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Quantum Tunneling Time: Relativistic Extensions

Dai-Yu Xu, Towe Wang, Xun Xue

Foundations of PhysicsSep 13, 20136 citations

Instantaneous tunneling of relativistic massive spin-0 particles

Philip Caesar Flores, Eric A. Galapon

The tunneling time problem earlier studied in Phys. Rev. Lett 108 170402 (2012) using a non-relativistic time-of-arrival (TOA) operator predicted that tunneling time is instantaneous. This raises the question on whether instantaneous tunneling time is a consequence of using a non-relativistic theory. Here, we extend the analysis by proposing a formalism on the construction of relativistic TOA-operators for spin-0 particles in the presence of an interaction potential via quantization. We then construct the corresponding barrier traversal time operator and impose the condition that the barrier height is less than the rest mass energy of the particle. We show that only the above-barrier energy components of the incident wavepacket's momentum distribution contribute to the barrier traversal time while the below-barrier components are transmitted instantaneously.The tunneling time problem earlier studied in Phys. Rev. Lett 108 170402 (2012) using a non-relativistic time-of-arrival (TOA) operator predicted that tunneling time is instantaneous. This raises the question on whether instantaneous tunneling time is a consequence of using a non-relativistic theory. Here, we extend the analysis by proposing a formalism on the construction of relativistic TOA-operators for spin-0 particles in the presence of an interaction potential via quantization. We then construct the corresponding barrier traversal time operator and impose the condition that the barrier height is less than the rest mass energy of the particle. We show that only the above-barrier energy components of the incident wavepacket's momentum distribution contribute to the barrier traversal time while the below-barrier components are transmitted instantaneously.

arXiv:2207.09040Jul 19, 20220 citations

Relativistic Formulation of Quantum Tunneling

WORLD SCIENTIFIC eBooksJan 1, 20030 citations

Instantaneous tunneling of relativistic massive spin-0 particles

Philip Caesar Flores, Eric A. Galapon

Abstract The tunneling time problem studied earlier in Phys. Rev. Lett. , 108 (2012) 170402, using a non-relativistic time-of-arrival (TOA) operator predicted that tunneling time is instantaneous. This raises the question whether instantaneous tunneling time is a consequence of using a non-relativistic theory. Here, we extend the analysis by proposing a formalism on the construction of relativistic TOA operators for spin-0 particles in the presence of an interaction potential V ( q ) via quantization. We then construct the corresponding barrier traversal time operator, and impose the condition that the barrier height V o is less than the rest mass energy of the particle. We show that only the above-barrier energy components of the incident wavepackets momentum distribution contribute to the barrier traversal time while the below-barrier components are transmitted instantaneously.Abstract The tunneling time problem studied earlier in Phys. Rev. Lett. , 108 (2012) 170402, using a non-relativistic time-of-arrival (TOA) operator predicted that tunneling time is instantaneous. This raises the question whether instantaneous tunneling time is a consequence of using a non-relativistic theory. Here, we extend the analysis by proposing a formalism on the construction of relativistic TOA operators for spin-0 particles in the presence of an interaction potential V ( q ) via quantization. We then construct the corresponding barrier traversal time operator, and impose the condition that the barrier height V o is less than the rest mass energy of the particle. We show that only the above-barrier energy components of the incident wavepackets momentum distribution contribute to the barrier traversal time while the below-barrier components are transmitted instantaneously.

Europhysics Letters (EPL)Dec 21, 20226 citations

Delay time computation for relativistic tunneling particles

Alex E. Bernardini

arXiv:0803.0953The European Physical Journal CMar 26, 20088 citations

Relativistic free-motion time-of-arrival operator for massive spin-0 particles with positive energy

Philip Caesar Flores, Eric A. Galapon

A relativistic version of the Aharonov-Bohm time-of-arrival operator for spin-0 particles was constructed by Razavi [Il Nuovo Cimento B 63, 271 (1969)]. We study the operator in detail by taking its rigged Hilbert space extension. It is shown that the rigged Hilbert space extension of the operator provides more insights into the time-of-arrival problem that goes beyond Razavi's original results. This allows us to use time-of-arrival eigenfunctions that exhibit unitary arrival to construct time-of-arrival distributions. The expectation value is also calculated and shown that particles can arrive earlier or later than expected classically. Last, the constructed time-of-arrival distribution and expectation value are shown to be consistent with special relativity.A relativistic version of the Aharonov-Bohm time-of-arrival operator for spin-0 particles was constructed by Razavi [Il Nuovo Cimento B 63, 271 (1969)]. We study the operator in detail by taking its rigged Hilbert space extension. It is shown that the rigged Hilbert space extension of the operator provides more insights into the time-of-arrival problem that goes beyond Razavi's original results. This allows us to use time-of-arrival eigenfunctions that exhibit unitary arrival to construct time-of-arrival distributions. The expectation value is also calculated and shown that particles can arrive earlier or later than expected classically. Last, the constructed time-of-arrival distribution and expectation value are shown to be consistent with special relativity.

arXiv:2203.00898Physical Review AJun 8, 202211 citations

Quantized relativistic time-of-arrival operators for spin-0 particles and the quantum tunneling time problem

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