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تسجيل مستخدم جديدA new magnetic monopole inspired by Berrys phase
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A new static and azimuthally symmetric magnetic monopolelike object, which looks like a Dirac monopole when seen from far away but smoothly changes to a dipole near the monopole position and vanishes at the origin, is discussed. This monopolelike object is inspired by an analysis of an exactly solvable model of Berrys phase in the parameter space. A salient feature of the monopolelike potential ${cal A}_{k}(r,theta)$ with a magnetic charge $e_{M}$ is that the Dirac string is naturally described by the potential ${cal A}_{k}(r,theta)$, and the origin of the Dirac string and the geometrical center of the monopole are displaced in the coordinate space. The smooth topology change from a monopole to a dipole takes place if the Dirac string, when coupled to the electron, becomes unobservable by satisfying the Dirac quantization condition. The electric charge is then quantized even if the monopole changes to a dipole near the origin. In the transitional region from a monopole to a dipole, a half-monopole with a magnetic charge $e_{M}/2$ appears.
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The smooth topology change of Berrys phase from a Dirac monopole-like configuration to a dipole configuration, when one approaches the monopole position in the parameter space, is analyzed in an exactly solvable model. A novel aspect of Berrys connec
tion ${cal A}_{k}$ is that the geometrical center of the monopole-like configuration and the origin of the Dirac string are displaced in the parameter space. Gauss theorem $int_{S}( ablatimes {cal A})cdot dvec{S}=int_{V} ablacdot ( ablatimes {cal A}) dV=0$ for a volume $V$ which is free of singularities shows that a combination of the monopole-like configuration and the Dirac string is effectively a dipole. The smooth topology change from a dipole to a monopole with a quantized magnetic charge $e_{M}=2pihbar$ takes place when one regards the Dirac string as unobservable if it satisfies the Wu-Yang gauge invariance condition. In the transitional region from a dipole to a monopole, a half-monopole appears with an observable Dirac string, which is analogous to the Aharonov-Bohm phase of an electron for the magnetic flux generated by the Cooper pair condensation. The main topological features of an exactly solvable model are shown to be supported by a generic model of Berrys phase.
The monopole-like singularity of Berrys adiabatic phase in momentum space and associated anomalous Poisson brackets have been recently discussed in various fields. With the help of the results of an exactly solvable version of Berrys model, we show t
hat Berrys phase does not lead to the deformation of the principle of quantum mechanics in the sense of anomalous canonical commutators. If one should assume Berrys phase of genuine Dirac monopole-type, which is assumed to hold not only in the adiabatic limit but also in the non-adiabatic limit, the deformation of the principle of quantum mechanics could take place. But Berrys phase of the genuine Dirac monopole-type is not supported by the exactly solvable version of Berrys model nor by a generic model of Berrys phase. Besides, the monopole-like Berrys phase in momentum space has a magnetic charge $e_{M}=2pihbar$, for which the possible anomalous term in the canonical commutator $[x_{k},x_{l}]=ihbarOmega_{kl}$ would become of the order $O(hbar^{2})$.
Berrys phase, which is associated with the slow cyclic motion with a finite period, looks like a Dirac monopole when seen from far away but smoothly changes to a dipole near the level crossing point in the parameter space in an exactly solvable model
. This topology change of Berrys phase is visualized as a result of lensing effect; the monopole supposed to be located at the level crossing point appears at the displaced point when the variables of the model deviate from the precisely adiabatic movement. The effective magnetic field generated by Berrys phase is determined by a simple geometrical consideration of the magnetic flux coming from the displaced Dirac monopole.
Magnetic monopoles have provided a rich field of study, leading to a wide area of research in particle physics, solid state physics, ultra-cold gases, superconductors, cosmology, and gauge theory. So far, no true magnetic monopoles were found experim
entally. Using the Aharonov-Bohm effect, one of the central results of quantum physics, shows however, that an effective monopole field can be produced. Understanding the effects of such a monopole field on its surroundings is crucial to its observation and provides a better grasp of fundamental physical theory. We realize the diffraction of fast electrons at a magnetic monopole field generated by a nanoscopic magnetized ferromagnetic needle. Previous studies have been limited to theoretical semiclassical optical calculations of the motion of electrons in such a monopole field. Solid state systems like the recently studied spin ice provide a constrained system to study similar fields, but make it impossible to separate the monopole from the material. Free space diffraction helps to understand the dynamics of the electron-monopole system without the complexity of a solid state system. The use of a simple object such as a magnetized needle will allow various areas of physics to use the general dynamical effects of monopole fields without requiring a monopole particle or specific solids which have internal monopole-like properties. The experiment performed here shows that even without a true magnetic monopole particle, the theoretical background on monopoles serves as a basis for experiments and can be applied to efficiently create electron vortices. Various predictions about angular momentum and general field effects can readily be studied using the available equipment. This realization provides insights for the scientific community on how to detect magnetic monopoles in high energy collisions, cosmological processes, or novel materials.
We show, by solving Maxwells equations, that an electric charge on the surface of a slab of a linear magnetoelectric material generates an image magnetic monopole below the surface provided that the magnetoelectric has a diagonal component in its mag
netoelectric response. The image monopole, in turn, generates an ideal monopolar magnetic field outside of the slab. Using realistic values of the electric- and magnetic- field susceptibilties, we calculate the magnitude of the effect for the prototypical magnetoelectric material Cr$_2$O$_3$. We use low energy muon spin rotation to measure the strength of the magnetic field generated by charged muons as a function of their distance from the surface of a Cr$_2$O$_3$ films, and show that the results are consistent with the existence of the monopole. We discuss other possible routes to detecting the monopolar field, and show that, while the predicted monopolar field generated by Cr$_2$O$_3$ is above the detection limit for standard magnetic force microscopy, detection of the field using this technique is prevented by surface charging effects.
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