Abstract
Driven-dissipative nonlinear systems exhibit rich critical behavior, related to bifurcation, bistability, and switching, which underlie key phenomena in areas ranging from physics, chemistry, and biology [T. Wilhelm, BMC Syst. Biol. 3, 90 (2009)] to social sciences and economics. The importance of rare fluctuations leading to a dramatic jump between two very distinct states, such as survival and extinction in population dynamics [A. (2008)], success and bankruptcy in economics [S. Ghashghaie et al., Nature (London) 381, 767 (1996)], and the occurrence of earthquakes [L. Knopoff and Y. Kagan, J. Geophys. Res. 82, 5647 (1977)] or of epileptic seizures [K. Lehnertz, Extreme Events in Nature and Society (Springer, Berlin, Heidelberg, 2006), pp. 123-143], have been already established. In the quantum domain, switching is of importance in both chemical reactions and the devices used in quantum state detection and amplification [R. Vijay et al., Rev. Sci. Instrum. 80, 111101 (2009)]. In particular, the simplest driven single oscillator model serves as an insightful starting point. Here we describe switching induced by quantum fluctuations and illustrate that an instanton approach within Keldysh field theory can provide a deep insight into such phenomena. We provide a practical recipe to compute the switching rates semi-analytically, which agrees remarkably well with exact solutions across a wide domain of drive amplitudes spanning many orders of magnitude. Being set up in the framework of Keldysh coherent states path integrals, our approach opens the possibility of studying quantum activation in many-body systems where other approaches are inapplicable.