Robert C. Hilborn

Einstein coefficients, cross sections, f values, dipole moments, and all that

The relationships among various parameters describing the strength of optical transitions in atoms and molecules are reviewed. The application of these parameters to the description of the interaction between nearly monochromatic, directional light beams and atoms and molecules is given careful attention. Common pitfalls in relating these parameters are pointed out.

Sea gulls, butterflies, and grasshoppers: A brief history of the butterfly effect in nonlinear dynamics

The butterfly effect has become a popular metaphor for sensitive dependence on initial conditions—the hallmark of chaotic behavior. I describe how, where, and when this term was conceived in the 1970s. Surprisingly, the butterfly metaphor was predated by more than 70 years by the grasshopper effect.

Why Many Undergraduate Physics Programs Are Good but Few Are Great

No single action, activity, or curricular reform will rescue a struggling physics department. Rather, it takes many elements, interacting over time, to make a department thrive.

A simple model for stochastic coherence and stochastic resonance

I describe a simple iterated map that displays two important noise-induced effects for nonlinear systems: stochastic coherence and stochastic resonance. The model requires only modest computational capabilities and some knowledge of nonlinear dynamics and illustrates the constructive role of noise in nonlinear systems.

Chaos and Nonlinear Dynamics: An Introduction for Scientists and Engineers

The phenomenology of chaos Towards a theory of nonlinear dynamics and chaos Quantifying chaos Special topics Appendices Index

Coherence resonance in models of an excitable neuron with noise in both the fast and slow dynamics

Abstract We demonstrate the existence of noise-induced regularity (coherence resonance) in both a discrete-time model and a continuous-time model of an excitable neuron. In particular, we show that the effects of noise added to the fast and slow dynamics of the models are significantly different. A Fokker–Planck analysis gives a quantitative explanation of the effects.

Identical particles in quantum mechanics revisited

The treatment of identical particles in quantum mechanics rests on two (related) principles: the spin‐statistics connection and the Symmetrization Postulate. In light of recent theories (such as q‐deformed commutators) that allow for ‘small’ violations of the spin‐statistics connection and the Symmetrization Postulate, we revisit the issue of how quantum mechanics deals with identical particles and how it supports or fails to support various philosophical stances concerning individuality. As a consequence of the expanded possibilities for quantum statistics, we argue that permutation symmetry is best formulated as a formal property of the state function describing the system of particles rather than as a property of the individual particles. 1 Introduction 2 Philosophical background 2.1 Important terminology 2.1.1 Identity 2.1.2 Indistinguishability 2.1.3 Indiscernibility 2.2 When are particles indistinguishable? 2.3 The Principle of the Identity of Indiscernibles and quantum mechanics 2.4 The Principle of the Identity of Indiscernibles and logic 2.5 Particle history 2.6 Transcendental individuality 3 Some quantum formalism 3.1 The Principle of Permutation Invariance and the Symmetrization Postulate 3.2 The configuration‐space approach 3.3 Commutators and anticommutators, and identical particle statistics 3.4 Q‐mutators 4 Identical particle statistics: a holistic point of view 5 Conclusions

Atoms in orthogonal electric and magnetic fields: A comparison of quantum and classical models

The well‐known Zeeman and Stark effects can lead to unusual atomic state dynamics when both magnetic and electric fields are present. In this paper we analyze quantum mechanical and classical models of the time evolution of the angular momentum of an atom in the presence of weak, orthogonal electric and magnetic fields. The anisotropic electric polarizability of the atom plays a crucial role in the dynamics. The classical model leads to nonlinear evolution equations, and we investigate how quantum mechanics ‘‘avoids’’ the nonlinearity. Finally, we note that the classical equations of motion are identical to those used to describe the time evolution of Stokes vectors for polarized light propagating in an optically nonlinear medium. The treatment is appropriate for an undergraduate course in quantum mechanics.

An Inexpensive, Reliable, High-Power Molecular Nitrogen Laser.

The design, construction, and performance of a low‐cost, transversely excited molecular nitrogen laser are described in detail. Peak powers of over 100 kW at pulse repetition rates of 20 pps have been achieved at a total cost, including vacuum pump and power supply, of under

Fermi–Dirac and Bose–Einstein distributions and the interaction of light with matter

800. Some simple experiments and demonstrations using this laser are suggested.