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We prove locality estimates, in the form of Lieb-Robinson bounds, for classical oscillator systems defined on a lattice.
Lieb, E.H. and Robinson, D.W.: The Finite Group Velocity of Quantum Spin Systems
1972
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Lanford, O.E., Lebowitz, J., Lieb, E.H. Time evolution of infinite anharmonic systems
1977
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C. Marchioro, A. Pellegrinotti, M. Pulvirenti, and L. Triolo, Velocity of a perturbation in infinite lattice systems
1978
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Bratteli, O. and Robinson D.W.: Operator Algebras and Quantum Statistical Mechanics. Volume 2
1997
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Hastings, M.B.: Lieb-Schultz-Mattis in Higher Dimensions
2004
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Bravyi, S. and Hastings, M.B. and Verstraete, F.: Lieb-Robinson bounds and the generation of correlations and topological quantum order
2006
Cited alongside, same era.
Hastings, M.B. and Koma, T.: Spectral Gap and Exponential Decay of Correlations
2006
Cited alongside, same era.
B. Nachtergaele, Y. Ogata, and R. Sims, Propagation of Correlations in Quantum Lattice Systems
2006
Cited alongside, same era.
Nachtergaele, B. and Sims, R.: Lieb-Robinson Bounds and the Exponential Clustering Theorem
2006
Cited alongside, same era.
Nachtergaele, B., Raz, H., Schlein, B., and Sims, R., Lieb-Robinson Bounds for Harmonic and Anharmonic Lattice Systems
Cited in the paper.
Nachtergaele, B. and Sims, R.: Locality Estimates for Quantum Spin Systems
Cited in the paper.
Agarwal, Ravi, Ryoo, Cheon, and Kim, Young-Ho New integral inequalities for iterated integrals with applications
2007
Later among the works it cites.
Buttà, P., Caglioti, E., Di Ruzza, S., and Marchioro, C. On the propagation of a perturbation in an anharmonic system
2007
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Hastings, M.B. An area law for one dimensional quantum systems
2007
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Nachtergaele, B. and Sims, R.: A Multi-Dimesional Lieb-Schultz-Mattis Theorem
2007
Later among the works it cites.
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