Evidence of a Critical Phase Transition in Purely Temporal Dynamics with Long-Delayed Feedback.

Experimental evidence of an absorbing phase transition, so far associated with spatiotemporal dynamics, is provided in a purely temporal optical system. A bistable semiconductor laser, with long-delayed optoelectronic feedback and multiplicative noise, shows the peculiar features of a critical phenomenon belonging to the directed percolation universality class. The numerical study of a simple, effective model provides accurate estimates of the transition critical exponents, in agreement with both theory and our experiment. This result pushes forward a hard equivalence of nontrivial stochastic, long-delayed systems with spatiotemporal ones and opens a new avenue for studying out-of-equilibrium universality classes in purely temporal dynamics.

[1]  Giacomelli,et al.  Relationship between delayed and spatially extended dynamical systems. , 1996, Physical review letters.

[2]  H. Hinrichsen.  Non-equilibrium critical phenomena and phase transitions into absorbing states , 2000, cond-mat/0001070.

[3]  Denis Mollison,et al.  Spatial Contact Models for Ecological and Epidemic Spread , 1977 .

[4]  Giovanni Giacomelli,et al.  Pattern formation in systems with multiple delayed feedbacks. , 2014, Physical review letters.

[5]  U. Täuber,et al.  Phase Transitions and Scaling in Systems Far From Equilibrium , 2016, 1604.04487.

[6]  M. Avila,et al.  Scale invariance at the onset of turbulence in Couette flow. , 2013, Physical review letters.

[7]  P. C. Hohenberg,et al.  Scaling Laws for Dynamic Critical Phenomena , 1969 .

[8]  E. Arimondo,et al.  Experimental signatures of an absorbing-state phase transition in an open driven many-body quantum system , 2016, 2017 Conference on Lasers and Electro-Optics Europe & European Quantum Electronics Conference (CLEO/Europe-EQEC).

[9]  J. P. Woerdman,et al.  Polarization fluctuations in vertical-cavity semiconductor lasers , 1998 .

[10]  S. Lepri.  Critical phenomena in delayed maps , 1994 .

[11]  Timothy Clarke,et al.  Physics I.2 , 2018 .

[12]  B. Widom,et al.  Equation of State in the Neighborhood of the Critical Point , 1965 .

[13]  Laurent Larger,et al.  Laser chimeras as a paradigm for multistable patterns in complex systems , 2014, Nature Communications.

[15]  Tomas Bohr,et al.  DIRECTED PERCOLATION UNIVERSALITY IN ASYNCHRONOUS EVOLUTION OF SPATIOTEMPORAL INTERMITTENCY , 1998 .

[16]  Laurent Larger,et al.  Virtual chimera states for delayed-feedback systems. , 2013, Physical review letters.

[17]  C. Thompson.  The Statistical Mechanics of Phase Transitions , 1978 .

[18]  M. Buchhold,et al.  Absorbing State Phase Transition with Competing Quantum and Classical Fluctuations. , 2016, Physical review letters.

[19]  M. Sano,et al.  A universal transition to turbulence in channel flow , 2015, Nature Physics.

[20]  Universal critical behavior of the synchronization transition in delayed chaotic systems. , 2005, Physical review. E, Statistical, nonlinear, and soft matter physics.

[21]  Juan M. López,et al.  Characteristic Lyapunov vectors in chaotic time-delayed systems. , 2010, Physical review. E, Statistical, nonlinear, and soft matter physics.

[22]  Y. Pomeau.  Front motion, metastability and subcritical bifurcations in hydrodynamics , 1986 .

[23]  Leo P. Kadanoff,et al.  Scaling and universality in statistical physics , 1990 .

[24]  J. Hammersley,et al.  Percolation processes , 1957, Mathematical Proceedings of the Cambridge Philosophical Society.

[25]  K. Takeuchi,et al.  Directed percolation criticality in turbulent liquid crystals. , 2007, Physical review letters.

[26]  J. P. Garrahan,et al.  Non-equilibrium universality in the dynamics of dissipative cold atomic gases , 2014, 1411.7984.

[27]  N. Goldenfeld,et al.  Directed percolation describes lifetime and growth of turbulent puffs and slugs. , 2011, Physical review. E, Statistical, nonlinear, and soft matter physics.

[28]  K. Wilson.  Renormalization Group and Critical Phenomena. II. Phase-Space Cell Analysis of Critical Behavior , 1971 .

[29]  Space representation of stochastic processes with delay. , 2007, Physical review. E, Statistical, nonlinear, and soft matter physics.

[30]  J. Hale.  Theory of Functional Differential Equations , 1977 .

[31]  B. Widom,et al.  Surface Tension and Molecular Correlations near the Critical Point , 1965 .

[32]  Peter Grassberger,et al.  On phase transitions in Schlögl's second model , 1982 .

[33]  K. Takeuchi,et al.  Experimental realization of directed percolation criticality in turbulent liquid crystals. , 2009, Physical review. E, Statistical, nonlinear, and soft matter physics.

[34]  Giovanni Giacomelli,et al.  Nucleation in bistable dynamical systems with long delay. , 2013, Physical review. E, Statistical, nonlinear, and soft matter physics.

[35]  Michael E. Fisher,et al.  Critical Exponents in 3.99 Dimensions , 1972 .

[36]  H. Janssen,et al.  On the nonequilibrium phase transition in reaction-diffusion systems with an absorbing stationary state , 1981 .

[37]  L. Kadanoff.  Scaling laws for Ising models near T(c) , 1966 .

[38]  Michael A. Zaks,et al.  Coarsening in a bistable system with long-delayed feedback , 2012 .

[39]  G. Giacomelli,et al.  Polarization competition and noise properties of VCSELs , 1998 .

[40]  K. Wilson.  Renormalization Group and Critical Phenomena. I. Renormalization Group and the Kadanoff Scaling Picture , 1971 .

[41]  STAT , 2019, Springer Reference Medizin.

[42]  Grégoire Lemoult,et al.  Directed percolation phase transition to sustained turbulence in Couette flow , 2016, Nature Physics.

[43]  J. D. Farmer,et al.  Chaotic attractors of an infinite-dimensional dynamical system , 1982 .

[44]  Meucci,et al.  Two-dimensional representation of a delayed dynamical system. , 1992, Physical review. A, Atomic, molecular, and optical physics.

[45]  Jonathan Keeling,et al.  Superradiant and lasing states in driven-dissipative Dicke models , 2017, 1710.06212.

[46]  T. Vogel.  Théorie des systèmes évolutifs , 1965 .

[47]  Giovanni Giacomelli,et al.  Spatio-temporal phenomena in complex systems with time delays , 2017, 2206.03120.

[48]  J Javaloyes,et al.  Arrest of Domain Coarsening via Antiperiodic Regimes in Delay Systems. , 2015, Physical review letters.