Abstract
For an interacting spatio-temporal lattice system we introduce a formal way of expressing multi-time correlation functions of local observables located at the same spatial point with a time state, i.e. a statistical distribution of configurations observed along a time lattice. Such a time state is defined with respect to a particular equilibrium state that is invariant under space and time translations. The concept is developed within the rule 54 reversible cellular automaton, for which we explicitly construct a matrix product form of the time state, with matrices that act on the three-dimensional auxiliary space. We use the matrix-product state to express equal-space time-dependent density-density correlation function, which, for special maximum-entropy values of equilibrium parameters, agrees with the previous results. Additionally, we obtain an explicit expression for the probabilities of observing all multi-time configurations, which enables us to study distributions of times between consecutive excitations and prove the absence of decoupling of timescales in the rule 54 model.
Original language | English |
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Article number | 335001 |
Journal | Journal of Physics A: Mathematical and Theoretical |
Volume | 53 |
Issue number | 33 |
DOIs | |
Publication status | Published - 21 Aug 2020 |
Bibliographical note
Publisher Copyright:© 2020 IOP Publishing Ltd.
Keywords
- cellular automata
- exact results
- matrix product ansatz
- multi-time correlations
- solvable lattice models
ASJC Scopus subject areas
- Statistical and Nonlinear Physics
- Statistics and Probability
- Modelling and Simulation
- Mathematical Physics
- General Physics and Astronomy