Pablico, Dean Alvin Lopez

College/Position: CAS, URDO
Designation: Coordinator, STIE
Area: Science, Technology, Industry and Energy

Research Engagement:

Publication
  • ► Moyal Deformation of the Classical Arrival Time (2024)

    Abstract: 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 problem anew within the phase space formulation of quantum mechanics. The resulting quantum image is a real-valued and time-reversal symmetric function in formal series of ℏ² with the classical arrival time as the leading term. It is obtained directly from the Moyal bracket relation with the system Hamiltonian and is hence interpreted as a Moyal deformation of the classical TOA. We investigate its properties and discuss how it bypasses the known obstructions to quantization by showing the isomorphism between and the rigged Hilbert space TOA operator constructed in Pablico and Galapon [Eur. Phys. J. Plus 138, 153 (2023)], which always satisfy the time-energy canonical commutation relation for arbitrary analytic potentials. We then examine TOA problems for a free particle and a quartic oscillator potential as examples.

    SDG: SDG 4, SDG 8, SDG 9, SDG 17

    Publication Link
  • ► Instantaneous tunneling time within the theory of time-of-arrival operators (2024)

    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 question on whether instantaneous tunneling time is simply an artifact of the chosen ordering rule. Here, we demonstrate that tunneling time vanishes for all possible quantum images of the classical arrival time, irrespective of the ordering rule between the position and momentum observables. The result still holds for TOA-operators that are constructed independent of canonical quantization, while still imposing the correct algebra defined by the time-energy canonical commutation relation.

    SDG: SDG 4, SDG 8, SDG 9, SDG 17

    Publication Link
  • ► The role of conjugacy in the dynamics of time of arrival operators (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. The solution enables us to investigate the time evolution of the eigenfunctions of the conjugacy-preserving TOA operators (CPTOA) and show that they exhibit unitary arrival at the intended arrival point at a time equal to their corresponding eigenvalues. We also compare the dynamics between the TOA operators constructed by quantization and those independent of quantization for specific interaction potentials. We find that the CPTOA operator possesses smoother and sharper unitary dynamics over the Weyl-quantized one within numerical accuracy.

    SDG: SDG 4, SDG 8, SDG 9, SDG 17

    Publication Link
  • ► Partial and full tunneling processes across potential barriers (2023)

    Abstract: We introduce the concept of partial and full tunneling processes to explain the seemingly contradictory non-zero and vanishing tunneling times often reported in the literature. Our analysis starts by considering the traversal time of a quantum particle through a potential barrier, including both above and below-barrier traversals, using the theory of time-of-arrival operators. We then show that there are three traversal processes corresponding to non-tunneling, full-tunneling, and partial tunneling. The distinction between the three depends on the support of the incident wavepackets energy distribution in relation to the shape of the barrier. Non-tunneling happens when the energy distribution of the quantum particle lies above the maximum of the potential barrier. Otherwise, full-tunneling process occurs when the energy distribution of the particle is below the minimum of the potential barrier. For this process, the obtained traversal time is interpreted as the tunneling time. Finally, the partial-tunneling process occurs when the energy distribution lies between the minimum and maximum of the potential barrier. This signifies that the quantum particle tunneled only through some portions of the potential barrier. We argue that the duration for a partial-tunneling process should not be interpreted as the tunneling time but instead as a partial traversal time to differentiate it from the full-tunneling process. We then show that a full-tunneling process is always instantaneous, while a partial-tunneling process takes a non-zero amount of time. We are then led to the hypothesis that experimentally measured non-zero and vanishing tunneling times correspond to partial and full-tunneling processes, respectively.

    SDG: SDG 4, SDG 8, SDG 9, SDG 17

    Publication Link
  • ► Quantum corrections to the Weyl quantization of the classical time of arrival (2022)

    Abstract: A time of arrival (TOA) operator that is conjugate with the system Hamiltonian was constructed by Galapon without canonical quantization in Galapon (J. Math. Phys. 45:3180–3215, 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 analytic potentials. In this paper, we give a full account of the said operator by explicitly solving all the terms in the expansion. We interpret the terms beyond the leading term as the quantum corrections to the Weyl quantization of the classical arrival time. These quantum corrections are expressed as some integrals of the interaction potential and their properties are investigated in detail. In particular, the quantum corrections always vanish for linear systems but nonvanishing for nonlinear systems. Finally, we consider the case of an anharmonic oscillator potential as an example.

    SDG: SDG 4, SDG 8, SDG 9, SDG 17

    Publication Link
  • ► Quantum traversal time across a potential well (2000)

    Abstract: We consider the quantum traversal time of an incident wave packet across a potential well using the theory of quantum time of arrival (TOA) operators. This is done by constructing the corresponding TOA operator across a potential well via quantization. The expectation value of the potential-well TOA operator is compared to the free-particle case for the same incident wave packet. The comparison yields a closed-form expression of the quantum well traversal time which explicitly shows the classical contributions of the positive and negative momentum components of the incident wave packet and a purely quantum-mechanical contribution significantly dependent on the well depth. An incident Gaussian wave packet is then used as an example. It is shown that for shallow potential wells, the quantum well traversal time approaches the classical traversal time across the well region when the incident wave packet is spatially broad and approaches the expected quantum free-particle traversal time when the wave packet is localized. For deep potential wells, the quantum traversal time oscillates from positive to negative, implying that the wave packet can be advanced or delayed.

    SDG: SDG 4, SDG 8, SDG 9, SDG 17

    Publication Link
    • On-going
    • Phase Space Approach to Quantum Time of Arrival Problems (2025), SDG 4, 9 – (STIE-25-8)
    Awards
    • International
      • Publication Award 2024, University of the Philippines Diliman, Philippines – 2024
      • Publication Award 2023, University of the Philippines Diliman, Philippines – 2023
      • Publication Award 2021, University of the Philippines Diliman, Philippines – 2021
    • Local
      • Excellence in Graduate Studies Award, University of the Philippines Diliman, Philippines – 2024
    Presentation
    • Moyal Deformation of the Classical Arrival Time (2025), SDG 4, 8, 9
    • Instantaneous quantum tunneling time within the theory of time-of-arrival operators (2024), SDG 4, 8, 9, 17
    • Construction and dynamics of algebra-preserving time of arrival operators (2024), SDG 4, 7, 9, 17
    • The free time of arrival problem in quantum phase space (2023), SDG 4, 8, 9, 17
    • Quantum corrections to the Weyl quantization of the classical time of arrival (2022), SDG 4, 8, 9, 17
    • A time of arrival operator for a quartic oscillator potential from the Moyal bracket formalism (2022), SDG 4, 8, 9, 17
    • Research Issues in the Philippines: Reflections (2021), SDG 4, 8, 9, 17
    Citations
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