Quantum entanglement at all distances

Quantum entanglement

at all distances

2021 H.L. Welsh Lectures in Physics University of Toronto

May 6, 2021Subir Sachdev

HARVARDTalk online: sachdev.physics.harvard.edu

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Newton showed (1687) that the same laws of motion applied onplanetary length scales (⇠ 1 trillion meters)

and the length scale of an apple tree (1 meter).

What happens on smaller and larger distances ?

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Newton showed (1687) that the same laws of motion applied onplanetary length scales (⇠ 1 trillion meters)

and the length scale of an apple tree (1 meter).

Going small…..

Hydrogen atom

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) 10�10 meters (<latexit sha1_base64="4vbYp/uxnYaIe3iHtQFjUzxZ00Y=">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</latexit>

The motion of the electron around the proton is not described bythe same theory as the motion of the planets around the sun.

Hydrogen atom

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) 10�10 meters (<latexit sha1_base64="4vbYp/uxnYaIe3iHtQFjUzxZ00Y=">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</latexit>

The motion of the electron around the proton is not described bythe same theory as the motion of the planets around the sun.

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It is described by the quantum theory

of Schrodinger and Heisenberg (1925).

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The most remarkable new idea in the quantum theory is theprinciple of superposition:

a physical system can be in asuperposition of two (or more) distinct states.

Quantum superposition in a hydrogen molecule

Hydrogen atom:

=1⌃2

(|⇥⇤⌅ � |⇤⇥⌅)

Hydrogen molecule:

= _

Quantum Entanglement

_

Einstein, Podolsky, Rosen (1935)


_



_


_

Quantum EntanglementEinstein, Podolsky, Rosen (1935)

Measurement of one electron instantaneously

determines the state of the other electron very far away


_


Measurement of one electron instantaneously

determines the state of the other electron very far away

http://nyti.ms/1OIO2WJ

SCIENCE

Sorry, Einstein. Quantum Study Suggests‘Spooky Action’ Is Real.By JOHN MARKOFF OCT. 21, 2015

In a landmark study, scientists at Delft University of Technology in theNetherlands reported that they had conducted an experiment that they say provedone of the most fundamental claims of quantum theory — that objects separated bygreat distance can instantaneously affect each other’s behavior.

The finding is another blow to one of the bedrock principles of standardphysics known as “locality,” which states that an object is directly influenced onlyby its immediate surroundings. The Delft study, published Wednesday in thejournal Nature, lends further credence to an idea that Einstein famously rejected.He said quantum theory necessitated “spooky action at a distance,” and he refusedto accept the notion that the universe could behave in such a strange andapparently random fashion.

In particular, Einstein derided the idea that separate particles could be“entangled” so completely that measuring one particle would instantaneouslyinfluence the other, regardless of the distance separating them.

Einstein was deeply unhappy with the uncertainty introduced by quantumtheory and described its implications as akin to God’s playing dice.

But since the 1970s, a series of precise experiments by physicists are1 of 2

© 2015 The New York Times Company

Part of the laboratory setup for an experiment

at Delft University of Technology, in which

two diamonds were set 1.3 kilometers apart, entangled and then shared information.

Going big (and heavy)…..

Objects so dense that light is gravitationally bound to them.

Black Holes

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We need corrections toNewton’s equationswhich are given byEinstein’s theory of

general relativity (1915),to describe black holes


Black Holes


Black Holes

Horizon radius R =2GM

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G Newton’s constant, c velocity of light, M mass of black holeFor M = earth’s mass, R ⇡ 9mm!

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We need corrections toNewton’s equationswhich are given byEinstein’s theory of

general relativity (1915),to describe black holes

LOFAR LBA Sky Survey showing 25000 supermassive black holes on 4% of the northern sky.

Obtained by 52 radio telescopes across Europe

de Gasperin et al. (2021)

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Each black hole has a size ⇠ 1010 meters,and is at the center of its own galaxy (like the Milky way)

Applying the theory of the very small

to the very big (black holes)….

