In quantum theory, electromagnetic gauge fields enter directly into the phase evolution of the wavefunction and can even influence quantum systems in regions where the associated electric and magnetic fields vanish. The Aharonov-Bohm effect demonstrates that such gauge fields produce observable consequences when a coherent quantum system encloses magnetic flux along a doubly connected path. This has led to the widespread view that curl-free gauge fields are undetectable in simply connected systems, giving rise to a form of topological blindness. Here we show that this conclusion is not fundamental. During nonequilibrium processes, collective quantum systems can develop transient responses to curl-free gauge fields without enclosing magnetic flux in a static geometry. Using superconducting condensates as a concrete example, we demonstrate that the evolving phase of the macroscopic wavefunction generates supercurrents and voltage pulses whose time integral is proportional to the open-path line integral of the vector potential. In contrast to the conventional Aharonov-Bohm effect, the resulting response is not restricted modulo the flux quantum and may greatly exceed the scale associated with static doubly connected geometries. The mechanism can be interpreted as a dynamical closure of the gauge contour in spacetime and is supported by gauge-invariant arguments, time-dependent Ginzburg-Landau theory modeling, and numerical simulations. These results establish a general principle for detecting curl-free gauge fields and suggest new approaches for probing hidden gauge structures in quantum matter and beyond.
In quantum theory, electromagnetic gauge fields enter directly into the phase evolution of the wavefunction and can even influence quantum systems in regions where the associated electric and magnetic fields vanish. The Aharonov-Bohm effect demonstrates that such gauge fields produce observable consequences when a coherent quantum system encloses magnetic flux along a doubly connected path. This has led to the widespread view that curl-free gauge fields are undetectable in simply connected systems, giving rise to a form of topological blindness. Here we show that this conclusion is not fundamental. During nonequilibrium processes, collective quantum systems can develop transient responses to curl-free gauge fields without enclosing magnetic flux in a static geometry. Using superconducting condensates as a concrete example, we demonstrate that the evolving phase of the macroscopic wavefunction generates supercurrents and voltage pulses whose time integral is proportional to the open-path line integral of the vector potential. In contrast to the conventional Aharonov-Bohm effect, the resulting response is not restricted modulo the flux quantum and may greatly exceed the scale associated with static doubly connected geometries. The mechanism can be interpreted as a dynamical closure of the gauge contour in spacetime and is supported by gauge-invariant arguments, time-dependent Ginzburg-Landau theory modeling, and numerical simulations. These results establish a general principle for detecting curl-free gauge fields and suggest new approaches for probing hidden gauge structures in quantum matter and beyond.
Previous time-dependent Ginzburg–Landau simulations demonstrated that Abrikosov vortex dynamics in superconductors can be influenced by Aharonov–Bohm-type curl-less vector potentials even in simply connected geometries, without closed-loop trajectories enclosing magnetic flux [A. M. Gulian et al., Phys. Lett. A 382 (2018) 1058]. The origin of this effect has remained unexplained. Here we investigate further nonequilibrium effects in which the relation between a curl-less vector potential and an evolving quantum state produces observable consequences. During transient nonequilibrium state evolution, collective quantum systems may develop measurable responses to curl-less gauge fields despite a simply connected final equilibrium configuration with no persistent current. Using superconducting condensates, we formulate protocols based on the gauge-invariant coupling between quantum phase and the curl-less vector potential, analyze their dynamics using time-dependent Ginzburg–Landau theory and interpret rapid phase formation within the Kibble–Zurek picture. The predicted transient supercurrents and voltage signals provide a physical interpretation of nonequilibrium sensitivity to curl-less gauge fields and motivate experimental tests.
