Author Archives: Eric A. Galapon
Galapon EA. 2017 The problem of missing terms in term by term integration involving divergent integrals. Proc. R. Soc. A 473: 20160567.
The operations of integration and summation cannot be interchanged arbitrarily. Some uniformity conditions must be satisfied in order for the interchange to be performed. If the conditions are not satisfied and the interchange is nevertheless carried out, some outrageous things happen. For example, the interchange may lead to an infinite series of divergent integrals; that… Read More »
P.C.M. Flores, R.C.F. Caballar, E.A. Galapon, “Synchronizing quantum and classical clocks made of quantum particles”, Physical Review A 94, 032123 (2016)
We demonstrate that the quantum corrections to the classical arrival time for a quantum object in a potential free region of space, as computed in Phys. Rev. A 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 wave function. This then implies… Read More »
How to integrate convergent integrals using divergent integrals
Methods abound in evaluating convergent integrals, for example, by substitution or by differential equations. In this post I show how divergent integrals may be used in evaluating convergent integrals by applying our recent results in the complex contour integral representations of the finite part of divergent integrals found here and here. To be concrete, let… Read More »
Is there a mass quantum operator?
Yes, there is a mass operator in the same way there is a spin operator. One of the central tenets of quantum mechanics is the one-to-one correspondence between what can be measured on a given system and an operator in the space of all possible states of the system. It asserts that to every quantity… Read More »
“The problem of missing terms in term by term integration involving divergent integrals” E. A. Galapon (2016) arXiv:1606.09382
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 »
Congratulations to Dr. Joseph Bunao for being NIP’s and CS’s most outstanding PhD graduate for 2016
Dr. Joseph Bunao is this year’s most outstanding PhD graduate of the National Institute of Physics and the College of Science of the University of the Philippines at Diliman for his excellent academic performance (1.016/1 average grade in graduate school) and outstanding research work (the lead author of three ISI-journal papers). Check out his papers:… Read More »
M.M. Flores and E.A. Galapon, “Mixtures of maximally entangled pure states” Annals of Physics 372 (2016) 297-308.
Abstract We study the conditions when mixtures of maximally entangled pure states 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 of mixing a number of pure… Read More »
What could have we been missing while Pauli’s Theorem was enforced?
This post is the online version of the write-up of the contributed talk I gave at the Time and Matter Colloquium held at Venice on August 11-17, 2002 at the Venice International University. It is part of the proceedings of the Colloquim published by World Scientific. Abstract Pauli’s theorem asserts that the canonical commutation relation… Read More »
Explainer Part 1: “Internal one degree of freedom is sufficient to induce exact decoherence” E.A. Galapon, 2016 EPL 113 60007.
The paper deals with the fundamental question of whether an environment, defined as a quantum system with an arbitrarily large or infinite number of unobservable degrees of freedom, 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… Read More »