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arXiv · 1705.04130

Relational time in anyonic systems

Aleksandrina Nikolova·Gavin Brennen·Tobias J. Osborne·Gerard Milburn·Thomas M. Stace
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Abstract

In a seminal paper (Page and Wootters 1983) Page and Wootters suggest 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 to relational time centres around the existence of a Hamiltonian and the subsequent constraint on physical states. In this paper we present a "state-centric" reformulation of the Page and Wootters model better suited to theories which intrinsically lack Hamiltonian dynamics, such as Chern--Simons theories. We describe relational time by encoding logical "clock" qubits into anyons---the topologically protected degrees of freedom in Chern--Simons theories. The timing resolution of such anyonic clocks is determined by the universality of the anyonic braid group, with non-universal models naturally exhibiting discrete time. We exemplify this approach using SU(2)$_2$ anyons and discuss generalizations to other states and models.

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Aleksandrina Nikolova, Gavin Brennen, Tobias J. Osborne, Gerard Milburn, Thomas M. Stace. 2017-05-11. Relational time in anyonic systems. https://doi.org/10.1103/physreva.97.030101

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