_

Quantum Entanglement across a black hole horizon

_


Black hole horizon

_

Black hole horizon


Black hole horizon


There is quantum entanglement between the inside and outside of

a black hole

Black hole horizon


Hawking (1975) used other arguments to show that black hole horizons have a temperature(The entanglement reasoning: to an outside observer, the state of the electron inside the

black hole cannot be known, and so the outside electron is in a random state. )

Going small and big…..

We don’t have a completely general quantum theory of black holes today.

Such a theory requires

that we understand multi-particle entanglement for

many-many particles.

We don’t have a completely general quantum theory of black holes today.

Such a theory requires

that we understand multi-particle entanglement for

many-many particles.

The problem of multi-particle entanglement also appears in other problems

in modern physics:

Quantum computing: control entanglement of many qubits

(really hard to isolate from the environment).

Quantum materials: crystals with multiple elements naturally display phases with multi-electron entanglement.


in modern physics:





in modern physics:





in modern physics:





in modern physics:




YBa2Cu3O6+x

High temperature superconductors

Julian Hetel and Nandini Trivedi, Ohio State University

Nd-Fe-B magnets, YBaCuO superconductor

pc

Strange Metal

The SYK model:a theory of entanglement,

from the very small to the very big…..

The SYK model has a scale-invariant entanglement structure:

i.e. electrons are entangled at all distance and time scales

In one set of variables, it describes

certain strange metals

In a dual set of variables it describes certain black holes

The Sachdev-Ye-Kitaev (SYK) model

Sachdev (2010), Kitaev (2015), Maldacena Stanford (2015)

Sachdev, Ye (1993)








Sachdev, Ye (1993)








Sachdev, Ye (1993)


Pick a set of random positions

Sachdev, Ye (1993); Kitaev (2015)

Place electrons randomly on some sites

The SYK modelSachdev, Ye (1993); Kitaev (2015)

The SYK model



The SYK model



Entangle electrons pairwise randomly

The SYK modelSachdev, Ye (1993); Kitaev (2015)

The SYK model



The SYK model



The SYK model



The SYK model



The SYK model



The SYK model



The SYK model



The SYK model



The SYK model



The SYK model



The SYK model



The SYK model



The SYK model



The SYK model



The SYK model










Sachdev, Ye (1993)

More on metals,

ordinary and strange)

Ordinary metals

Ordinary metals are shiny, and they conduct heat and electricity efficiently. Each atom donates electrons which

are delocalized throughout the entire crystal

Almost all many-electron systems are described by the quasiparticle concept: a quasiparticle is an “excited lump” in the many-electron state which responds just like an ordinary particle. The existence of quasiparticles implies limited many-particle entanglement

R.D. Mattuck

Current flow with quasiparticles

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Flowing quasiparticles scatter o↵ eachother in a typical scattering time ⌧

This time is much longer than a limiting

‘Planckian time’~

kBT.

The long scattering time implies thatquasiparticles are well-defined.

18

Table 1 | Slope of T-linear resistivity and Planckian limit in seven materials.

Material n (1027 m-3)

m*(m0)

A1 / d (! / K)

h / (2e2 TF)(! / K)

⍺

Bi2212 p = 0.23 6.8 8.4 ± 1.6 8.0 ± 0.9 7.4 ± 1.4 1.1 ± 0.3

Bi2201 p ~ 0.4 3.5 7 ± 1.5 8 ± 2 8 ± 2 1.0 ± 0.4

LSCO p = 0.26 7.8 9.8 ± 1.7 8.2 ± 1.0 8.9 ± 1.8 0.9 ± 0.3

Nd-LSCO p = 0.24 7.9 12 ± 4 7.4 ± 0.8 10.6 ± 3.7 0.7 ± 0.4

PCCO x = 0.17 8.8 2.4 ± 0.1 1.7 ± 0.3 2.1 ± 0.1 0.8 ± 0.2

LCCO x = 0.15 9.0 3.0 ± 0.3 3.0 ± 0.45 2.6 ± 0.3 1.2 ± 0.3

TMTSF P = 11 kbar 1.4 1.15 ± 0.2 2.8 ± 0.3 2.8 ± 0.4 1.0 ± 0.3

Table 1 | Slope of T-linear resistivity vs Planckian limit in seven materials.

