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The Estimation of Tunneling Time by the use of Nelson's Quantum Stochastic Process: Towards a comparison with a neutron interference experiment

T. Hashimoto, Takeo Tomomura

Published Jul 1, 2000• 1 citation
Publisher
DOI
10.1142/9789812792761_0004

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The problem of tunneling time associated with the passage of a particle through a tunneling barrier seems very simple. But it turns out to be very deceptive by the lack of a time operator and there is no clear consensus about simple expression for the tunneling time. In this paper we evaluate the tunneling time based on Nelson's quantum stochastic process approach. This approach describes the motion of a particle by a stochastic differentia1 equation and gives a sample paths. The ensemble of the paths reproduce the predictions given by ordinary quantum mechanics in an average. Each sample path has its own time dependent history, which enables us make a virtual quantum experiment. We formulate the tunneling time based on this approach and compare it with the Larmor time estimated from an experimental measurement of Larmor precession angles of tunneling neutrons.
A generalization of Grover's algorithm, L. Accardi and R. Sabbadini characterization of product measures by an integrability condition, N. Asai tunnelling effect based on the Nelson's quantum stochastic process approach - comparison with a neutron spin echo experiment, T. Hasimoto and T. Tomomura Gibbs state, quadratic embedding and central limit theorem on large graphs, A. Hora algebraic stochastic differential equations and a Fubini theorem for symmetrized double quantum stochastic product integrals, R.L. Hudson some properties of a random field derived by variational calculus, K.S. Lee a stochastic expression of a semi-group generated by the Levy Laplacian, K. Nishi et al quantum logical gate based on electron spin resonance, M. Ohya et al. (Part contents).