arXiv subjects

Shoju Kudaka

Publications and source records attributed to Shoju Kudaka.

5 recordsLinked to original sources

arXiv2011

A mathematically rigorous approach raises questions concerning the generalized Hartman effect

With reference to a particle tunneling through two successive barriers, it seems to have been generally accepted that the tunneling time does not depend on the separation distance between the barriers. This phenomenon has been called the {\it generalized Hartman effect}. In this letter, we point out a lack of mathematical rigour in the reasoning by which this effect was deduced about ten years ago. A mathematically rigorous treatment shows us that the tunneling time does indeed depend on the length of the free space between the barriers.

quant-ph↗

arXiv2005

Proper Time for Spin 1/2 Particles

We find a quantum mechanical formulation of proper time for spin 1/2 particles within the framework of the Dirac theory. It is shown that the rate of proper time can be represented by an operator called the ` ` tempo operator'', and that the proper time itself be given by the integral of the expectation value of the operator. The tempo operator has some terms involving the Pauli spin matrices, and the evolution of the proper time is influenced by the spin state via these terms. The relation between the tempo operator and the metric tensor is elucidated.

quant-ph↗

arXiv2004

A Quantum Theoretical Formulation of Proper Time for Spin 1/2 Particles

We find a quantum mechanical formulation of proper time for spin 1/2 particles within the framework of the Dirac theory. It is shown that an operator corresponds to the rate of the proper time and that the operator contains terms which oscillate with a very high frequency. We deduce, as an effect of these terms, the existence of an interference between the magnetic field and the rate of proper time. There is a possibility that the conclusion derived in this letter has some implications for astrophysics.

quant-ph↗

arXiv1999

Uncertainty principle for proper time and mass II

When we quantize a system consisting of a single particle, the proper time $τ$ and the rest mass $m$ are usually dealt with as parameters. In the present article, however, we introduce a new quantization rule by which these quantities are regarded as operators in addition to the position and the momentum. Applying this new rule to a scalar particle and to a particle with spin $ 1/2 $, we analyze the time evolution of the operator $τ$. In the former case, the evolution of the proper time perfectly matches several well-established classical formulae. In the case of the particle with spin 1/2, our new rule implies that an oscillation appears in the time evolution of the operator $τ$. This oscillation is similar to Zitterbewegung which is well-known in the ordinary Dirac theory. We formulate one physical effect of this oscillation by considering the interaction with a gravitational field, and estimate how small it is.

quant-ph↗

arXiv1999

Uncertainty principle for proper time and mass

We review Bohr's reasoning in the Bohr-Einstein debate on the photon box experiment. The essential point of his reasoning leads us to an uncertainty relation between the proper time and the rest mass of the clock. It is shown that this uncertainty relation can be derived if only we take the fundamental point of view that the proper time should be included as a dynamic variable in the Lagrangian describing the system of the clock. Some problems and some positive aspects of our approach are then discussed.

quant-ph↗