Journal ArticleDOI
Analytic Aharonov-Bohm rings — Currents readout from Zeeman spectrum
Mufei Xiao,Armando Reyes-Serrato +1 more
TLDR
In this article, the authors developed and analyzed a model for quantum rings in which persistent currents are induced by Aharonov-Bohm (AB) or other similar effects, based on a centric and annual potential profile.Abstract:
This paper reports the work on the development and analysis of a model for quantum rings in which persistent currents are induced by Aharonov–Bohm (AB) or other similar effects. The model is based on a centric and annual potential profile. The time-independent Schrodinger equation including an external magnetic field and an AB flux is analytically solved. The outputs, namely energy dispersion and wavefunctions, are analyzed in detail. It is shown that the rotation quantum number m is limited to small numbers, especially in weak confinement, and a conceptual proposal is put forward for acquiring the flux and eventually estimating the persistent currents in a Zeeman spectroscopy. The wavefunctions and electron distributions are numerically studied and compared to one-dimensional (1D) quantum well. It is predicated that the model and its solutions, eigen energy structure and analytic wavefunctions, would be a powerful tool for studying various electric and optical properties of quantum rings.read more
Citations
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Rényi and Tsallis Entropies of the Aharonov–Bohm Ring in Uniform Magnetic Fields
TL;DR: It is proved that there is the only orbital for which both Rényi and Tsallis uncertainty relations turn into the identity at α=1/2, which is not necessarily the lowest-energy level.
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Quantum information measures of the Aharonov–Bohm ring in uniform magnetic fields
TL;DR: In this article, it was shown that a variation of the position Shannon entropy or Onicescu energy with the AB field uniquely determines an associated persistent current as a function of ϕ A B at B = 0.
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R\'{e}nyi and Tsallis entropies of the Aharonov-Bohm ring in uniform magnetic fields
TL;DR: In this paper, the uncertainty relation of Renyi and Tsallis one-parameter functionals was investigated in the position and momentum spaces for the azimuthally symmetric 2D nanoring that is placed into the combination of the transverse uniform magnetic field and the Aharonov-Bohm (AB) flux.
References
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Quantal phase factors accompanying adiabatic changes
TL;DR: In this article, it was shown that the Aharonov-Bohm effect can be interpreted as a geometrical phase factor and a general formula for γ(C) was derived in terms of the spectrum and eigen states of the Hamiltonian over a surface spanning C.
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Significance of Electromagnetic Potentials in the Quantum Theory
Yakir Aharonov,D. Bohm +1 more
TL;DR: In this article, it was shown that there exist effects of potentials on charged particles, even in the region where all the fields (and therefore the forces on the particles) vanish.
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Phase Change During a Cyclic Quantum Evolution
Yakir Aharonov,Jeeva Anandan +1 more
TL;DR: A new geometric phase factor is defined for any cyclic evolution of a quantum system, independent of the phase factor relating the initial and final state vectors and the Hamiltonian, for a given projection of the evolution on the projective space of rays of the Hilbert space.
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Topological Quantum Effects for Neutral Particles
Yakir Aharonov,Aharon Casher +1 more
TL;DR: In this article, the effective Lagrangian was derived to describe the interaction between a charged particle and a magnetic moment in the nonrelativistic limit, and it was shown that neutral particles with a magnetic moments will exhibit the Aharonov-Bohm effect in certain circumstances.
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Josephson behavior in small normal one-dimensional rings
TL;DR: In this paper, a superconducting ring of normal metal driven by an external magnetic flux acts like a Josephson junction, except that 2e is replaced by e.g.