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Physical Review A

Decay of an unstable state

Marvin R. Young, Surendra Singh

Published Feb 1, 1985• 14 citations
Publisher

Abstract

The first-passage-time problem associated with the decay of an unstable state is considered and analytic expressions for the first-passage-time distributions are derived. These expressions are quite general and are applicable to a large class of stochastic processes.
DOI
10.1103/physreva.31.888

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First-passage phenomena play a fundamental role in classical stochastic processes. We here exactly solve a quantum first-passage time problem for quantum diffusion driven by measurement noise, a generalization of classical Brownian motion. Such continuous monitoring may trap the measured quantum system in a decoherence-free subspace, a fraction of the available state space that is isolated from the surroundings, and thus plays an important role in quantum information science. We analytically determine the first-passage time distribution, whose form neither depends on the system Hamiltonian nor on the measurement operator, and is therefore universal. These results provide a general framework to investigate the first-passage statistics of diffusive quantum trajectories.