Category Archives: Preprints

P.C.M. Flores and E.A. Galapon, “Instantaneous tunneling of relativistic massive spin-0 particles,” https://arxiv.org/abs/2207.09040

By | July 20, 2022
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The tunneling time problem earlier studied in \href{https://link.aps.org/doi/10.1103/PhysRevLett.108.170402}{Phys. Rev. Lett. \textbf{108}, 170402 (2012)} using a non-relativistic time-of-arrival (TOA) operator predicted that tunneling time is instantaneous implying that the wavepacket becomes superluminal below the barrier. The non-relativistic treatment raises the question whether the superluminal behavior is a mere non-relativistic phenomenon or an an inherent quantum effect… Read More »

D.A.L. Pablico and E.A. Galapon, “Quantum corrections to the Weyl quantization of the classical time of arrival,” https://arxiv.org/abs/2205.08694

By | May 19, 2022
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A time of arrival (TOA) operator that is conjugate with the system Hamiltonian was constructed by Galapon without canonical quantization in [J. Math. Phys. \textbf{45}, 3180 (2004)]. The constructed operator was expressed as an infinite series but only the leading term was investigated which was shown to be equal to the Weyl-quantized TOA-operator for entire… Read More »

C.D. Tica and E.A. Galapon, “Finite-Part Integration of the Generalized Stieltjes Transform and its dominant asymptotic behavior for small values of the parameter” arXiv:1703.07979.

By | March 24, 2017
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The paper addresses the exact evaluation of the generalized Stieltjes transform about from which the asymptotic behavior of for small parameters is directly extracted. An attempt to evaluate the integral by expanding the integrand about and then naively integrating the resulting infinite series term by term lead to an infinite series whose terms are divergent… Read More »

“The problem of missing terms in term by term integration involving divergent integrals” E. A. Galapon (2016) arXiv:1606.09382

By | July 1, 2016
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Term by term integration is one of the frequently used methods in evaluating integrals and in constructing asymptotic expansions of integrals. It typically involves expanding the integrand or a factor of it and then interchanging the order of summation and integration. Sometimes this formal manipulation leads to an infinite series involving divergent integrals. This calls… Read More »

Mixture of entangled pure states with maximally mixed one-qudit reduced density matrices (M.M. Flores and E.A. Galapon, arXiv:1512.05539)

By | December 18, 2015
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Abstract We study the conditions when mixtures of entangled pure states with maximally mixed one-qudit reduced density matrices remain entangled. We found that the resulting mixed state remains entangled when the number of entangled pure states to be mixed is less than or equal to the dimension of the pure states. For the latter case… Read More »

Synchronizing quantum and classical clocks made of quantum particles (arXiv:1512.05034 P.C.M. Flores, E.A. Galapon, R.C.F. Caballar)

By | December 17, 2015
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We demonstrate that the quantum corrections to the classical arrival time for a quantum object in a potential free region of space, as computed by Galapon [Phys. Rev. A {\bf 80}, 030102(R) (2009)], can be eliminated up to a given order of ℏ by choosing an appropriate position-dependent phase for the object’s wavefunction. This then… Read More »

The Cauchy principal value and the finite part integral as values of absolutely convergent integrals (E.A. Galapon , arXiv:1512.01323)

By | December 7, 2015
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Abstract The divergent integral , for and , is assigned, under certain conditions, the value equal to the simple average of the contour integrals , where () is a path that starts from and ends at , and which passes above (below) the pole at . It is shown that this value, which we refer… Read More »

Particle detection and non-detection in a quantum time of arrival measurement (D. Sombillo and E.A. Galapon, Annals of Physics, 364, 261–273 (2016))

By | November 30, 2015
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Abstract The standard time-of-arrival distribution cannot reproduce both the temporal and the spatial profile of the modulus squared of the time-evolved wave function for an arbitrary initial state. In particular, the time-of-arrival distribution gives a non-vanishing probability even if the wave function is zero at a given point for all values of time. This poses… Read More »

Explainer Part 1: “Exactly decohering quantum measurement without environment” E.A. Galapon, arXiv:1505.06908, 26 May 2015.

By | June 2, 2015
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The paper deals with the fundamental question of whether an environment is necessary or not to enforce quantum decoherence on quantum measuring instruments. The paper gives an unambiguous answer to the question as summarized by its Abstract: Current quantum orthodoxy claims that the statistical collapse of the wave-function arises from the interaction of the measuring… Read More »