quantum circuit model of black hole evaporation
play

Quantum Circuit Model of Black Hole Evaporation Yasusada Nambu - PowerPoint PPT Presentation

Oct 06, 2023 •973 likes •1.2k views

Quantum Circuit Model of Black Hole Evaporation Yasusada Nambu Nagoya University, Japan QIST@YITP , Kyoto June 12, 2019 T.Tokuzumi, A.Matsumura, Y.Nambu Quantum circuit model of black hole evaporation, CQG 35 (2018) 235013

  1. Quantum Circuit Model of Black Hole Evaporation Yasusada Nambu Nagoya University, Japan QIST@YITP , Kyoto June 12, 2019 T.Tokuzumi, A.Matsumura, Y.Nambu “Quantum circuit model of black hole evaporation”, CQG 35 (2018) 235013 QIST2019-talk.key - 2019 � 6 � 12 �

  2. <latexit sha1_base64="PGCgjAPOVA5zKzonoSsHTNnP0o=">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</latexit> <latexit sha1_base64="PGCgjAPOVA5zKzonoSsHTNnP0o=">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</latexit> <latexit sha1_base64="PGCgjAPOVA5zKzonoSsHTNnP0o=">ADE3icjVFBa9RQEJ6kautW7bYqCF6Cy4oXl7elUBUKpV4WQWi3ri30tSFJZ9dHk/dC3tvFNQ3e/QF68KTgQfwLgqAevHj0B/gQTxW8OLBSTYitlacR+bN+2a+mXyMH4dCG8b2LHvs2PET4xMnK5OnTp+Zqk7P3NWqnwTYCVSoknXf0xgKiR0jTIjrcYJe5Ie45u/czPNrA0y0UPKOGca4GXk9Kboi8AxBbvXhLo+14IkneyG63OB9o7tpK1vgcaK2XcF1P3JT6YoFlm1xIbtm6OBWenWOx8K5zVWEPc8VDhVku+QONlpqZVwZEaH+W/ZWO3OrNdZghTmHg2YZ1KC0ZV9Axy2QUEAfYgAQYKhOAQPNJ0NaAKDmLBNSAlLKBJFHiGDCnH7VIVU4RG6Q75Hr40SlfTOe+qCHdCUkL6EmA7U2Sf2ku2zD+wV+8J+HNkrpQ5Dwg35X1PrR9bm8/L/HtLtj+Zg7E49urD6/T94Ed0G7v3m/YOTazTQhWuFNkFa4wLJVQejDoMHT/ZXb7Tr6WX2nH0lvc/YHntHiuXgW/BiBdtPoUILax5cz+GgM9u43mArc7XFpXJzE3ARLsEVWs8LEILlqFDYz9bk9Y567z92H5tv7Xfj0ptq+SchT/M/vgT9DXG1A=</latexit> <latexit sha1_base64="PGCgjAPOVA5zKzonoSsHTNnP0o=">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</latexit> <latexit sha1_base64="s+RdOQzBjtiw+Aknm8SyRxcs3RM=">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</latexit> <latexit sha1_base64="s+RdOQzBjtiw+Aknm8SyRxcs3RM=">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</latexit> <latexit sha1_base64="s+RdOQzBjtiw+Aknm8SyRxcs3RM=">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</latexit> <latexit sha1_base64="s+RdOQzBjtiw+Aknm8SyRxcs3RM=">ACqHicSyrIySwuMTC4ycjEzMLKxs7BycXNw8vHLyAoFacX1qUnBqanJ+TXxSRlFicmpOZlxpaklmSkxpRUJSamJuUkxqelO0Mkg8vSy0qzszPCympLEiNzU1Mz8tMy0xOLAEKxQuIhMR72MakFSUmVxvWVlvEFGQq+NbGCygb6BmAgQImwxDKUGaAgoB8gf0MQwpDPkMyQylDLkMqQx5DCVAdg5DIkMxEYzGDIYMBQAxWIZqoFiRUBWJlg+laGWgQuotxSoKhWoIhEomg0k04G8aKhoHpAPMrMYrDsZaEsOEBcBdSowqBpcNVhp8NnghMFqg5cGf3CaVQ0oRIoXgIkYbaq4lQLsg/k7kognQSxJ7Ugnr9LIvg7EfpygXQJQwZCHx49ID+WMKQxWID9lgn0awFYBOTrZIgJZVXTPwdbBalWqxksMngN9O9Cg5sGh4E+ziv7krw0MDVoNgMXMIM0aMHkxFqpGepZxBouzgBI05DgZpBiUGDWD0mDM4MHgwBDCEAq2tYljAsJhFZM2UyBTOFMkRCkTI1SPMAMKYEoCABG9mnM=</latexit> Black Hole Evaporation and Monogamy E arly emitted R adiation ER J ust emitted R adiation JR Hawking radiation BH particles are created around BH horizon 1 e � 4 ⇡ M! i n i j n i i BH ˝ j n i i JR Y X j i H D n i D 0 i entangled pair of particles black hole 1 thermal property T H D 8 ⇡ M ● Gravitational energy of BH is extracted by particle creation ● We want to know about Final state of evaporating system ? Possible scenario, remnant ? information issue ? � 2 QIST2019-talk.key - 2019 � 6 � 12 �

