This chapter surveys modern progress in physics on the topic of “decoherence,” the physical process by which irreversible behavior can occur in wave systems. A substantial part of the chapter discusses a proposal by the author of this book for a spontaneous collapse theory that is connected to decoherence.

This chapter discusses what we mean by particle detectors and “quantum jumps.” Modern results are presented that show that particle detection is not instantaneous, and that the photoelectric effect does not prove the existence of particles; it is a purely wavelike effect. The Born rule for random clicks of measurements in detectors is introduced and discussed, and quantum “uncertainty” is introduced.

In Chapter 6, we discuss quantum jumps, or leaps, beginning with a historical discussion of quantum jumps, or leaps, and giving the motivating example of blinking atoms in trapped ions and quantum jumps in superconducting circuits. Despite the disruptive name, we discuss how jumps fit into the category of continuous measurement. In some cases, quantum jumps can be predicted, and even reversed. We build up the mathematical formalism by discussing the quantum Zeno effect, Lindblad-type master equations, leading to jump and no-jump dynamics - an inseparable combination of discrete and continuous dynamics. In fact, the discrete nature of the jump is illusory. We discuss the dynamics of a quantum jump and the transition from jumps to diffusion.

In this chapter we discuss the effects of losses on quantum optical systems. We discuss quantum jumps and master equations. We introduce the notion of using fictitious beam splitters to model losses. We introduce the decoherence of pure quantum mechanical states into a statistical mixture.

Experimental chapter that presents experimental devices that allow us to detect individual quantum systems and observe quantum jumps occurring at random times. Described: superconducting single photon detectors, detection of arrays of ions and atoms, the shelving technique that allows us to measure the quantum state of the single atom, state selective field ionization of single Rydberg atoms, detection of single molecules on a surface by confocal microscopy, articial atoms in circuit quantum electrodynamics (cQED)

Here we discuss the possible relation ofour generalconjecture on global attractors ofnonlinear Hamiltonian PDEs todynamicaltreatment of Bohr's postulates and of wave--particle duality, which are fundamental postulates of quantum mechanics, in the context of couplednonlinear Maxwell--SchrödingerandMaxwell--Dirac equations. The problem of adynamicaltreatment was the main inspiration for our theoryof global attractors ofnonlinear Hamiltonian PDEs.