Data di Pubblicazione:
2020
Citazione:
The semi-classical limit with a delta potential / C. Cacciapuoti, D. Fermi, A. Posilicano. - In: ANNALI DI MATEMATICA PURA ED APPLICATA. - ISSN 1618-1891. - (2020). [10.1007/s10231-020-01002-4]
Abstract:
We consider the semi-classical limit of the quantum evolution of Gaussian coherent states whenever the Hamiltonian H is given, as sum of quadratic forms, by H=h(2)/2m d(2)/d(x2)+alpha delta 0 , with alpha is an element of R and delta(0) the Dirac delta-distribution at x=0 . We show that the quantum evolution can be approximated, uniformly for any time away from the collision time and with an error of order (h) over bar (3/2-lambda), 0<3/2, by the quasi-classical evolution generated by a self-adjoint extension of the restriction to C-c(infinity)(M-0)M-0:={(q,p) is an element of R-2 vertical bar q not equal 0 times}, of (-i times) the generator of the free classical dynamics; such a self-adjoint extension does not correspond to the classical dynamics describing the complete reflection due to the infinite barrier. Similar approximation results are also provided for the wave and scattering operators.
Tipologia IRIS:
01 - Articolo su periodico
Keywords:
semiclassical dynamics; delta-interactions; coherent states; scattering theory
Elenco autori:
C. Cacciapuoti, D. Fermi, A. Posilicano
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