Buildup and decay dynamics of exponentially modulated quantum waves in resonant structures
Por:
Amador-Bartolini, D., Villavicencio, J., Romo, R., Hernandez-Maldonado, A.
Publicada:
1 ene 2021
Resumen:
We derive an exact analytic solution of time-dependent Schrodinger's
equation for cutoff quantum waves with exponential modulation to explore
the dynamics along the internal region of a one-dimensional potential of
arbitrary shape. The modulation of the wave packet is controlled by a
single parameter given by its momentum distribution width, Delta, which
allows to explore on the same footing the transient features of both
cutoff spatially localized wave packets and extended plane waves. From
the formal solution, we derive a simple and reliable formula that
accurately describes both the buildup and decay of the probability
density inside a resonant structure. The buildup-decay formula involves
two exponential terms governed respectively by the resonance width
Gamma(1) of the lowest resonance of the system and the width (Gamma)
over bar of a `virtual' state induced by the incident wave packet.
During the buildup process, we demonstrate that the contributions of
both Gamma(1) and (Gamma) over bar become essential. In the decay
process, on the other hand, we find that there are two regimes
characterized by a critical value Delta(c), such that for Delta >
Delta(c) the exponential decay is governed by Gamma(1), while for Delta
< Delta(c) the exponential decay is governed by <(Gamma)over bar>. We
also derive an analytic formula for a relevant timescale for the
buildup-decay process, which depends in a simple fashion on the decay
rates Gamma(1) and (Gamma) over bar. Deviations from the exponential
decay law at long times are also discussed.
Filiaciones:
Amador-Bartolini, D.:
Univ Autonoma Baja California, Fac Ciencias Ingn & Tecnol, Unidad Valle Palmas, Tijuana, Baja California, Mexico
Villavicencio, J.:
(Corresponding Author), Univ Autonoma Baja California, Fac Ciencias, Apartado Postal 1880, Ensenada 22800, Baja California, Mexico
(Corresponding Author), Univ Nacl Autonoma Mexico, Ctr Nanociencias & Nanotecnol, Apartado Postal 14, Ensenada 22800, BC, Mexico
Univ Autonoma Baja California, Fac Ciencias, Apartado Postal 1880, Ensenada 22800, Baja California, Mexico
Univ Nacl Autonoma Mexico, Ctr Nanociencias & Nanotecnol, Apartado Postal 14, Ensenada 22800, BC, Mexico
Romo, R.:
Univ Autonoma Baja California, Fac Ciencias, Apartado Postal 1880, Ensenada 22800, Baja California, Mexico
Hernandez-Maldonado, A.:
Univ Autonoma Baja California, Fac Ciencias Ingn & Tecnol, Unidad Valle Palmas, Tijuana, Baja California, Mexico
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