International Association of Mathematical Physics Bulletin October 2024
Bulletin-Oct2024-print
D.A.L Pablico and E.A. Galapon, “Moyal deformation of the classical arrival time,” J. Math. Phys. 65, 102104 (2024)
The quantum time of arrival (TOA) problem requires the statistics of measured arrival times given only the initial state of a particle. Following the standard framework of quantum theory, the problem translates into finding an appropriate quantum image of the classical arrival time , usually in operator form . In this paper, we consider the… Read More »
A new generation of mathematical physicists is needed
According to a commentary in Physics Today, a new generation of mathematical physicists is needed to “simplify the statistical physics of complex biological systems by recasting it as the exploration of measurable physical parameters in low-dimensional spaces. … Their solutions will require designing new asymptotic approximation methods and numerical simulations of the inherently stochastic particle… Read More »
J.C.A. Casapao and E.A. Galapon, “Entanglement witnesses with local partial ordering,” arXiv:2409.17689
We investigate a class of entanglement witnesses where each witness is formulated as a difference of two product observables. These observables are decomposable into positive semidefinite local operators that obey a partial ordering rule defined over all their possible expectation values. We provide a framework to construct these entanglement witnesses along with some examples. We… Read More »
P.C.M. Flores, D.A.L Pablico and E.A. Galapon, “Instantaneous tunneling time within the theory of time-of-arrival operators,” arXiv:2409.12389
It has been shown in \href{this https URL}{\textit{Phys. Rev. Lett.}, \textbf{108} 170402 (2012)}, that quantum tunneling is instantaneous using a time-of-arrival (TOA) operator constructed by Weyl quantization of the classical TOA. However, there are infinitely many possible quantum images of the classical TOA, leaving it unclear if one is uniquely preferred over the others. This… Read More »
N.L.R. Rojas and E.A. Galapon, “Terminating Poincare asymptotic expansion of the Hankel transform of entire exponential type functions,” arXiv:2409.10948
We perform an asymptotic evaluation of the Hankel transform, , for arbitrarily large of an entire exponential type function, , of type by shifting the contour of integration in the complex plane. Under the situation that has an odd parity with respect to and the condition that the asymptotic parameter is greater than the type… Read More »
R.J.C. Bagunu and E.A. Galapon, “Quantization of the Hamilton Equations of Motion,” arXiv:2409.03348
One of the fundamental problems in quantum mechanics is finding the correct quantum image of a classical observable that would correspond to experimental measurements. We investigate for the appropriate quantization rule that would yield a Hamiltonian that obeys the quantum analogue of Hamilton’s equations of motion, which includes differentiation of operators with respect to another… Read More »
R.A.E. Farrales and E.A. Galapon, “Characteristic time operators as quantum clocks,” arXiv:2409.03364
We consider the characteristic time operator T introduced in [E. A. Galapon, Proc. R. Soc. Lond. A, 458:2671 (2002)] which is bounded and self-adjoint. For a semibounded discrete Hamiltonian H with some growth condition, T satisfies the canonical relation [T,H]|ψ⟩=iℏ|ψ⟩ for |ψ⟩ in a dense subspace of the Hilbert space. While T is not covariant,… Read More »
D.A.L. Pablico, J.J.P. Magadan, C.A.L Arguelles and E.A. Galapon, “The role of conjugacy in the dynamics of time of arrival operators,” Physics Letters A 523, 129778 (2024)
Abstract The construction of time of arrival (TOA) operators canonically conjugate to the system Hamiltonian entails finding the solution of a specific second-order partial differential equation called the time kernel equation (TKE). In this paper, we provide an exact analytic solution of the TKE for a special class of potentials satisfying a specific separability condition.… Read More »
International Conference on Analysis and Applications in Honor of Roderick C. Wong’s 80th Birthday
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