Comparison of the measured slope of the T-linear resistivity in the T = 0 limit,

A1 , with the value predicted by the Planckian limit (Eq. 1; penultimate column),

for four hole-doped cuprates (Bi2212, Bi2201, LSCO and Nd-LSCO), two

electron-doped cuprates (PCCO and LCCO) and the organic conductor

(TMTSF)2PF6 , as discussed in the text (and Supplementary Information).

The ratio α of the experimental value, A1☐ = A1 / d, over the predicted value,

is given in the last column. Although A1☐ varies by a factor 5, the ratio m* / n

(~1/TF) is seen to vary by the same amount, so that α = 1.0 in all cases,

within error bars.

A. Legros, S. Benhabib, W. Tabis, F. Laliberté, M. Dion, M. Lizaire, B. Vignolle, D. Vignolles, H. Raffy, Z. Z. Li, P. Auban-Senzier, N. Doiron-Leyraud, P. Fournier, D. Colson, L. Taillefer, and C. Proust, Nature Physics 15, 142 (2019)

1

⌧= ↵

kBT

~<latexit sha1_base64="Q0pGo+lkjPvE7fTn3atRPbcYr7A=">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</latexit>

<latexit sha1_base64="nz362owMyLtIFSUrWy76tt2XzQA=">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</latexit>

Electron scattering time ⌧ in 7 di↵erent strange metals

18

Table 1 | Slope of T-linear resistivity and Planckian limit in seven materials.

Material n (1027 m-3)

m*(m0)

A1 / d (! / K)

h / (2e2 TF)(! / K)

⍺

Bi2212 p = 0.23 6.8 8.4 ± 1.6 8.0 ± 0.9 7.4 ± 1.4 1.1 ± 0.3

Bi2201 p ~ 0.4 3.5 7 ± 1.5 8 ± 2 8 ± 2 1.0 ± 0.4

LSCO p = 0.26 7.8 9.8 ± 1.7 8.2 ± 1.0 8.9 ± 1.8 0.9 ± 0.3

Nd-LSCO p = 0.24 7.9 12 ± 4 7.4 ± 0.8 10.6 ± 3.7 0.7 ± 0.4

PCCO x = 0.17 8.8 2.4 ± 0.1 1.7 ± 0.3 2.1 ± 0.1 0.8 ± 0.2

LCCO x = 0.15 9.0 3.0 ± 0.3 3.0 ± 0.45 2.6 ± 0.3 1.2 ± 0.3

TMTSF P = 11 kbar 1.4 1.15 ± 0.2 2.8 ± 0.3 2.8 ± 0.4 1.0 ± 0.3

Table 1 | Slope of T-linear resistivity vs Planckian limit in seven materials.

Comparison of the measured slope of the T-linear resistivity in the T = 0 limit,

A1 , with the value predicted by the Planckian limit (Eq. 1; penultimate column),

for four hole-doped cuprates (Bi2212, Bi2201, LSCO and Nd-LSCO), two

electron-doped cuprates (PCCO and LCCO) and the organic conductor

(TMTSF)2PF6 , as discussed in the text (and Supplementary Information).

The ratio α of the experimental value, A1☐ = A1 / d, over the predicted value,

is given in the last column. Although A1☐ varies by a factor 5, the ratio m* / n

(~1/TF) is seen to vary by the same amount, so that α = 1.0 in all cases,

within error bars.

A. Legros, S. Benhabib, W. Tabis, F. Laliberté, M. Dion, M. Lizaire, B. Vignolle, D. Vignolles, H. Raffy, Z. Z. Li, P. Auban-Senzier, N. Doiron-Leyraud, P. Fournier, D. Colson, L. Taillefer, and C. Proust, Nature Physics 15, 142 (2019)

1

⌧= ↵

kBT

~<latexit sha1_base64="Q0pGo+lkjPvE7fTn3atRPbcYr7A=">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</latexit>

Remarkable recent observation of‘Planckian’ strange metal transport in cuprates,pnictides, magic-angle graphene, andultracold atoms: the resistivity, ⇢, is

⇢ =m⇤

ne21

⌧

with a universal scattering rate

1

⌧⇡ kBT

~ ,

independent of the strength of interactions!

