Coherent states on the circle: semiclassical matrix elements in the context of Kummer functions and the Zak transformation

Giesel K, Winnekens D (2023)

Publication Type: Journal article

Publication year: 2023

Journal

Physica Scripta

Book Volume: 98

Article Number: 095220

Journal Issue: 9

DOI: 10.1088/1402-4896/aceabd

Abstract

We extend former results for coherent states on the circle in the literature in two ways. On the one hand, we show that expectation values of fractional powers of momentum operators can be computed exactly analytically by means of Kummer’s confluent hypergeometric functions. Earlier, these expectation values have only been obtained by using suitable estimates. On the other hand, we consider the Zak transformation not only to map harmonic oscillator coherent states to coherent states on the circle as it has been discussed before, but we also use the properties of the Zak transformation to derive a relation between matrix elements with respect to coherent states in L 2 ( R ) and L 2(S 1). This provides an alternative way for computing semiclassical matrix elements for coherent states on the circle. In certain aspects, this method simplifies the semiclassical computations in particular if one is only interested in the classical limit, that is the zeroth order term in the semiclassical expansion.

Authors with CRIS profile

Kristina Giesel Professur für Theoretische Physik David Winnekens Chair for Theoretical Physics III (Quantum Gravity)

How to cite

APA:

Giesel, K., & Winnekens, D. (2023). Coherent states on the circle: semiclassical matrix elements in the context of Kummer functions and the Zak transformation. Physica Scripta, 98(9). https://dx.doi.org/10.1088/1402-4896/aceabd

MLA:

Giesel, Kristina, and David Winnekens. "Coherent states on the circle: semiclassical matrix elements in the context of Kummer functions and the Zak transformation." Physica Scripta 98.9 (2023).

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