We investigate the motion of bound state poles in two quantum wave guides laterally coupled through a window. The imaginary momentum i k at the bound state poles is studied as a function of the size a of the window. Both bound and virtual states appear as a spans the whole range from 0 up to infinity. We are able to find simple scaling laws relating the critical value of the window size at which the n--th bound state appears to the number n of bound states, in the limit of large n. A similar relation is also provided for the slope and the second derivative of the pole trajectories in the (k, a) plane. These relations are characterized by an extremely high numerical accuracy. We also evaluate the exact value of the first two derivatives for a=0.
Asymptotic properties of bound states in coupled quantum wave guides
MAGLIONE, ENRICO;CATTAPAN, GIORGIO
2006
Abstract
We investigate the motion of bound state poles in two quantum wave guides laterally coupled through a window. The imaginary momentum i k at the bound state poles is studied as a function of the size a of the window. Both bound and virtual states appear as a spans the whole range from 0 up to infinity. We are able to find simple scaling laws relating the critical value of the window size at which the n--th bound state appears to the number n of bound states, in the limit of large n. A similar relation is also provided for the slope and the second derivative of the pole trajectories in the (k, a) plane. These relations are characterized by an extremely high numerical accuracy. We also evaluate the exact value of the first two derivatives for a=0.Pubblicazioni consigliate
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