Current flow without quasiparticles

<latexit sha1_base64="T8j69x3gdBMLJctbK1AFSUAji44=">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</latexit>

<latexit sha1_base64="nz362owMyLtIFSUrWy76tt2XzQA=">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</latexit>

Electron scattering time ⌧ in 7 di↵erent strange metals

More on quantum black holes

J. D. Bekenstein, PRD 7, 2333 (1973)S. W. Hawking, Nature 248, 30 (1974)

Quantum Black holes

• Black holes have an entropy anda temperature, TH = ~c3/(8⇡GMkB).

• The entropy is proportional totheir surface area.

• They relax to thermal equilib-rium in a Planckian time⇠ ~/(kBTH).

<latexit sha1_base64="CtCuY4XtgqWdISPYGjZpgV6IJPk=">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</latexit><latexit sha1_base64="CtCuY4XtgqWdISPYGjZpgV6IJPk=">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</latexit><latexit sha1_base64="CtCuY4XtgqWdISPYGjZpgV6IJPk=">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</latexit><latexit sha1_base64="CtCuY4XtgqWdISPYGjZpgV6IJPk=">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</latexit>

J. D. Bekenstein, PRD 7, 2333 (1973)S. W. Hawking, Nature 248, 30 (1974)

Quantum Black holes





All many-body quantum systems (without quantum gravity)

have an entropy proportional to their volume !?!?

Bekenstein-Hod Universal Bound onInformation Emission Rate Is Obeyed byLIGO-Virgo Binary Black Hole RemnantsGregorio Carullo, Danny Laghi, John Veitch, andWalter Del Pozzo

Phys. Rev. Lett. 126, 161102 (2021)

Published April 22, 2021

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The combination of gravitational-wave and x-ray observations ofneutron stars provides new insight into the structure of thesestars, as well as new confirmation of Einstein’s theory of gravity.Read More »

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Black Holes Obey Information-EmissionLimitsApril 22, 2021 • Physics 14, s47

An analysis of the gravitational waves emitted from black hole mergers confirms that black holes are the fastestknown information dissipaters.

The extreme nature of black holes means that they o!er unique opportunities for testing the limits of physics laws.One law that researchers have wanted to test in this way is the one describing the maximum rate at whichinformation can flow out from a system. But until recently, this test was impossible with black holes because of alack of suitable candidates. That changed with the first measurements of gravitational waves. Now, an analysis ofthe gravitational waves detected from eight black hole mergers confirms that the law applies to these extremeobjects [1].

Any perturbed object will emit information about its state until it returns to equilibrium. Theory predicts a limit tothe rate of this information emission, with that limit depending on the object’s temperature and its relaxation time(how fast it regains equilibrium). For freshly merged black holes, these parameters are encoded in the emittedgravitational waves.

Of the roughly 50 black hole mergers so-far detected, researchers from the University of Pisa, Italy, and theUniversity of Glasgow, UK, selected eight from which they could make confident measurements of relaxation times.For each of these mergers, the team calculated the maximum average rate of information emission per unit ofenergy. They found that these rates are the fastest for any known object: about bits per second perjoule, or 75% of the theoretical maximum. At this extreme rate, perturbed black holes broadcast information at arate roughly 11 orders of magnitude higher than those involving “everyday” room-temperature objects that areroughly a meter wide.

The result confirms that black holes obey fundamental principles of general relativity, information theory, andthermodynamics—a finding that the team says wasn’t guaranteed to be true. Any future extensions to generalrelativity, they say, must obey this information bound as well.

–Christopher Crockett

Christopher Crockett is a freelance writer based in Arlington, Virginia.

References1. G. Carullo et al., “Bekenstein-Hod universal bound on information emission rate is obeyed by LIGO-Virgo

binary black hole remnants,” Phys. Rev. Lett. 126, 161102 (2021).

