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 »

The one-sided and full Hilbert transforms are evaluated exactly by means of the method of finite-part integration [E.A. Galapon, \textit{Proc. Roy. Soc. A} \textbf{473}, 20160567 (2017)]. In general, the result consists of two terms—the first is an infinite series of finite part of divergent integrals, and the second is a contribution arising from the singularity… Read More »

Abstract We consider the characteristic time operator introduced in Galapon (2002) [26] which is bounded and self-adjoint. For a semibounded discrete Hamiltonian with some growth condition, satisfies the canonical relation for in a dense subspace of the Hilbert space. While is not covariant, we show that it still satisfies the canonical relation in a set… Read More »

Abstract It was shown in Phys. Rev. Lett. 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 raises the… Read More »

Bulletin-Oct2024-print

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 »

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 »

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 »