The DOI matches its Crossref record; 20 of the 20 references it cites were found in a registry or an index.
Universal Correlations in a Nonlinear Periodic 1D System
Abstract
When a periodic 1D system described by a tight-binding model is uniformly initialized with equal amplitudes at all sites, yet with completely random phases, it evolves into a thermal distribution with no spatial correlations. However, when the system is nonlinear, correlations are spontaneously formed. We find that for strong nonlinearities, the intensity histograms approach a narrow Gaussian distributed around their mean and phase correlations are formed between neighboring sites. Sites tend to be out of phase for a positive nonlinearity and in phase for a negative one. Most impressively, the field correlation takes a universal shape independent of parameters. These results are relevant to bosonic gas in 1D optical lattices as well as to nonlinear optical waveguide arrays, which are used to demonstrate experimentally some of the features of this equilibrium state.
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“Except for very specific cases (Rasmussen et al., 2000;Silberberg et al., 2009;Klaers et al., 2010;Hafezi, Adhikari, and Taylor, 2015;Lebreuilly et al., 2017), the resulting state of the light field is thus quite distinct from a thermal equilibrium state.”
From Topological photonics (2019) · cites this paper as Silberberg et al., 2009
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Cites
Absence of Diffusion in Certain Random Lattices
Anderson, P. W. (1958) · Physical Review · doi:10.1103/physrev.109.1492 · Cited by 12,468
�ber die Quantenmechanik der Elektronen in Kristallgittern
Bloch, F. (1929) · Zeitschrift f�r Physik · doi:10.1007/bf01339455 · Cited by 3,436
Kinoshita, T., Wenger, T., & Weiss, D. S. (2006) · Nature · doi:10.1038/nature04693 · Cited by 1,997
Discretizing light behaviour in linear and nonlinear waveguide lattices
Christodoulides, D. N., Lederer, F., & Silberberg, Y. (2003) · Nature · doi:10.1038/nature01936 · Cited by 1,692
Self-citationDiscrete Spatial Optical Solitons in Waveguide Arrays
Eisenberg, H. S., Silberberg, Y., Morandotti, R., Boyd, A. R., & Aitchison, J. S. (1998) · Physical Review Letters · doi:10.1103/physrevlett.81.3383 · Cited by 1,286
Self-citationFlach, S., & Willis, C. R. (1998) · Physics Reports · doi:10.1016/s0370-1573(97)00068-9 · Cited by 1,221
Discrete self-focusing in nonlinear arrays of coupled waveguides
Christodoulides, D. N., & Joseph, R. I. (1988) · Optics Letters · doi:10.1364/ol.13.000794 · Cited by 1,181
Lederer, F., Stegeman, G. I., Christodoulides, D. N., Assanto, G., Segev, M., & Silberberg, Y. (2008) · Physics Reports · doi:10.1016/j.physrep.2008.04.004 · Cited by 1,180
Self-citationDiscrete Solitons and Breathers with Dilute Bose-Einstein Condensates
Trombettoni, A., & Smerzi, A. (2001) · Physical Review Letters · doi:10.1103/physrevlett.86.2353 · Cited by 922
The discrete self-trapping equation
Eilbeck, J. C., Lomdahl, P. S., & Scott, A. C. (1985) · Physica D: Nonlinear Phenomena · doi:10.1016/0167-2789(85)90012-0 · Cited by 624
Cited by
Ozawa, T., Price, H. M., Amo, A., Goldman, N., Hafezi, M., Lu, L., Rechtsman, M. C., Schuster, D., Simon, J., Zilberberg, O., et al. (2019) · Reviews of Modern Physics · doi:10.1103/revmodphys.91.015006 · Cited by 3,722
Metadata
- Authors
- Silberberg, Y., Lahini, Y., Bromberg, Y., Small, E., & Morandotti, R.
- Venue
- Physical Review Letters
- Publisher
- American Physical Society (APS)
- Published
- 2009-06-12
- Volume
- 102
- Issue
- 23
- ISSN
- 0031-9007
- 1079-7114
- Cited by
- 36
- References
- 20
- Language
- en
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- Silberberg, Y., Lahini, Y., Bromberg, Y., Small, E., & Morandotti, R. (2009). Universal Correlations in a Nonlinear Periodic 1D System. Physical Review Letters. https://doi.org/10.1103/physrevlett.102.233904
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Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
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