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evidence case (amax ¼ bmax ¼ 100), we employ aconservative choice. In Fig. 2 we display, in blue, themedian and 90% credible intervals of the posterior prob-ability distributions pðHjDN; a; bÞ. Single-event likeli-hoods are shown in gray for comparison. We finallycompute the probability that the Bekenstein-Hod bound(gold vertical line) is obeyed on a population level, bycomputing the p-value (p ≔ pðH < 1jDN; a; bÞ) for eachof a; b sample obtained from Eq. (3). The result yields a p-value distribution strongly peaked towards unity withmedian and 90% credible levels given by p ¼ 0.94þ0.05

−0.14,where p ¼ 1 would indicate perfect agreement with theprediction, while p ¼ 0 perfect disagreement. TheBekenstein-Hod bound is respected with very high con-fidence by the observed BBH population. As an additionalcheck, we compared our result with the correspondingvalue coming from a naive point-estimate of the averageHlikelihood, the latter being insensitive to specific hierar-chical modeling choices. A weighted average over singleevents likelihoods, with weights given by the respectiveevidences, yields the red curve displayed in Fig. 2, corre-sponding to p ¼ 0.93. The excellent agreement betweenthis un-modelled estimate and the median of the hierar-chical population posterior confirms the robustness of theadopted population model.Conclusions.—BHs are expected to be the fastest dis-

sipating objects in the Universe, in the sense that they

possess the shortest possible relaxation time for a giventemperature [18]. In this Letter, we obtained an observa-tional verification of the Bekenstein-Hod informationemission bound using a Bayesian time-domain analysisapplied to the binary black holes of the LIGO-VirgoGWTC-2 catalog. The result is consistent with the pre-dictions of GR, BH thermodynamics, and informationtheory. Our analysis provides the first experimental veri-fication of a long-standing prediction on the dynamicalinformation-emission process of a BH.Software.—Open-software PYTHON packages, accessible

through PyPi, used in this work comprise CORNER,GWSURROGATE, H5PY, MATPLOTLIB, NUMBA, NumPy,SciPy, SEABORN, and surfinBH [74,75,86–92].

The authors would like to thank Aditya Vijaykumar,Giancarlo Cella, and Tjonnie Li for stimulating discussionsand Huan Yang, Alessandro Pesci for comments on themanuscript. J. V. was partially supported by STFC GrantNo. ST/K005014/2. This research has made use of data,software, and/or web tools obtained from the GravitationalWave Open Science Center [93], a service of LIGOLaboratory, the LIGO Scientific Collaboration, and theVirgo Collaboration. LIGO is funded by the U.S. NationalScience Foundation. Virgo is funded by the French CentreNational de Recherche Scientifique (CNRS), the ItalianIstituto Nazionale di Fisica Nucleare (INFN), and the DutchNikhef, with contributions by Polish and Hungarianinstitutes.

[1] R. Penrose, Phys. Rev. Lett. 14, 57 (1965).[2] S. W. Hawking and G. F. R. Ellis, The Large Scale Structure

of Space-Time (Cambridge University Press, Cambridge,England, 1973).

[3] V. Ginzburg and L. Ozernoy, Zh. Eksp. Teor. Fiz. 147, 1030(1964).

[4] A. Doroshkevic, Y. B. Zeldovich, and I. Novikov, Sov. Phys.JETP 36, 1 (1965).

[5] W. Israel, Phys. Rev. 164, 1776 (1967).[6] B. Carter, Phys. Rev. Lett. 26, 331 (1971).[7] S. W. Hawking, Commun. Math. Phys. 25, 152 (1972).[8] D. C. Robinson, Phys. Rev. Lett. 34, 905 (1975).[9] P. O. Mazur, J. Phys. A 15, 3173 (1982).

[10] G. Bunting, Ph. D. thesis University of New England,Armidale, N. S. W. (1983, to be published).

[11] F. Pretorius, Gravitational Wave Observation of Dynamical,Strong-Field Gravity, Stephen Hawking 75th BirthdayConference on Gravity and Black Holes (DAMTP, Cambridge,2017).

[12] M. Dafermos and I. Rodnianski, Clay Math. Proc. 17, 97(2013).

[13] C. W. Misner, K. S. Thorne, and J. A. Wheeler, GravitationCosmol. (1973).

[14] S. W. Hawking, Commun. Math. Phys. 43, 199 (1975).[15] R. Brito, V. Cardoso, and P. Pani, Classical Quantum

Gravity 32, 134001 (2015).

