Non-adiabatic effects in quantum escapes with a time-dependent potential
School of Science and Technology, Kwansei Gakuin
Gakuen, Sanda city
Received in final form: 28 August 2013
Published online: 7 October 2013
Non-adiabatic effects in quantum escapes of a particle via a time-dependent potential barrier in a semi-infinite one-dimensional space are discussed. We describe the time-evolution of escape states in terms of scattering states of the open system with a time-periodic potential by Floquet’s theorem and the Lippmann-Schwinger equation, and calculate concretely the probability P(t) for a particle to remain in the initially 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 potential leads to a faster exponential decay of P(t), while it can rather enhance the probability P(t) decaying as a power. An explanation based on an average of adiabatic decays of P(t) is given to describe qualitatively these contrastive properties of P(t) in different types of decay. By investigating quantitative differences between the survival probability given from a direct solution of the Schrödinger equation with the time-oscillating potential and that obtained by an average of adiabatic decays, we clarify non-adiabatic effects in the decay time and the power decay magnitude of P(t).
Key words: Mesoscopic and Nanoscale Systems
© EDP Sciences, Società Italiana di Fisica and Springer-Verlag, 2013