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Quantum particle escape from a time-dependent confining potential

Quantum escape of a particle via a time-dependent confining potential in a semi-infinite one-dimensional space is discussed. We describe the time-evolution of escape states in terms of scattering states of the quantum open system, and calculate the probability $P(t)$ for a particle to remain in the confined region at time $t$ in the case of a delta-function potential with a time-oscillating magnitude. The probability $P(t)$ decays exponentially in time at early times, then decays as a power later, along with a time-oscillation in itself. We show that a larger time-oscillation amplitude of the confining potential leads to a faster exponential decay of the probability $P(t)$, while it can rather enhance the probability $P(t)$ decaying as a power. These contrastive behaviors of the probability $P(t)$ in different types of decay are discussed quantitatively by using the decay time and the power decay magnitude of the probability $P(t)$.