Download Presentation
Download Policy: The content available on the website is offered to you 'AS IS' for your personal information and use only. It cannot be commercialized, licensed, or distributed on other websites without prior consent from the author. To download a presentation, simply click this link. If you encounter any difficulties during the download process, it's possible that the publisher has removed the file from their server.

Recommend

A Model of Black Hole Evaporation and 4D Weyl Anomaly RIKEN-iTHES Yuki Yokokura with H. Kawai

A Model of Black Hole Evaporation and 4D Weyl Anomaly RIKEN-iTHES Yuki Yokokura with H. Kawai

A Model of Black Hole Evaporation and 4D Weyl Anomaly RIKEN-iTHES Yuki Yokokura with H. Kawai (kyoto university) [H. Kawai and Y. Y, Universe 3, 51, (2017)] 2017 August 7 @ Strings and Fields Motivation What is the black hole in

537 views • 27 slides
A Brief Review of Quantum Information Aspects of Black Hole Evaporation Reference: M. Hotta and

A Brief Review of Quantum Information Aspects of Black Hole Evaporation Reference: M. Hotta and

A Brief Review of Quantum Information Aspects of Black Hole Evaporation Reference: M. Hotta and A. Sugita, Prog. Theor. Exp. Phys, 123B04 (2015). M. Hotta, R. Schtzhold and W. G. Unruh, Phys. Rev. D 91, 124060 (2015). M. Hotta, Y. Nambu, and

1.33k views • 105 slides
An Approach to the information problem in a Self-consistent Model of the Black Hole Evaporation

An Approach to the information problem in a Self-consistent Model of the Black Hole Evaporation

An Approach to the information problem in a Self-consistent Model of the Black Hole Evaporation Yuki Yokokura(YITP) (with H. Kawai) (Based on my PhD thesis and H. Kawai, Y. Matsuo, and Y. Yokokura, International Journal of Modern Physics A,

363 views • 20 slides
Soft-Hair Enhanced Entanglement Beyond Page Curves in Black-Hole Evaporation Qubit Models

Soft-Hair Enhanced Entanglement Beyond Page Curves in Black-Hole Evaporation Qubit Models

Soft-Hair Enhanced Entanglement Beyond Page Curves in Black-Hole Evaporation Qubit Models Masahiro Hotta Tohoku University Based on M. Hotta, Y. Nambu and K. Yamaguchi, arXiv:1706.07520 . Introduction Large black-hole spacetimes are

834 views • 60 slides
Search for Primordial Black Hole Evaporation with VERITAS Simon Archambault, for the VERITAS

Search for Primordial Black Hole Evaporation with VERITAS Simon Archambault, for the VERITAS

Search for Primordial Black Hole Evaporation with VERITAS Simon Archambault, for the VERITAS Collaboration 1 20/07/2017 Black Holes 4 types of black holes Stellar-mass black holes Supermassive black holes Intermediate-mass

749 views • 19 slides
Evaporating Black Hole and Partial Deconfinement Masanori Hanada University of Southampton 28

Evaporating Black Hole and Partial Deconfinement Masanori Hanada University of Southampton 28

Evaporating Black Hole and Partial Deconfinement Masanori Hanada University of Southampton 28 Dec 2018 @ YITP , Kyoto Holographic Principle Black Hole Non-gravitational systems Quantum gravity Equivalent Matrix Model Super

1.23k views • 80 slides
Some real-time aspects of quantum black hole Masanori Hanada Hana Da Masa Nori

