walks: From Cold Atoms to Humans and Robots”
  • Place of Presentation: Bad Honnef (Germany)
  • Year and Date: 2016-05-25
  • Int'l Joint Research / Invited
• [Presentation] Anomalous dynamics of Langevin equation with fluctuating diffusivity in equilibrium case and non-equilibrium case (2015)
  • Author(s): Takuma Akimoto
  • Organizer: Anomalous diffusion: wild and bad? Fundamentals & models for modern complex systems
  • Place of Presentation: Bad Wildbad (Germany)
  • Year and Date: 2015-10-03
  • Int'l Joint Research / Invited
• [Presentation] 不均一環境内における拡散係数の分布極限法則 (2015)
  • Author(s): 秋元琢磨
  • Organizer: ランダム力学系 とその応用
  • Place of Presentation: 京都大学（京都市・京都府）
  • Year and Date: 2015-09-27
  • Invited
• [Presentation] Fluctuations of time-averaged diffusion coefficients in annealed transit time model (2015)
  • Author(s): Takuma Akimoto
  • Organizer: KIAS workshop on anomalous dynamics in biological systems
  • Place of Presentation: Seoul (Korea)
  • Year and Date: 2015-09-03
  • Int'l Joint Research / Invited
• [Presentation] Fluctuation analysis of time-averaged mean square displacements of single trajectories (2015)
  • Author(s): Takuma Akimoto
  • Organizer: The 4th IGER International Symposium on Science of Molecular Assembly and Biomolecular systems
  • Place of Presentation: Nagoya, Japan
  • Year and Date: 2015-08-31
  • Int'l Joint Research / Invited
• [Presentation] Anomalous fluctuations in inhomogeneous diffusion processes (2015)
  • Author(s): Takuma Akimoto
  • Organizer: Stochastic modeling of anomalous dynamics in complex physical and biological systems
  • Place of Presentation: Wroclaw (Poland)
  • Year and Date: 2015-05-14
  • Int'l Joint Research / Invited
• [Presentation] リヤプノフ指数が0である弱いカオス系における新しい分布極限定理 (2015)
  • Author(s): 秋元琢磨
  • Organizer: 日本物理学会
  • Place of Presentation: 早稲田大学（東京都・新宿区）
  • Year and Date: 2015-03-21 – 2015-03-24
• [Presentation] Langevin equation with fluctuating diffusivity (2015)
  • Author(s): T. Akimoto
  • Organizer: 2015 Mini Stat Mech Meeting
  • Place of Presentation: Berkeley（CA, USA）
  • Year and Date: 2015-01-09 – 2015-01-11
• [Presentation] 揺らぐ拡散係数を持つランジュバン方程式 (2015)
  • Author(s): 秋元琢磨
  • Organizer: ソフトマター研究会
  • Place of Presentation: 名古屋大学（愛知県・名古屋市）
  • Year and Date: 2015-01-06 – 2015-01-08
• [Presentation] 拡散過程において時間平均量の揺らぎの解析からわかる事 (2014)
  • Author(s): 秋元琢磨
  • Organizer: 理論と実験 2014
  • Place of Presentation: 広島大学（広島県・東広島市）
  • Year and Date: 2014-10-09 – 2014-10-10
  • Invited
• [Presentation] Anomalous water dynamics near the surface of a cell membrane (2014)
  • Author(s): 秋元琢磨
  • Organizer: The 8th Mini- Symposium on Liquids
  • Place of Presentation: 岡山大学（岡山県・岡山市）
  • Year and Date: 2014-07-05
  • Invited
• [Remarks]
  • URL: https://akimototakuma.wordpress.com/