FIG. 2. Median and 90% credible levels on the Bekenstein-Hodparameter H parent distribution, obtained through a hierarchicalmodel (blue area). Single-events likelihood (grey curves) are alsodisplayed, together with their evidence-weighted average (redcurve). The probability that the bound (gold dashed line) isobeyed by the whole population are p ¼ 0.94þ0.05

−0.14 when assum-ing the posterior distribution and p ¼ 0.93 when assuming theaverage likelihood.

PHYSICAL REVIEW LETTERS 126, 161102 (2021)

161102-5


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<latexit sha1_base64="NYV50rAFYBh9+xBO5uYZuT4tlWg=">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</latexit>

H =1

⇡

~/⌧kBT

<latexit sha1_base64="0MzAhnjjiB+8vi+leNIWcqikgk4=">AAACb3icdVHPaxNBFJ6sVWv8FfXgQSgPg6CXsBs0SW9FD/VYwbSFbAhvZ99mh87OLDOzScOSv9Fz/4rSQ6/WyTYFFX0w8PG977338U1SSmFdGF60gns79x883H3Ufvzk6bPnnRcvj62uDKcx11Kb0wQtSaFo7ISTdFoawiKRdJKcfdn0TxZkrNDqu1uVNC1wrkQmODpPzToiTmguVM1JOTLr9qHBhXArWOKCQCeWzKJRWtBZHMMIUpFlZLwaEon8DHItyYLN9RIQDEk8b/TgREHtmFR6t3rW6Ya9cBjtfxyAB015MBjt94cjiLZMl23raNa5jFPNq8KPc4nWTqKwdNMajRNc0rodV5ZKbwHnNPFQYUF2WjeRrOGdZ1LItPHPe23Y3ydqLKxdFYlXFuhy+3dvQ/6rN6lcNprWQpWVI8VvD2WVBKdhk6/PxxB3cuUBciO8V+A5GuQ+A7/Jkv8iNXd5HTs6d0uR+jt11Psk1Cahuxjg/+C434sGvf63fvfg8zarXfaGvWXvWcSG7IB9ZUdszDj7wa7ZT3bTugpeB3sB3EqD1nbmFfujgg+/AF7HwTM=</latexit>

Gravity waveobservations of

8 di↵erent black holesshow a relaxation time

<latexit sha1_base64="uZo4+K0ICGy97TDkA18xLXYWSns=">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</latexit>

⌧ ⇠ ~kBT

G. Carullo, D. Laghi, J. Veitch, W. Del Pozzo, Phys. Rev. Lett. 126, 161102 (2021)

Quantum Black holes





All many-body quantum systems (without quantum gravity)

have an entropy proportional to their volume !?!?

Quantum Black holes





Black holes are represented as a `hologram’ by a quantum many-body system in one lower dimension.

Duality: a `change of variables’ between the

many-particle configurations and the metric of spacetime

Susskind, Maldacena…..

Quantum Black holes





<latexit sha1_base64="MwKVLllYoBfoa2syIZk0F5hPa7g=">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</latexit>

The hologram of a black holein d dimensions

is a quantum many-particle systemin (d� 1) dimensions

which relaxes to thermal equilibriumin a Planckian time ⇠ ~/(kBT )

~x⇣

Maxwell’s electromagnetism and Einstein’s general relativity

allow black hole solutions with a net charge

<latexit sha1_base64="3TvePHqqtGIwJTVVK4N0Hs5Uw1Q=">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</latexit>

The near-horizongeometry of a

charged black hole isone-dimensional (⇣)

~x⇣

Maxwell’s electromagnetism and Einstein’s general relativity

allow black hole solutions with a net charge

The hologram of the 1+1 dimensional gravity near the

horizon of a charged black hole is the 0+1 dimensional

SYK model

Sachdev (2010); Kitaev (2015); Sachdev (2015); Maldacena, Stanford, Yang (2016) ; Moitra, Trivedi, Vishal (2018) ; Gaikwad, Joshi, Mandal, Wadia (2018); Iliesiu, Turaci (2020)








Sachdev, Ye (1993)

Documents

Quantum entanglement at all distances