Yale University Applied Physics

Title: Einstein's unknown insight and the problem of quantizing chaotic motion

Abstract: In 1917 Einstein authored a little-known paper on the problem of generalizing the old quantum theory to problems with several degrees of freedom that are not separable. He laid the foundation for such a method, which is now known as Einstein-Brillouin-Keller quantization. However he pointed out that the method fails if there do not exist a number of integrals of motion equal to the number of degrees of freedom, i.e. unless the system is integrable. He suggests that non-integrable classical dynamics is typical and presents an open problem for quantum theory. This brilliant insight was ignored until the late sixties when it became well-known to physicists that partially chaotic motion is indeed generic in classical mechanical systems. The problem noted by Einstein was never fully overcome, but alternative approaches to connecting quantum mechanics to classical mechanics were developed and applied to interesting problems in atomic, condensed matter and optical physics. I will review Einstein's arguments and then mention a few applications of "quantum chaos theory", focusing on the topic of chaotic dielectric microlasers studied at Yale and elsewhere.