Alternative quantisation condition for wavepacket dynamics in a hyperbolic double well

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Alternative quantisation condition for wavepacket dynamics in a hyperbolic double well

Kufel, DS; Chomet, H; Figueira de Morisson Faria, C; (2021) Alternative quantisation condition for wavepacket dynamics in a hyperbolic double well. Journal of Physics A: Mathematical and Theoretical , 54 , Article 035304. 10.1088/1751-8121/abd267. Green open access

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Abstract

We propose an analytical approach for computing the eigenspectrum and corresponding eigenstates of a hyperbolic double well potential of arbitrary height or width, which goes beyond the usual techniques applied to quasi-exactly solvable models. We map the time-independent Schrödinger equation onto the Heun confluent differential equation, which is solved by using an infinite power series. The coefficients of this series are polynomials in the quantisation parameter, whose roots correspond to the system's eigenenergies. This leads to a quantisation condition that allows us to determine a whole spectrum, instead of individual eigenenergies. This method is then employed to perform an in depth analysis of electronic wave-packet dynamics, with emphasis on intra-well tunneling and the interference-induced quantum bridges reported in a previous publication Chomet et al (2019 New J. Phys. 21 123004). Considering initial wave packets of different widths and peak locations, we compute autocorrelation functions and Wigner quasiprobability distributions. Our results exhibit an excellent agreement with numerical computations, and allow us to disentangle the different eigenfrequencies that govern the phase-space dynamics.

Type:	Article
Title:	Alternative quantisation condition for wavepacket dynamics in a hyperbolic double well
Open access status:	An open access version is available from UCL Discovery
DOI:	10.1088/1751-8121/abd267
Publisher version:	http://doi.org/10.1088/1751-8121/abd267
Language:	English
Additional information:	This work is licensed under a Creative Commons Attribution 4.0 International License. The images or other third party material in this article are included in the Creative Commons license, unless indicated otherwise in the credit line; if the material is not included under the Creative Commons license, users will need to obtain permission from the license holder to reproduce the material. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/
UCL classification:	UCL UCL > Provost and Vice Provost Offices > UCL BEAMS UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences > Dept of Physics and Astronomy
URI:	https://discovery.ucl.ac.uk/id/eprint/10119718