Fetching the paper…

Reading the bibliography…

2015

Entanglement and Fast Quantum Thermalization in Heavy Ion Collisions

Ho, Chiu Man, Hsu, Stephen D. H.

Original
PDF
Post on X

Understand

Let $A$ be subsystem of a larger system $A \cup B$, and $\psi$ be a typical state from the subspace of the Hilbert space ${\cal H}_{AB}$ satisfying an energy constraint.

Then $\rho_A(\psi)= {\rm Tr}_B | \psi \rangle \langle \psi |$ is nearly thermal.
We discuss how this observation is related to fast thermalization of the central region ($\approx A$) in heavy ion collisions, where $B$ represents other degrees of freedom (soft modes, hard jets, collinear particles) outside of $A$.
Entanglement between the modes in $A$ and $B$ plays a central role: the entanglement entropy $S_A$ increases rapidly in the collision.

Entanglement and Fast Quantum Thermalization in Heavy Ion Collisions · Around

Built on

H. T. Elze, Nucl. Phys. B 436
1995
Earlier work this paper cites.
H. T. Elze, Phys. Lett. B 369
1996
Earlier work this paper cites.
U. H. Danielsson, E. Keski-Vakkuri and M. Kruczenski, JHEP 0002
2000
Earlier work this paper cites.
P. F. Kolb, P. Huovinen, U. W. Heinz and H. Heiselberg, Phys. Lett. B 500
2001
Earlier work this paper cites.
P. Huovinen, P. F. Kolb, U. W. Heinz, P. V. Ruuskanen and S. A. Voloshin, Phys. Lett. B 503
2001
Earlier work this paper cites.
J. Gemmer, M. Michel and G. Mahler, Quantum Thermodynamics: Emergence of Thermodynamic Behavior Within Composite Quantum Systems
2004
Earlier work this paper cites.
M. Ledoux, The Concentration of Measure Phenomenon
2005
Earlier work this paper cites.
S. Popescu, A. J. Short and A. Winter, Nature Physics
2006
Earlier work this paper cites.

Similar

S. Goldstein, J. L. Lebowitz, R. Tumulka, and N. Zanghi, Phys. Rev. Lett. 96
2006
Cited alongside, same era.
S. Ryu and T. Takayanagi, Phys. Rev. Lett. 96
2006
Cited alongside, same era.
N. Linden, S. Popescu, A. J. Short, A. Winter, Phys. Rev. E 79
Original
2009
Cited alongside, same era.
J. von Neumann, Zeitschrift fuer Physik 57
Original
2010
Cited alongside, same era.
S. Goldstein, J. L. Lebowitz, R. Tumulka, N. Zanghi, European Phys. J. H 35
Original
2010
Cited alongside, same era.
J. Abajo-Arrastia, J. Aparicio and E. Lopez, JHEP 1011

Then

B. Muller and A. Schafer, Int. J. Mod. Phys. E 20
Original
2011
Later among the works it cites.
P. M. Chesler and L. G. Yaffe, Phys. Rev. Lett. 106
Original
2011
Later among the works it cites.
V. Balasubramanian, A. Bernamonti, J. de Boer, N. Copland, B. Craps, E. Keski-Vakkuri, B. Muller and A. Schafer et al
Original
2011
Later among the works it cites.
S. Goldstein, T. Hara, H. Tasaki, Phys. Rev. Lett. 111
Original
2013
Later among the works it cites.
C. Gale, S. Jeon and B. Schenke, Int. J. Mod. Phys. A 28
Original
2013

Beyond the bibliography

alphaXiv searches the wider corpus for related work and actual follow-ups.

Open on alphaXiv

alphaXiv is searching for related work…

2010

Cited alongside, same era.

T. Takayanagi and T. Ugajin, JHEP 1011

2010

Cited alongside, same era.

J. Casalderrey-Solana, H. Liu, D. Mateos, K. Rajagopal and U. A. Wiedemann, arXiv:1101.0618 [hep-th]

Cited in the paper.

We can motivate the result by considering a spin state of the form ψ = ( 1 / 2 N ) ∑ exp ( i θ ( σ 1 , … , σ N ) ) | σ 1 , … , σ N ⟩ \psi=(1/2^{N})\sum\exp(i\theta(\sigma_{1},\dotsc,\sigma_{N}))\,|\sigma_{1},\dotsc,\sigma_{N}\rangle , where σ i = ± \sigma_{i}=\pm . Tracing over all but the first n n spins ( N ≫ n N\gg n ) yields an approximately diagonal density matrix ≈ 𝟏 / 2 n \approx{\bf 1}/2^{n} . The off-diagonal entries are small for generic (random) functions θ \theta due to cancellations. This example is only illustrative, however, because ψ \psi is not entirely typical – we have assumed equal probabilities for ψ \psi to be found in each | σ 1 , … , σ N ⟩ |\sigma_{1},\dotsc,\sigma_{N}\rangle state

Cited in the paper.

G. Westfall, private communication

Cited in the paper.

For an overview, including discussion of results on boundary thermalization, see CERN lectures by Takayanagi: http://www2.yukawa.kyoto-u.ac.jp/~tadashi.takayanagi/CERNEE.pdf

Cited in the paper.

Later among the works it cites.

P. M. Chesler and L. G. Yaffe, JHEP 1407

2014

Later among the works it cites.

S. Goldstein, T. Hara, H. Tasaki, New J. Phys. 17

2015

Closest in time.