Anomalous Directed Percolation on a Dynamic Network using Rydberg Facilitation
Abstract: The facilitation of Rydberg excitations in a gas of atoms provides an ideal model system to study epidemic evolution on (dynamic) networks and self organization of complex systems to the critical point of a non-equilibrium phase transition. Using Monte-Carlo simulations and a machine learning algorithm we show that the universality class of this phase transition can be tuned. The classes include directed percolation (DP), the most common class in short-range spreading models, and mean-field (MF) behavior, but also different types of anomalous directed percolation (ADP), characterized by rare long-range excitation processes. In a frozen gas, ground state atoms that can facilitate each other form a static network, for which we predict DP universality. Atomic motion then turns the network into a dynamic one with long-range (Levy-flight type) excitations. This leads to continuously varying critical exponents corresponding to the ADP universality class, eventually reaching MF behavior. These findings also explain the recently observed critical exponent of Rydberg facilitation in an ultra-cold gas experiment [Helmrich et al., Nature 577, 481 (2020)], which was in between DP and MF values.
- H. Hinrichsen, Non-equilibrium critical phenomena and phase transitions into absorbing states, Advances in physics 49, 815 (2000).
- P. Bak, C. Tang, and K. Wiesenfeld, Self-organized criticality, Physical Review A 38, 364 (1988).
- P. Bak, How nature works: the science of self-organized criticality (Springer Science & Business Media, 2013).
- A. Sornette and D. Sornette, Self-organized criticality and earthquakes, Europhysics Letters 9, 197 (1989).
- B. Drossel and F. Schwabl, Self-organized critical forest-fire model, Physical review letters 69, 1629 (1992).
- L. A. Adamic and B. A. Huberman, Power-law distribution of the world wide web, science 287, 2115 (2000).
- H.-K. Janssen, On the nonequilibrium phase transition in reaction-diffusion systems with an absorbing stationary state, Zeitschrift für Physik B Condensed Matter 42, 151 (1981).
- P. Grassberger, On phase transitions in schlögl’s second model, Zeitschrift für Physik B Condensed Matter 47, 365 (1982).
- H. Hinrichsen, Non-equilibrium phase transitions, Physica A: Statistical Mechanics and its Applications 369, 1 (2006).
- M. Munoz, G. Grinstein, and R. Dickman, Phase structure of systems with infinite numbers of absorbing states, Journal of statistical physics 91, 541 (1998).
- D. Mollison, Spatial contact models for ecological and epidemic spread, Journal of the Royal Statistical Society: Series B (Methodological) 39, 283 (1977).
- P. Grassberger, Fractals in physics, edited by L. Pietronero and E. Tosatti (Elsevier, 2012).
- P. Holme and J. Saramäki, Temporal networks, Physics reports 519, 97 (2012).
- K. Zhao, M. Karsai, and G. Bianconi, Entropy of dynamical social networks, PloS one 6, e28116 (2011).
- A. Browaeys and T. Lahaye, Many-body physics with individually controlled Rydberg atoms, Nature Physics 16, 132 (2020).
- D. Marković and C. Gros, Power laws and self-organized criticality in theory and nature, Physics Reports 536, 41 (2014).
- D. Brady and M. Fleischhauer, Mean-field approach to rydberg facilitation in a gas of atoms at high and low temperatures, Physical Review A 108, 052812 (2023).
- H. Hinrichsen, Non-equilibrium phase transitions with long-range interactions, Journal of Statistical Mechanics: Theory and Experiment 2007, P07006 (2007).
- G. Lindblad, On the generators of quantum dynamical semigroups, Communications in Mathematical Physics 48, 119 (1976).
- P. J. Huber, Robust Estimation of a Location Parameter, The Annals of Mathematical Statistics 35, 73 (1964).
Paper Prompts
Sign up for free to create and run prompts on this paper using GPT-5.
Top Community Prompts
Collections
Sign up for free to add this paper to one or more collections.