Some real-time aspects of quantum black hole Masanori Hanada Hana Da Masa Nori

Some real-time aspects of quantum black hole Masanori Hanada Hana Da Masa Nori July 12, 2018 @ Vienna Holography Black QFT = Hole Holography Black QFT = Hole For imaginary time, lattice simulation is powerful and probably

829 views • 67 slides
Black Hole Attractors and Superconformal Quantum Mechanics Davide Gaiotto

Black Hole Attractors and Superconformal Quantum Mechanics Davide Gaiotto

Black Hole Attractors and Superconformal Quantum Mechanics Davide Gaiotto dgaiotto@fas.harvard.edu Harvard University joint work with Aaron Simons, Andrew Strominger, Xi Yin hep-th/ 0412322 hep-th/ 0412179 Black Hole Attractors and

932 views • 67 slides
Black Hole Thermodynamics Robert M. Wald I. Black Holes; Event Horizons and Killing Horizons II.

Black Hole Thermodynamics Robert M. Wald I. Black Holes; Event Horizons and Killing Horizons II.

Black Hole Thermodynamics Robert M. Wald I. Black Holes; Event Horizons and Killing Horizons II. The First Law of Black Hole Mechanics and Black Hole Entropy III. Dynamic and Thermodynamic Stability of Black Holes IV. Quantum Aspects of Black

1.74k views • 116 slides
Quantum Coarse-graining behind black holes Arvin Shahbazi-Moghaddam with Ven Chandrasekaran and

Quantum Coarse-graining behind black holes Arvin Shahbazi-Moghaddam with Ven Chandrasekaran and

Quantum Coarse-graining behind black holes Arvin Shahbazi-Moghaddam with Ven Chandrasekaran and Raphael Bousso Berkeley June 4th, 2019 Black hole second law A Black holes are thermodynamic objects with S BH = 4 G Black hole second law

636 views • 32 slides
The quantum fate of black hole horizons Sergey Solodukhin LMPT (Tours)/CERN Talk at RTG

The quantum fate of black hole horizons Sergey Solodukhin LMPT (Tours)/CERN Talk at RTG

The quantum fate of black hole horizons Sergey Solodukhin LMPT (Tours)/CERN Talk at RTG Models of Gravity workshop, 19-20 February 2018, Bremen With Cl ement Berthiere and Deb Sarkar; arXiv:1712.09914 Sergey Solodukhin The quantum

553 views • 32 slides
The black hole information paradox and the fate of the infalling observer Kyriakos Papadodimas

The black hole information paradox and the fate of the infalling observer Kyriakos Papadodimas

The black hole information paradox and the fate of the infalling observer Kyriakos Papadodimas CERN and University of Groningen Quantum Gravity in Paris 2017 Motivations Black hole information paradox What happens when crossing the horizon?

1.19k views • 64 slides
ATP Evaporation Plant ATP - Evaporation Unpacking ATP - Evaporation Positioning The Effects

ATP Evaporation Plant ATP - Evaporation Unpacking ATP - Evaporation Positioning The Effects

ATP Evaporation Plant ATP - Evaporation Unpacking ATP - Evaporation Positioning The Effects ATP - Evaporation Lifting In Vessels ATP - Evaporation Valve &amp; Pump Skid ATP - Evaporation X2 Effects in position ATP - Evaporation Vaccum

440 views • 13 slides
Black hole X-ray binaries V: Formation and evolution of black hole binaries Thomas J. Maccarone

Black hole X-ray binaries V: Formation and evolution of black hole binaries Thomas J. Maccarone

Black hole X-ray binaries V: Formation and evolution of black hole binaries Thomas J. Maccarone Jan 14, 2017, 2nd Fudan Winter School on Black Hole Astrophysics Overview Phenomena associated with binary evolution Formation of close binaries

651 views • 30 slides
Geometry of Higher-Dimensional Black Hole Thermodynamics (hep-th/0510139) Narit Pidokrajt (work

Geometry of Higher-Dimensional Black Hole Thermodynamics (hep-th/0510139) Narit Pidokrajt (work

Geometry of Higher-Dimensional Black Hole Thermodynamics (hep-th/0510139) Narit Pidokrajt (work with Jan E. Aman) Quantum and Field Theory Fysikum, Stockholms Universitet Abstract We apply the Ruppeiner theory to black hole

298 views • 14 slides
Constructing black holes and black hole microstates String theory and the fuzzball proposal Cl

