Details
| Original language | English |
|---|---|
| Article number | 22 |
| Journal | Journal of High Energy Physics |
| Volume | 2013 |
| Issue number | 4 |
| Publication status | Published - 3 Apr 2013 |
Abstract
Many proposed quantum mechanical models of black holes include highly non-local interactions. The time required for thermalization to occur in such models should reflect the relaxation times associated with classical black holes in general relativity. Moreover, the time required for a particularly strong form of thermalization to occur, sometimes known as scrambling, determines the time scale on which black holes should start to release information. It has been conjectured that black holes scramble in a time logarithmic in their entropy, and that no system in nature can scramble faster. In this article, we address the conjecture from two directions. First, we exhibit two examples of systems that do indeed scramble in logarithmic time: Brownian quantum circuits and the antiferromagnetic Ising model on a sparse random graph. Unfortunately, both fail to be truly ideal fast scramblers for reasons we discuss. Second, we use Lieb-Robinson techniques to prove a logarithmic lower bound on the scrambling time of systems with finite norm terms in their Hamiltonian. The bound holds in spite of any nonlocal structure in the Hamiltonian, which might permit every degree of freedom to interact directly with every other one.
Keywords
- Black Holes, Lattice Integrable Models, M(atrix) Theories, Quantum Dissipative Systems
ASJC Scopus subject areas
- Physics and Astronomy(all)
- Nuclear and High Energy Physics
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In: Journal of High Energy Physics, Vol. 2013, No. 4, 22, 03.04.2013.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Towards the fast scrambling conjecture
AU - Lashkari, Nima
AU - Stanford, Douglas
AU - Hastings, Matthew
AU - Osborne, Tobias
AU - Hayden, Patrick
PY - 2013/4/3
Y1 - 2013/4/3
N2 - Many proposed quantum mechanical models of black holes include highly non-local interactions. The time required for thermalization to occur in such models should reflect the relaxation times associated with classical black holes in general relativity. Moreover, the time required for a particularly strong form of thermalization to occur, sometimes known as scrambling, determines the time scale on which black holes should start to release information. It has been conjectured that black holes scramble in a time logarithmic in their entropy, and that no system in nature can scramble faster. In this article, we address the conjecture from two directions. First, we exhibit two examples of systems that do indeed scramble in logarithmic time: Brownian quantum circuits and the antiferromagnetic Ising model on a sparse random graph. Unfortunately, both fail to be truly ideal fast scramblers for reasons we discuss. Second, we use Lieb-Robinson techniques to prove a logarithmic lower bound on the scrambling time of systems with finite norm terms in their Hamiltonian. The bound holds in spite of any nonlocal structure in the Hamiltonian, which might permit every degree of freedom to interact directly with every other one.
AB - Many proposed quantum mechanical models of black holes include highly non-local interactions. The time required for thermalization to occur in such models should reflect the relaxation times associated with classical black holes in general relativity. Moreover, the time required for a particularly strong form of thermalization to occur, sometimes known as scrambling, determines the time scale on which black holes should start to release information. It has been conjectured that black holes scramble in a time logarithmic in their entropy, and that no system in nature can scramble faster. In this article, we address the conjecture from two directions. First, we exhibit two examples of systems that do indeed scramble in logarithmic time: Brownian quantum circuits and the antiferromagnetic Ising model on a sparse random graph. Unfortunately, both fail to be truly ideal fast scramblers for reasons we discuss. Second, we use Lieb-Robinson techniques to prove a logarithmic lower bound on the scrambling time of systems with finite norm terms in their Hamiltonian. The bound holds in spite of any nonlocal structure in the Hamiltonian, which might permit every degree of freedom to interact directly with every other one.
KW - Black Holes
KW - Lattice Integrable Models
KW - M(atrix) Theories
KW - Quantum Dissipative Systems
UR - http://www.scopus.com/inward/record.url?scp=84876358832&partnerID=8YFLogxK
U2 - 10.1007/JHEP04(2013)022
DO - 10.1007/JHEP04(2013)022
M3 - Article
AN - SCOPUS:84876358832
VL - 2013
JO - Journal of High Energy Physics
JF - Journal of High Energy Physics
SN - 1126-6708
IS - 4
M1 - 22
ER -