Details
| Original language | English |
|---|---|
| Article number | 030101 |
| Journal | Physical Review A |
| Volume | 97 |
| Issue number | 3 |
| Early online date | 12 Mar 2018 |
| Publication status | Published - Mar 2018 |
Abstract
In a seminal paper [Phys. Rev. D 27, 2885 (1983)10.1103/PhysRevD.27.2885], Page and Wootters suggest that time evolution could be described solely in terms of correlations between systems and clocks, as a means of dealing with the "problem of time" stemming from vanishing Hamiltonian dynamics in many theories of quantum gravity. Their approach seeks to identify relational dynamics given a Hamiltonian constraint on the physical states. Here we present a "state-centric" reformulation of the Page and Wootters model better suited to cases where the Hamiltonian constraint is satisfied, such as anyons emerging in Chern-Simons theories. We describe relational time by encoding logical "clock" qubits into topologically protected anyonic degrees of freedom. The minimum temporal increment of such anyonic clocks is determined by the universality of the anyonic braid group, with nonuniversal models naturally exhibiting discrete time. We exemplify this approach by using SU(2)2 anyons and discuss generalizations to other states and models.
ASJC Scopus subject areas
- Physics and Astronomy(all)
- Atomic and Molecular Physics, and Optics
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In: Physical Review A, Vol. 97, No. 3, 030101, 03.2018.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Relational time in anyonic systems
AU - Nikolova, A.
AU - Brennen, G. K.
AU - Osborne, Tobias J.
AU - Milburn, G. J.
AU - Stace, T. M.
N1 - Funding information: This work was supported by the Australian Research Council Centre of Excellence for Engineered Quantum Systems (Grant No. CE 110001013). T.J.O. was supported by the DFG through SFB 1227 (DQ-mat) and the RTG 1991, the ERC grants QFTCMPS and SIQS, and the cluster of excellence EXC201 Quantum Engineering and Space-Time Research.
PY - 2018/3
Y1 - 2018/3
N2 - In a seminal paper [Phys. Rev. D 27, 2885 (1983)10.1103/PhysRevD.27.2885], Page and Wootters suggest that time evolution could be described solely in terms of correlations between systems and clocks, as a means of dealing with the "problem of time" stemming from vanishing Hamiltonian dynamics in many theories of quantum gravity. Their approach seeks to identify relational dynamics given a Hamiltonian constraint on the physical states. Here we present a "state-centric" reformulation of the Page and Wootters model better suited to cases where the Hamiltonian constraint is satisfied, such as anyons emerging in Chern-Simons theories. We describe relational time by encoding logical "clock" qubits into topologically protected anyonic degrees of freedom. The minimum temporal increment of such anyonic clocks is determined by the universality of the anyonic braid group, with nonuniversal models naturally exhibiting discrete time. We exemplify this approach by using SU(2)2 anyons and discuss generalizations to other states and models.
AB - In a seminal paper [Phys. Rev. D 27, 2885 (1983)10.1103/PhysRevD.27.2885], Page and Wootters suggest that time evolution could be described solely in terms of correlations between systems and clocks, as a means of dealing with the "problem of time" stemming from vanishing Hamiltonian dynamics in many theories of quantum gravity. Their approach seeks to identify relational dynamics given a Hamiltonian constraint on the physical states. Here we present a "state-centric" reformulation of the Page and Wootters model better suited to cases where the Hamiltonian constraint is satisfied, such as anyons emerging in Chern-Simons theories. We describe relational time by encoding logical "clock" qubits into topologically protected anyonic degrees of freedom. The minimum temporal increment of such anyonic clocks is determined by the universality of the anyonic braid group, with nonuniversal models naturally exhibiting discrete time. We exemplify this approach by using SU(2)2 anyons and discuss generalizations to other states and models.
UR - http://www.scopus.com/inward/record.url?scp=85044136468&partnerID=8YFLogxK
U2 - 10.1103/PhysRevA.97.030101
DO - 10.1103/PhysRevA.97.030101
M3 - Article
AN - SCOPUS:85044136468
VL - 97
JO - Physical Review A
JF - Physical Review A
SN - 2469-9926
IS - 3
M1 - 030101
ER -