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Effective dimension, level statistics, and integrability of Sachdev-Ye-Kitaev-like models One-day workshop for QFT and string theory Dec. 14, 2018 @ Osaka city university Keywords: Eiki Iyoda Chaos and SYK model (University of Tokyo)

  1. Effective dimension, level statistics, 
 and integrability of 
 Sachdev-Ye-Kitaev-like models One-day workshop for QFT and string theory Dec. 14, 2018 @ Osaka city university Keywords: Eiki Iyoda Chaos and SYK model (University of Tokyo) the role of disorder in SYK E. Iyoda, H. Katsura, and T. Sagawa, Phys. Rev. D 98 , 086020 (2018)

  2. Background 1/3: chaos and SYK model Chaos : "High sensitivity to initial conditions" e.g. the butterfly effect quantum "analogues" → quantum chaos SYK model (Sachdev-Ye-Kitaev model) Model of N randomly interacting fermions Attracted attentions in holography, condensed matter, quantum information, etc....

  3. <latexit sha1_base64="4gZa2TCo3TcKBsqitXaPUZ+Ppn4=">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</latexit> <latexit sha1_base64="pB8AlDpt5wZIc0uUPNaljDLgjEs=">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</latexit> Background 2/3: Blackhole information paradox Quantum mechanics : information is never lost Unitary time evolution General relativity : information is "lost" because the Hawking radiation is "thermal" Hawking radiation Black hole How to bridge these two conflicting theories?

  4. Background 3/3: "Chaotic bound and SYK" Thought experiment by Hayden-Preskill (2007) → "Blackhole reflects quantum information like a mirror." To make the phenomena possible, BH should be a very good scrambler of quantum information. Besides, BH is the "fastest scrambler" in nature. Hayden-Preskill, Sekino-Susskind In the sense of "the chaotic bound", proven by Maldacena-Shenker-Stanford. SYK model saturates the chaotic bound.

  5. Background 3/3: "Chaotic bound and SYK" Thought experiment by Hayden-Preskill (2007) → "Blackhole reflects quantum information like a mirror." To make the phenomena possible, BH should be a very good scrambler of quantum information. Besides, BH is the "fastest scrambler" in nature. Hayden-Preskill, Sekino-Susskind In the sense of "the chaotic bound", proven by Maldacena-Shenker-Stanford. SYK model saturates the chaotic bound. We will review.

  6. What I will talk about.... " SYK model and chaos " attracts attention not only in high-energy physics, but also in condensed matter physics.

  7. What I will talk about.... " SYK model and chaos " attracts attention not only in high-energy physics, but also in condensed matter physics. I study statistical physics. - thermalization - dynamics of Q-info...

  8. What I will talk about.... " SYK model and chaos " attracts attention not only in high-energy physics, but also in condensed matter physics. I study statistical physics. - thermalization - dynamics of Q-info... 1. Review 1.1 Chaos and quantum chaos 1.2 Information paradox and chaotic bound 1.3 SYK model 2. Wishart SYK model "The role of disorder in SYK model" E. Iyoda, H. Katsura, and T. Sagawa, PRD 98 , 086020 (2018) or 1806.10405

  9. <latexit sha1_base64="4qiEzFSrngIb0hx2n3+D/rc+G4=">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</latexit> <latexit sha1_base64="EXZ15h8kry6xo4sJxmlxFK8pcEg=">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</latexit> <latexit sha1_base64="FhGw+n3sGcia8LUeaz1E64YOY=">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</latexit> <latexit sha1_base64="En263AEUmrv0t1sv+wzVzgW/aOc=">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</latexit> Chaos High sensitivity to initial conditions e.g. the butterfly effect Small deviation is amplified by chaotic dynamics. : Lyapunov exponent trajectory 2 trajectory 1 Time

  10. Chaos Examples 1. billiard potential 2. time dependent external field: Kicked rotator model 3. interaction: double pendulum, coupled oscillator How about chaos in quantum systems?

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