Aharonov-Bohm effect in phase space
- URL: http://arxiv.org/abs/2211.13199v2
- Date: Tue, 13 Feb 2024 17:25:41 GMT
- Title: Aharonov-Bohm effect in phase space
- Authors: Jose A. R. Cembranos, David Garc\'ia-L\'opez and Zoe G. del Toro
- Abstract summary: We characterize for the first time the Aharonov-Bohm effect within two different formalisms of quantum mechanics.
The aim is to obtain a consistent description of the quantum system by means of the quasiprobability Wigner function.
We study the Aharonov-Bohm effect within them for two specific cases: One determined by a non-zero electric potential, and another determined by a non-zero magnetic vector potential.
- Score: 0.0
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: The Aharonov-Bohm effect is a genuine quantum effect typically characterized
by a measurable phase shift in the wave function for a charged particle that
encircles an electromagnetic field located in a region inaccessible to the
mentioned particle. However, this definition is not possible in the majority of
the phase space descriptions since they are based on quasiprobability
distributions. In this work, we characterize for the first time the
Aharonov-Bohm effect within two different formalisms of quantum mechanics. One
of them is the phase-space formalism relying on the canonical commutation
relations and Weyl transform. In this framework, the aim is to obtain a
consistent description of the quantum system by means of the quasiprobability
Wigner function. The other one is the Segal-Bargmann formalism, which we
mathematically describe and connect with quantum mechanics by means of the
commutation relations of the creation and annihilation operators. After an
introduction of both formalisms, we study the Aharonov-Bohm effect within them
for two specific cases: One determined by a non-zero electric potential, and
another determined by a non-zero magnetic vector potential. Subsequently, we
obtain a more general description of the Aharonov-Bohm effect that encompasses
the two previous cases and that we prove to be equivalent to the well-known
description of this effect in the usual quantum mechanics formalism in
configuration space. Finally, we delve into the Aharonov-Bohm effect, employing
a density operator to depict states with positional and momentum uncertainty,
showcasing its manifestation through distinctive interference patterns in the
temporal evolution of Wigner functions under an electric potential, and
emphasizing the intrinsically quantum nature of this phenomenon.
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