Non-adiabatic effects in quantum escapes with a time-dependent potential

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 a...

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Bibliographic Details
Published in:The European physical journal. B, Condensed matter physics Condensed matter physics, 2013-10, Vol.86 (10), Article 417
Main Authors: Taniguchi, Tooru, Sawada, Shin-ichi
Format: Article
Language:English
Subjects:
Complex Systems
Condensed Matter Physics
Condensed matter: electronic structure, electrical, magnetic, and optical properties
Electronic transport in condensed matter
Exact sciences and technology
Fluid- and Aerodynamics
Physics
Physics and Astronomy
Regular Article
Solid State Physics
Theory of electronic transport
scattering mechanisms
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Summary: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 ).
ISSN:1434-6028
1434-6036
DOI:10.1140/epjb/e2013-40519-y