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An upper bound on transport · Around

2017

An upper bound on transport

Hartman, Thomas, Hartnoll, Sean A., Mahajan, Raghu

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The linear growth of operators in local quantum systems leads to an effective lightcone even if the system is non-relativistic.

We show that consistency of diffusive transport with this lightcone places an upper bound on the diffusivity: $D \lesssim v^2 \tau_\text{eq}$.
The operator growth velocity $v$ defines the lightcone and $\tau_\text{eq}$ is the local equilibration timescale, beyond which the dynamics of conserved densities is diffusive.
We verify that the bound is obeyed in various weakly and strongly interacting theories.

Built on

L. P. Kadanoff and P. C. Martin, Ann. Phys. 24
1963
Earlier work this paper cites.
I. Muller, Z. Phys. 198
1967
Earlier work this paper cites.
E. H. Lieb and D. W. Robinson, Communications in Mathematical Physics 28
1972
Earlier work this paper cites.
W. Israel, Annals Phys. 100
1976
Earlier work this paper cites.
J. Orenstein, G. A. Thomas, A. J. Millis, S. L. Cooper, D. H. Rapkine, T. Timusk, L. F. Schneemeyer, and J. V. Waszczak, Phys. Rev. B 42
1990
Earlier work this paper cites.
Z. Schlesinger, R. T. Collins, F. Holtzberg, C. Feild, G. Koren, and A. Gupta, Phys. Rev. B 41
1990
Earlier work this paper cites.
V. J. Emery and S. A. Kivelson, Phys. Rev. Lett. 74
1995
Earlier work this paper cites.
S. Sachdev, Quantum Phase Transitions (Cambridge University Press, Cambridge, UK, 1999)
1999
Earlier work this paper cites.
G. T. Horowitz and V. E. Hubeny, Phys. Rev. D62
2000
Earlier work this paper cites.
G. Policastro, D. T. Son, and A. O. Starinets, Phys. Rev. Lett. 87
2001
Earlier work this paper cites.
D. Orgad, S. A. Kivelson, E. W. Carlson, V. J. Emery, X. J. Zhou, and Z. X. Shen, Phys. Rev. Lett. 86
2001
Earlier work this paper cites.
A. Lanzara, P. V. Bogdanov, X. J. Zhou, S. A. Kellar, D. L. Feng, E. D. Lu, T. Yoshida, H. Eisaki, A. Fujimori, K. Kishio, J.-I. Shimoyama, T. Noda, S. Uchida, Z. Hussain, and Z.-X. Shen, Nature 412
2001
Earlier work this paper cites.
U. W. Heinz and P. F. Kolb, Statistical QCD. Proceedings, International Symposium, Bielefeld, Germany, August 26-30, 2001 , Nucl. Phys. A702
2002
Earlier work this paper cites.
O. Gunnarsson, M. Calandra, and J. E. Han, Rev. Mod. Phys. 75
2003
Earlier work this paper cites.
D. v. d. Marel, H. J. A. Molegraaf, J. Zaanen, Z. Nussinov, F. Carbone, A. Damascelli, H. Eisaki, M. Greven, P. H. Kes, and M. Li, Nature 425
2003
Earlier work this paper cites.
X. J. Zhou, T. Yoshida, A. Lanzara, P. V. Bogdanov, S. A. Kellar, K. M. Shen, W. L. Yang, F. Ronning, T. Sasagawa, T. Kakeshita, T. Noda, H. Eisaki, S. Uchida, C. T. Lin, F. Zhou, J. W. Xiong, W. X. Ti, Z. X. Zhao, A. Fujimori, Z. Hussain, and Z.-X. Shen, Nature 423
2003
Earlier work this paper cites.
N. E. Hussey, K. Takenaka, and H. Takagi, Phil. Mag. 84
2004
Earlier work this paper cites.
P. Calabrese and J. L. Cardy, J. Stat. Mech. 0504
2005
Earlier work this paper cites.
P. Kovtun, D. T. Son, and A. O. Starinets, Phys. Rev. Lett. 94
2005
Earlier work this paper cites.
S. Bravyi, M. B. Hastings, and F. Verstraete, Phys. Rev. Lett. 97
2006
Earlier work this paper cites.
P. Calabrese and J. L. Cardy, Phys. Rev. Lett. 96
2006
Earlier work this paper cites.
A. Adams, N. Arkani-Hamed, S. Dubovsky, A. Nicolis, and R. Rattazzi, JHEP 10
2006
Earlier work this paper cites.
D. T. Son and A. O. Starinets, Ann. Rev. Nucl. Part. Sci. 57
Original
2007
Earlier work this paper cites.
A. M. Läuchli and C. Kollath, Journal of Statistical Mechanics: Theory and Experiment 2008
2008
Earlier work this paper cites.
R. Baier, P. Romatschke, D. T. Son, A. O. Starinets, and M. A. Stephanov, JHEP 04
Original
2008
Earlier work this paper cites.
M. Brigante, H. Liu, R. C. Myers, S. Shenker, and S. Yaida, Phys. Rev. Lett. 100
Original
2008
Earlier work this paper cites.
S. R. Manmana, S. Wessel, R. M. Noack, and A. Muramatsu, Phys. Rev. B 79
2009
Earlier work this paper cites.
G. Festuccia and H. Liu, Adv. Sci. Lett. 2
Original
2009
Earlier work this paper cites.
J. Morgan, V. Cardoso, A. S. Miranda, C. Molina, and V. T. Zanchin, JHEP 09
Original
2009
Earlier work this paper cites.
D. M. Hofman, Nucl. Phys. B823
Original
2009
Earlier work this paper cites.
L. Luo and J. E. Thomas, Journal of Low Temperature Physics 154
2009
Earlier work this paper cites.

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