Tunneling dynamics in relativistic and nonrelativistic wave equations
- Departamento de Quimica-Fisica, UPV-EHU, Apartado 644, 48080 Bilbao, (Spain)
- Instituto de Fisica, Universidad Nacional Autonoma de Mexico, Apartado Postal 20 364, 01000 Mexico, D.F., (Mexico)
- Facultad de Ciencias, Universidad Autonoma de Baja California, Apartado Postal 1880, 22800 Ensenada, Baja California, (Mexico)
We obtain the solution of a relativistic wave equation and compare it with the solution of the Schroedinger equation for a source with a sharp onset and excitation frequencies below cutoff. A scaling of position and time reduces to a single case all the (below cutoff) nonrelativistic solutions, but no such simplification holds for the relativistic equation, so that qualitatively different ''shallow'' and ''deep'' tunneling regimes may be identified relativistically. The nonrelativistic forerunner at a position beyond the penetration length of the asymptotic stationary wave does not tunnel; nevertheless, it arrives at the traversal (semiclassical or Buettiker-Landauer) time {tau}. The corresponding relativistic forerunner is more complex: it oscillates due to the interference between two saddle-point contributions and may be characterized by two times for the arrival of the maxima of lower and upper envelopes. There is in addition an earlier relativistic forerunner, right after the causal front, which does tunnel. Within the penetration length, tunneling is more robust for the precursors of the relativistic equation.
- OSTI ID:
- 20640140
- Journal Information:
- Physical Review. A, Vol. 68, Issue 3; Other Information: DOI: 10.1103/PhysRevA.68.032101; (c) 2003 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA); ISSN 1050-2947
- Country of Publication:
- United States
- Language:
- English
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