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arXiv:2106.07311 · Journal of Physics Communications

Coherent states for a system of an electron moving in a plane

Isiaka Aremua, Laure Gouba

Published Aug 1, 2021• 3 citations
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Abstract

Abstract In this paper, we construct the coherent states for a system of an electron moving in a plane under uniform external magnetic and electric fields. These coherent states are built in the context of both discrete and continuous spectra and satisfy the Gazeau-Klauder coherent state properties Gazeau and Klauder (1999 J. Phys. A: Math. Gen. 32, 123–132).

DOI
10.1088/2399-6528/ac1d30

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Abstract In this paper, we construct the coherent states for a system of an electron moving in a plane under uniform external magnetic and electric fields. These coherent states are built in the context of both discrete and continuous spectra and satisfy the Gazeau-Klauder coherent state properties Gazeau and Klauder (1999 J. Phys. A: Math. Gen. 32, 123–132).
Abstract In this work, we construct different classes of coherent states related to a quantum system, recently studied in [1], of an electron moving in a plane in uniform external magnetic and electric fields which possesses both discrete and continuous spectra. The eigenfunctions are realized as an orthonormal basis of a suitable Hilbert space appropriate for building the related coherent states. These latter are achieved in the context where we consider both spectra purely discrete obeying the criteria that a family of coherent states must satisfy.
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In the spirit of some earlier work on the construction of vector coherent states (VCS) over matrix domains, we compute here such states associated to some physical Hamiltonians. In particular, we construct vector coherent states of the Gazeau–Klauder type. As a related problem, we also suggest a way to handle degeneracies in the Hamiltonian for building coherent states. Specific physical Hamiltonians studied include a single photon mode interacting with a pair of fermions, a Hamiltonian involving a single boson and a single fermion, a charged particle in a three-dimensional harmonic force field and the case of a two-dimensional electron placed in a constant magnetic field, orthogonal to the plane which contains the electron. In this last example, which is related to the fractional quantum Hall effect, an interesting modular structure emerges for two underlying von Neumann algebras, related to opposite directions of the magnetic field. This leads to the existence of coherent states built out of Kubo-Martin-Schwinger (KMS) states for the system.