Constructing black holes and black hole microstates String theory and the fuzzball proposal Cl

Introduction : black hole issues and entropy counting The fuzzball proposal Constructing three-charge supersymmetric solutions Non-BPS extremal black holes Conclusion and perspectives Constructing black holes and black hole microstates String

1.37k views • 95 slides
The F he Four our Wind inds Education, 179,180 (1903) Angels are now restraining the winds of

The F he Four our Wind inds Education, 179,180 (1903) Angels are now restraining the winds of

The F he Four our Wind inds Education, 179,180 (1903) Angels are now restraining the winds of strife that they may not blow until the world shall be warned of its coming doom, but a storm is gathering, ready to burst upon the earth, and

567 views • 33 slides
THE THE ANGELIC ANGELIC RIGHTS MOVEM RIGHTS MOVEMENT ENT A CLOSER LOOK AT THE WAR IN HEAVEN

THE THE ANGELIC ANGELIC RIGHTS MOVEM RIGHTS MOVEMENT ENT A CLOSER LOOK AT THE WAR IN HEAVEN

THE THE ANGELIC ANGELIC RIGHTS MOVEM RIGHTS MOVEMENT ENT A CLOSER LOOK AT THE WAR IN HEAVEN AND ON EARTH KEY QUESTIONS What does Gods order and government look like? Was Lucifers rebellion in Heaven a rights

402 views • 29 slides
Constructing Antidictionaries in Output-Sensitive Space Lorraine Ayad Golnaz Badkobeh Gabriele

Constructing Antidictionaries in Output-Sensitive Space Lorraine Ayad Golnaz Badkobeh Gabriele

Constructing Antidictionaries in Output-Sensitive Space Lorraine Ayad Golnaz Badkobeh Gabriele Fici Alice H eliou Solon Pissis LSD/LAW 2019 London, UK, 7-8 Feb. 2019 L. Ayad, G. Badkobeh, G. Fici, A. H eliou, S. Pissis Constructing

560 views • 36 slides
Formal Models of Language Paula Buttery Dept of Computer Science &amp; Technology, University of

Formal Models of Language Paula Buttery Dept of Computer Science &amp; Technology, University of

Formal Models of Language Paula Buttery Dept of Computer Science &amp; Technology, University of Cambridge Paula Buttery (Computer Lab) Formal Models of Language 1 / 31 Regular grammars give us linear trees guard start S the A B girl

476 views • 31 slides
Homotopy Type Theory and Algebraic Model Structures (II) Christian Sattler School of Mathematics

Homotopy Type Theory and Algebraic Model Structures (II) Christian Sattler School of Mathematics

Homotopy Type Theory and Algebraic Model Structures (II) Christian Sattler School of Mathematics University of Leeds Topologie Alg ebrique et Applications Paris, 2nd December 2016 1 Current status Last talk: (1) algebraic weak

330 views • 32 slides
THE PERSEVERING PILGRIM TRUTH ON THE WEB MINISTRIES --- WWW.TOTW.ORG --- A CHURCH OF GOD AT

THE PERSEVERING PILGRIM TRUTH ON THE WEB MINISTRIES --- WWW.TOTW.ORG --- A CHURCH OF GOD AT

THE PERSEVERING PILGRIM TRUTH ON THE WEB MINISTRIES --- WWW.TOTW.ORG --- A CHURCH OF GOD AT WOODSTOCK Exodus 23:14-16 Three times thou shalt keep a feast unto me in the year. Thou shalt keep the feast of unleavened bread: (thou shalt eat

660 views • 46 slides
Investigation of the front end electronics for the proton radius experiments Alexander Inglessi

Investigation of the front end electronics for the proton radius experiments Alexander Inglessi

Investigation of the front end electronics for the proton radius experiments Alexander Inglessi PNPI Gatchina TPC Collaboration Meeting 10 March 2020 TU Mainz TPC prototype Active target: gas target + ionization chamber 4 64 8

462 views • 18 slides
Spiritual Counsel in Nahjul Balagha Session Three Ponder and Comment It can be said of

Spiritual Counsel in Nahjul Balagha Session Three Ponder and Comment It can be said of

Spiritual Counsel in Nahjul Balagha Session Three Ponder and Comment It can be said of mawizah that if it comes forth from the soul then it necessarily alights upon the heart. Otherwise it does not go beyond a listener s ears.

398 views • 9 slides

More recommend