Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · 1806.04282

The role of electron orbital angular momentum in the Aharonov-Bohm effect revisited

Masashi Wakamatsu·Yoshio Kitadono·Liping Zou·Pengming Zhang
View original source ↗Read source document ↗Export metadata ↓

Abstract

This is a brief review on the theoretical interpretation of the Aharonov-Bohm effect, which also contains our new insight into the problem. A particular emphasis is put on the unique role of electron orbital angular momentum, especially viewed from the novel concept of the physical component of the gauge field, which has been extensively discussed in the context of the nucleon spin decomposition problem as well as the photon angular momentum decomposition problem. Practically, we concentrate on the frequently discussed idealized setting of the Aharonov-Bohm effect, i.e. the interference phenomenon of the electron beam passing around the infinitely-long solenoid. One of the most puzzling observations in this Aharonov-Bohm solenoid effect is that the pure-gauge potential outside the solenoid appears to carry non-zero orbital angular momentum. Through the process of tracing its dynamical origin, we try to answer several fundamental questions of the Aharonov-Bohm effect, which includes the question about the reality of the electromagnetic potential, the gauge-invariance issue, and the non-locality interpretation, etc.

Explore related subjects

quant-phhep-th

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Masashi Wakamatsu, Yoshio Kitadono, Liping Zou, Pengming Zhang. 2018-08-21. The role of electron orbital angular momentum in the Aharonov-Bohm effect revisited. https://doi.org/10.1016/j.aop.2018.08.010

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Quantum complexity and generalized area law in fully connected models

The area law for entanglement entropy captures a fundamental constraint on the complexity of quantum many-body ground states and enables their efficient description. While the area law is rigorously established in one dimension, its status in higher-dimensional local systems remains unresolved, and it does not hold in general for geometrically non-local systems. Here, we establish a generalized area law for gapped ground states of fully connected Hamiltonians. We show that the bipartite entanglement entropy grows at most logarithmically with system size despite the absence of geometric locality. In the ground state, each site is only weakly entangled with the rest, while configurations with extensive local fluctuations are strongly suppressed, effectively restricting the accessible Hilbert space. As a consequence, the ground state admits a matrix product state approximation with polynomial bond dimension with respect to the system size at fixed accuracy. In the permutation-invariant setting, we further prove a constant entanglement bound and demonstrate that the gapped ground state can be computed in time polylogarithmic in the system size. These results show that low entanglement complexity need not rely on geometric locality, broadening the conceptual and computational scope of area laws.

quant-ph↗
arXiv2026

Quantum Mechanics as a Reversible Diffusion Theory

This paper proposes an interpretation of quantum mechanics, relying on the time-symmetric stochastic dynamics of quantum particles and on non-classical probability theory. Our main purpose is to demonstrate that the wave function and its complex conjugate can be interpreted as complex probability distributions in two complex diffusion equations related to non-real forward and backward in time stochastic motions respectively. We say non-real because Schroedinger forward and backward diffusions describe both reversible (real trajectories) and irreversible trajectories (non-real trajectories). The reversible trajectories are the only real trajectories and are given by the intersection of those forward and backward processes. It turns out that if we translate this intersection using set-theoretic language, we are led to a reversible diffusion described by Born rule probabilities. This proposal is useful also for explaining more about the role of complex numbers in quantum mechanics that produces this so-called "wave-like" nature of quantum reality. Our perspective also challenges the notion of physical superposition and aims at a derivation of superposition principle not based on the linearity of Schroedinger's equation but relying on pure probability theory. Moreover, it is suggested that, embracing the idea of stochastic processes in quantum theory, explains the reasons for the appearance of classical behavior in large objects, in contrast to the quantum behavior of small ones. In other words, we claim that a combination of a probabilistic and no-ontic view (neither epistemic though) of the wave function with a stochastic hidden-variables approach, may provide some insight into the quantum physical reality and potentially establish the groundwork for a novel interpretation of quantum mechanics.

quant-ph↗
arXiv2026

Flexible Qubit Allocation of Network Resource States

The Quantum Internet is still in its infancy, yet identifying scalable and resilient quantum network resource states is an essential task for realizing it. We explore the use of graph states with flexible, non-trivial qubit-to-node assignments. This flexibility enables adaptable engineering of the entanglement topology of an arbitrary quantum network. In particular, we focus on cluster states with arbitrary allocation as network resource states and as a promising candidate for a \textit{network core}-level entangled resource, due to its intrinsic flexible connectivity properties and resilience to particle losses. We introduce a modeling framework for overlaying entanglement topologies on physical networks and demonstrate how optimized and even random qubit assignment creates shortcuts and improves robustness and memory savings, while reducing the worst-case hop distance between remote network nodes, when compared to conventional approaches.

quant-ph↗