The role of conjugacy in the dynamics of time of arrival operators
arXiv:2404.16298 · doi:10.1016/j.physleta.2024.129778
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.
arXiv comment23 pages
References in corpus (19)
- Pauli's Theorem and Quantum Canonical Pairs: The Consistency Of a Bounded, Self-Adjoint Time Operator Canonically Conjugate to a Hamiltonian with Non-empty Point Spectrum
- Confined Quantum Time of Arrivals
- Time-of-arrival distribution for arbitrary potentials and Wigner's time-energy uncertainty relation
- The attoclock and the tunnelling time debate
- Self-adjoint Time Operator is the Rule for Discrete Semibounded Hamiltonians
- Transition from discrete to continuous time of arrival distribution for a quantum particle
- Time of arrival in the presence of interactions
- Shouldn't there be an antithesis to quantization?
- How to Introduce Time Operator
- Confined Quantum Time of Arrival for Vanishing Potential
- An Introduction to the Quantum Backflow Effect
- Quantum Arrival Time Formula from Decoherent Histories
- Quantizations of the classical time of arrival and their dynamics
- Consistent histories, the quantum Zeno effect, and time of arrival
- The time distribution of quantum events
- Quantum-Classical Correspondence of Dynamical Observables, Quantization and the Time of Arrival Correspondence Problem
- Quantum delay in the time of arrival of free-falling atoms
- Time of arrival operator in the momentum space
- Formulation of causality-preserving quantum time of arrival theory