The scattering of electrons by an Aharonov--Bohm field is considered from the viewpoint of quantum-mechanical problem of constructing a self-adjoint Hamiltonian for the Pauli equation. The correct domain for the self-adjoint Hamiltonian, which takes into account explicitly the electron spin is found. A one-parameter self-adjoint extension of the Hamiltonian for spin-polarized electrons in the Aharonov--Bohm field is selected. The correct domain of the self-adjoint Hamiltonian can contain regular and singular (at the point ${\bf r}=0$) square-integrable functions on the half-line with measure $rdr$. We argue that the physical reason of the existence of singular functions is the additional attractive potential, which appear due to the interaction between the spin magnetic moment of fermion and Aharonov--Bohm magnetic field. The scattering amplitude and cross section are obtained for spin-polarized electrons scattered by the Aharonov--Bohm field. It is shown that in some range of the extension parameter there appears a bound state. Since the Hamiltonian of the nonrelativistic Dirac--Pauli equation for a massive neutral fermion with the anomalous magnetic moment (AMM) in the electric field of a linear charge aligned perpendicularly to the fermion motion has the form of the Hamiltonian for the Pauli equation in the Aharonov--Bohm flux tube, we also calculate the scattering amplitude and cross section for the neutral fermion.
The Aharonov-Casher and scalar Aharonov-Bohm topological effects
我们重新审视拓扑和非局部性质的Aharonov-Casher和标量Aharonov-Bohm相位效应。U（1）规范结构的基础被明确展示。阐明了拓扑Aharonov-Casher相和标量Aharonov-Bohm相产生的条件。我们分析了M. Peshkin和H. J. Lipkin（Phys. Rev. Lett. 74，2847（1995）），并表明他们是基于错误的哈密顿量，这导致他们的结论不正确。
Aharonov-Bohm (AB) and Aharonov-Casher (AC) effects are treated fully relativistically in 2+1 dimensions. The influences of the relevant geometric and topological phases on an entangled spin-1/2 system are studied. It is shown that for the AC case the correlation function of the Clauser-Horne-Shimony-Holt (CHSH) inequality for certain choices of the spin measurements depends on the AC phase explicitly.
A quaternionic analog of the Aharonov-Bohm effect is developed without the usual anti-hermitian operators in quaternionic quantum mechanics (QQM). A quaternionic phase links the solutions obtained to ordinary complex wave functions, and new theoretical studies and experimental tests are possible for them.
We use a covariant formalism that is capable of describing the electric and magnetic versions of the Aharonov-Bohm effect, as well as the Aharonov-Casher effect, through local interactions of charges and currents with the quantum electromagnetic field. By considering that only local interactions of a quantum particle with the quantum field can affect its behavior, we show that the magnetic Aharonov-Bohm effect must be present even if the solenoid generating the magnetic field is shielded by a perfect conductor, as experimentally demonstrated.
Although the Aharonov-Bohm and related effects are familiar in solid state and high energy physics, the nonlocality of these effects has been questioned. Here we show, for the first time, that the Aharonov-Bohm effect has two very different aspects. One aspect is instantaneous and nonlocal; the other aspect, which depends on entanglement, unfolds continuously over time. While local, gauge-invariant variables may occasionally suffice for explaining the continuous aspect, we argue that they cannot explain the instantaneous aspect. Thus the Aharonov-Bohm effect is, in general, nonlocal.
Quantum mechanics in noncommutative space modifies the standard result of the Aharonov-Bohm effect for electrons and other recent quantum effects. Here we obtain the phase in noncommutative space for the Spavieri effect, a generalization of Aharonov-bohm effect which involving a coherent superposition of particles with opposite charges moving along single open interferometric path. By means of the experimental considerations a limit $\sqrtθ\simeq\left( 0,13T\text{eV}\right) ^{-1}$ is achieved, improving by 10 orders of magnitude the derived by Chaichian et. al. for the Aharonov-Bohm effect. It…
In the original setting of the Aharonov-Bohm, the gauge invariant physical longitudinal mode of the vector potential, which is written by the gauge invariant physical current $(-e)\barψ{\boldsymbol γ} ψ$, gives the desired contribution to the Aharonov-Bohm effect. While the scalar mode of the vector potential, which changes under the gauge transformation so that it is the unphysical mode, give no contribution to the Aharonov-Bohm effect. Then Aharonov-Bohm effect really occurs by the physical longitudinal mode in the original Aharonov-Bohm's setting. In the setting of Tonomura {\it et al.}, wh…
An experiment is proposed in which the Aharonov-Bohm effect can be veryfied through a spectroscopic measurement. The apparatus consists of gaseous hydrochloric acid (HCl) immersed in the vector potential ${\bf A}$ present in the center of a toroidal coil, where ${\bf B}=0$. Changes due to ${\bf A}$ in the absorption spectrum of the gas are investigated.
