Escape behavior of a quantum particle in a loop coupled to a lead
- Department of Physics, Kwansei Gakuin University, Sanda 669-1337 (Japan)
We consider a one-dimensional loop of circumference L crossed by a constant magnetic flux {Phi} and connected to an infinite lead with coupling parameter {epsilon}. Assuming that the initial state {psi}{sub 0} of the particle is confined inside the loop and evolves freely, we analyze the time evolution of the nonescape probability P({psi}{sub 0},L,{Phi},{epsilon},t), which is the probability that the particle will still be inside the loop at some later time t. In appropriate units, we found that P({psi}{sub 0},L,{Phi},{epsilon},t)=P{sub {infinity}}({psi}{sub 0},{Phi})+{Sigma}{sub k=1}{sup {infinity}}C{sub k}({psi}{sub 0},L,{Phi},{epsilon})/t{sup k}. The constant P{sub {infinity}}({psi}{sub 0},{Phi}) is independent of L and {epsilon}, and vanishes if {psi}{sub 0} has no bound state components or if |cos({Phi})|{ne}1. The coefficients C{sub 1}({psi}{sub 0},L,{Phi},{epsilon}) and C{sub 3}({psi}{sub 0},L,{Phi},{epsilon}) depend on the initial state {psi}{sub 0} of the particle, but only the momentum k={Phi}/L is involved. There are initial states {psi}{sub 0} for which P({psi}{sub 0},L,{Phi},{epsilon},t){approx}C{sub {delta}}({psi}{sub 0},L,{Phi},{epsilon})/t{sup {delta}}, as t{yields}{infinity}, where {delta}=1 if cos({Phi})=1 and {delta}=3 if cos({Phi}){ne}1. Thus, by submitting the loop to an external magnetic flux, one may induce a radical change in the asymptotic decay rate of P({psi}{sub 0},L,{Phi},{epsilon},t). Interestingly, if cos({Phi})=1, then C{sub 1}({psi}{sub 0},L,{Phi},{epsilon}) decreases with {epsilon} (i.e., the particle escapes faster in the long run) while in the case cos({Phi}){ne}1, the coefficient C{sub 3}({psi}{sub 0},L,{Phi},{epsilon}) increases with {epsilon} (i.e., the particle escapes slower in the long run). Assuming the particle to be initially in a bound state of the loop with {Phi}=0, we compute explicit relations and present some numerical results showing a global picture in time of P({psi}{sub 0},L,{Phi},{epsilon},t). Finally, by using the pseudospectral method, we consider the interacting case with soft-core Coulomb potentials.
- OSTI ID:
- 22095559
- Journal Information:
- Physical Review. A, Vol. 84, Issue 6; Other Information: (c) 2011 American Institute of Physics; Country of input: International Atomic Energy Agency (IAEA); ISSN 1050-2947
- Country of Publication:
- United States
- Language:
- English
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