Complex dynamical systems, ranging from ecosystems to financial markets and the climate, can have tipping points at which a sudden shift to a contrasting dynamical regime may occur. Although predicting such critical points before they are reached is extremely difficult, work in different scientific fields is now suggesting the existence of generic early-warning signals that may indicate for a wide class of systems if a critical threshold is approaching.

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Early-warning signals for critical transitions

Tipping points in complex systems may imply risks of unwanted collapse, but also opportunities for positive change. Our capacity to navigate such risks and opportunities can be boosted by combining emerging insights from two unconnected fields of research. One line of work is revealing fundamental architectural features that may cause ecological networks, financial markets, and other complex systems to have tipping points. Another field of research is uncovering generic empirical indicators of the proximity to such critical thresholds. Although sudden shifts in complex systems will inevitably continue to surprise us, work at the crossroads of these emerging fields offers new approaches for anticipating critical transitions.

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Anticipating Critical Transitions

Publisher Summary This chapter describes the coherent population trapping in laser spectroscopy. Coherent population trapping may be also described as the pumping of the atomic system in a particular state, the coherent superposition of the atomic states, which is a nonabsorbing state. The exciting radiation creates an atomic coherence, such that the atom's evolution is prepared exactly out of phase with the incoming radiation and no absorption takes place. The chapter discusses the basic properties of an atomic system prepared with the coherent population-trapping superposition of states and outlines experimental observations concerned with the establishment of coherent trapping in different discrete systems. The chapter also discusses the theoretical and experimental aspects of trapping that involve states of the continuum and reviews the theoretical and experimental features associated with coherent population trapping in laser cooling, adiabatic transfer, lasing without inversion, pulse matching, and photon statistics. The theoretical aspect of coherent population trapping created by spontaneous emission is also discussed in the chapter.

Coherent Population Trapping in Laser Spectroscopy

The anomalous properties of cold and supercooled water, such as the fact that at sufficiently low temperatures it becomes more compressible and less dense when cooled, and more fluid when compressed, have attracted the attention of physical scientists for a long time. The discovery in the 1970s that several thermodynamic and transport properties of supercooled water exhibit a pronounced temperature dependence and appear to diverge slightly below the homogeneous nucleation temperature inspired a large number of experimental and theoretical studies. Likewise, an important body of work on glassy water has been stimulated by experiments, starting in the mid-1980s and continuing to this date, which suggest that vitreous water can exist in at least two apparently distinct forms. A coherent theory of the thermodynamic and transport properties of supercooled and glassy water does not yet exist. Nevertheless, significant progress towards this goal has been made during the past 20 years. This article summarizes the known experimental facts and reviews critically theoretical and computational work aimed at interpreting the observations and providing a unified viewpoint on cold, non-crystalline, metastable states of water.

https://iopscience.iop.org/article/10.1088/0953-8984/15/45/R01/pdf

Supercooled and glassy water

心臓病診療プラクティス 16. 心不全を癒す

We review publications on transverse dynamics in cavity nonlinear optics during the years 2000–2003 Topics covered are transverse pattern dynamics, localized structures, scaling of turn-on transients, properties of nonlinear PDEs, VCSELs, quadratic media, light valves with optical feedback, quantum properties of light, and quantum images

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Transverse dynamics in cavity nonlinear optics (2000–2003)

Critical slowing down near a bifurcation or limit point leads to a dynamical hysteresis that cannot be avoided by sweeping a control parameter slowly through the critical point. This paper analytically illustrates, with the help of a simple model, the bifurcation shift. We describe an inexpensive experiment using a semiconductor laser where this phenomenon occurs near the threshold of a semiconductor laser.

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Critical slowing down at a bifurcation

Optical bistability III

We provide a comprehensive analysis of the standard model of the bidirectional ring laser in which only one mode can be supported in each direction and in the limit that the polarization can be eliminated adiabatically. The interaction between the two counterpropagating modes can be derived and it is most naturally viewed as a coupling between them via scattering from a spatial grating formed in the population inversion. If the grating is a sufficiently small modulation of the spatial average of the population inversion, it can be approximated by a sinusoidal function. A systematic derivation of the model with only a sinusoidal grating for the homogeneously broadened case is presented that reveals and corrects errors in several previously published analyses. The stability of the steady-state solution is analyzed. The bidirectional steady-state solution is unstable and the unidirectional steady-state solutions may be stable or unstable depending on the parameters. The well-established result of bistability between the two modes when the cavity is tuned to resonance is recovered, a result that persists, in part, even when the losses between the two modes are different.

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Bidirectional ring laser: Stability analysis and time-dependent solutions

We study the five semiclassical laser equations in the mean-field limit for the simple model of two-level atoms with homogeneous broadening in a single-mode unidirectional ring cavity, taking into account detuning between atomic and cavity frequencies. Our analysis concentrates on the properties of the laser at and beyond the second thresh-old in the bad-cavity case. We first show that the position of the second threshold depends on the excitation mechanism: When the pump parameter is increased either adiabatically or abruptly, two different thresholds occur. The sequence of periodic and chaotic solutions beyond the second threshold is then discussed as a function of the detuning and the pump parameter.

Paul Mandel

Papers

Transverse dynamics in cavity nonlinear optics (2000–2003)

Critical slowing down at a bifurcation

Optical bistability III

Bidirectional ring laser: Stability analysis and time-dependent solutions

Influence of detuning on the properties of laser equations