When the magnetic vector potential is expressed in terms of the magnetic field it, is found to be explicitly non-local in space. This gives support to the conclusions of Aharonov et al. in a recent comment, that the Aharonov-Bohm effect may be interpreted as being either due to a local gauge potential or else due to non-local gauge-invariant fields but not due to local gauge-invariant fields.
In the Landau problem on the two-dimensional plane, magnetic translation of a quantum wave can be induced by an in-plane electric field. The geometric phase accompanying such magnetic translation around a closed path differs from the topological phase of Aharonov and Bohm in two essential aspects: The wave is in direct contact with the magnetic flux and the geometric phase has an opposite sign from the Aharonov-Bohm phase. We show that magnetic translation on the two-dimensional cylinder implemented by the Schrödinger time evolution truly leads to the Aharonov-Bohm effect. The magnetic field n…
Decades ago, Aharonov and Bohm showed that electrons are affected by electromagnetic potentials in the absence of forces due to fields. Zeilinger's theorem describes this absence of classical force in quantum terms as the "dispersionless" nature of the Aharonov-Bohm effect. Shelankov predicted the presence of a quantum "force" for the same Aharonov-Bohm physical system as elucidated by Berry. Here, we report an experiment designed to test Shelankov's prediction and we provide a theoretical analysis that is intended to elucidate the relation between Shelankov's prediction and Zeilinger's theore…
The Aharonov-Bohm effect is considered by most authors as a quantum effect, but a generally accepted explanation does not seem to be available. The phenomenon is studied here under the assumption that hypothetical electric dipole distributions configured by moving charges in the solenoid act on the electrons as test particles. The relative motions of the interacting charged particles introduce relativistic time dilations. The massless dipoles are postulated as part of an impact model that has recently been proposed to account for the far-reaching electrostatic forces between charged particles …
Reply to "Comment on "Aharonov-Casher and Scalar Aharonov-Bohm Topological Effects""
在这个答复中，我们认为（一）汉密尔顿，方程。(17)在我们的论文中（Phys. Rev. Lett. 108，070405（2012）），绝对是洛伦兹不变量;（ii）生成拓扑Aharonov-Casher（AC）和标量Aharonov-Bohm（SAB）效应的条件是必要的和物理上有意义的;（iii）在Phys. Rev. Lett. 74，2847（1995）和arXiv：1311.4011不适合描述极化的旋量粒子。
This paper formulates generalized versions of the general principle of relativity and of the principle of equivalence that can be applied to general abstract spaces. It is shown that when the principles are applied to the Hilbert space of a quantum particle, its law of coupling to electromagnetic fields is obtained. It is suggested to understand the Aharonov-Bohm effect in light of these principles, and the implications for some related foundational controversies are discussed.
Comment on "Aharonov-Casher and Scalar Aharonov-Bohm Topological Effects"
在这篇评论中，我们指出（i）哈密顿量，方程。(17)在信中（物理学评论Lett。108，070405（2012）），不是相对论性的哈密顿量，（ii）那么在信中的条件对于拓扑AC和SAB效应是不相关的，以及（iii）结论性地，Peshkin和Lipkin（Phys. Rev. Lett. 74，2847（1995））对于固定自旋具有相同的$U(1)_{mm}$规范结构，因此是正确的，但他们对自旋自相关的错误解释导致了错误的结论。
Another manifestation of the Aharonov-Bohm effect is introduced to chemistry, in fact to nuclear dynamics and high-resolution molecular spectroscopy. As demonstrated, the overall rotation of a symmetric-top molecule influences the dynamics of an internal vibrational motion in a way that is analogous to the presence of a solenoid carrying magnetic flux. To a good approximation, the low-energy rovibrational energy-level structure of the quasistructural molecular ion H5+ can be understood entirely in terms of this effect.
