TY - JOUR
T1 - Semiclassical construction of Green's functions for multidimensional systems with barrier tunneling
AU - Kay, Kenneth G.
N1 - Publisher Copyright:
© 2017 American Physical Society.
PY - 2017/10/27
Y1 - 2017/10/27
N2 - We develop a treatment that divides phase space into regions bounded by surfaces and forms the energy-dependent semiclassical Green's function from short classical trajectory segments confined to the individual regions. We use this to generalize Bogomolny's quantization method to systems with barrier tunneling. Combined with an appropriate treatment of tunneling amplitudes, this yields a unified semiclassical framework that uses ordinary, real trajectories in classically allowed regions and imaginary-time trajectories in forbidden regions to obtain energies, decay rates, and wave functions for arbitrary states of multidimensional systems undergoing tunneling. Because the trajectory segments in the allowed region are short, components in the Green's function expression can be numerically evaluated using semiclassical initial value methods, yielding a promising approach for practical calculations.
AB - We develop a treatment that divides phase space into regions bounded by surfaces and forms the energy-dependent semiclassical Green's function from short classical trajectory segments confined to the individual regions. We use this to generalize Bogomolny's quantization method to systems with barrier tunneling. Combined with an appropriate treatment of tunneling amplitudes, this yields a unified semiclassical framework that uses ordinary, real trajectories in classically allowed regions and imaginary-time trajectories in forbidden regions to obtain energies, decay rates, and wave functions for arbitrary states of multidimensional systems undergoing tunneling. Because the trajectory segments in the allowed region are short, components in the Green's function expression can be numerically evaluated using semiclassical initial value methods, yielding a promising approach for practical calculations.
UR - http://www.scopus.com/inward/record.url?scp=85032450301&partnerID=8YFLogxK
U2 - 10.1103/physreva.96.042116
DO - 10.1103/physreva.96.042116
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AN - SCOPUS:85032450301
SN - 2469-9926
VL - 96
JO - Physical Review A
JF - Physical Review A
IS - 4
M1 - 042116
ER -