The Aharonov-Bohm (AB) effect highlights the fundamental role of electromagnetic potentials in quantum mechanics, manifesting as a phase shift for a charged particle in field-free regions. While well-established for static magnetic fluxes, the effect's behavior under time-varying fluxes remains an open and debated question. Employing the WKB method, we derive the AB phase shift for a time-dependent magnetic vector potential, demonstrating that for circular paths in the quasistatic regime, it is proportional to the time-averaged enclosed magnetic flux, ΔφAB=T1∫0TeΦ(t)dt, with the total phase shift, including kinetic contributions, equaling eΦ(0). For non-circular paths, the phase shift depends on both the flux history and path geometry, revealing the effect's hybrid nature involving gauge potentials and induced electric fields. We verify the consistency of our gauge choice with Maxwell's equations and discuss the implications for local versus nonlocal interpretations of the AB effect. We also generalize the results to scenarios with nonzero external magnetic fields, where the enclosed flux is through the actual electron paths, and for circular paths of radius R, the AB phase shift is also proportional to the time average of the enclosed flux Φenc(R,t), with the total phase shift depending only on the initial enclosed flux eΦenc(R,0); for general non-circular paths, the external magnetic field affects trajectories and phase accumulation through the Lorentz force, leading to additional path dependence. These findings clarify the role of gauge-dependent potentials and induced fields in the generalized AB effect, offering new theoretical insights and potential applications in quantum technologies.
We present a rigorous no-go theorem that excludes \emph{all} gauge-invariant dynamical explanations of the generalized, time-dependent Aharonov--Bohm (AB) effect. In this generalization, the AB phase is determined by the time-averaged magnetic flux enclosed by the particle's path, ΔϕAB=ℏe⋅T1∫0TΦ(t)dt. Using a carefully designed protocol in which a constant flux Φ persists only for a finite interval Δt after wavepacket splitting and is switched to zero before detection, we demonstrate that during the phase-generating period all gauge-invariant observables of the electron remain identical to those in a zero-flux experiment. Relativistic causality further prohibits backreaction from the source. Consequently, no gauge-invariant quantity---whether local or nonlocal, field-based or source-mediated---can account for the observed phase, which depends solely on flux history. We also critically examine Healey's holonomy interpretation and show that it, too, fails to explain the time-dependent AB effect, as its static formalism lacks the dynamical structure needed to capture temporal averaging. This result establishes the inescapable physical reality of gauge potentials in quantum theory and clarifies the foundational status of the AB effect as a genuine manifestation of potentials rather than fields.
The Aharonov-Bohm (AB) effect, wherein an electron acquires a phase shift in a field-free region due to electromagnetic potentials, poses a profound challenge to the ontology of quantum mechanics and gauge theories. This paper demonstrates that gauge-invariant explanations, which attribute the phase to measurable quantities, rely on nonlocal and discontinuous mechanism and fail to account for its continuous accumulation along the electron's path—a process evident in the generalized AB effect, where a time-varying magnetic flux induces a phase that builds gradually over time, as predicted by quantum mechanics. Through a new analysis spanning quantum mechanics and quantum electrodynamics, I argue that the electromagnetic potentials Aμ, fixed in the Lorenz gauge, emerge as the fundamental physical reality, offering a local, relativistically consistent account of the phase’s generation. This exclusion of gauge-invariant paradigms reverberates across gauge theories: it redefines the Higgs mechanism, favoring dynamic potentials over static invariants, and extends to general relativity, where gravitational potentials gμν may anchor spacetime’s substantival reality via a gravitational AB effect. By unraveling the AB phase’s continuous generation—locally mediated by potentials—this study not only addresses a long-standing conundrum but also bridges electromagnetic, gravitational, and Yang-Mills frameworks, offering a unified potential-centric perspective with novel implications for physics and philosophy.
The Aharonov-Bohm (AB) effect is a pure quantum effect that implies a measurable phase shift in the wave function for a charged particle that encircles a magnetic flux located in a region inaccessible to the particle. Classically, such a nonlocal effect appears to be impossible since the Lorentz force depends on only the magnetic field at the location of the particle. In quantum mechanics, the Hamiltonian, and thus the Schr\"odinger equation, has a local coupling between the current due to the particle and the electromagnetic vector potential A, which extends to the entire space beyond the region with finite magnetic field. This has sometimes been interpreted as meaning that in quantum mechanics A is in some sense more ``fundamental'' than B in spite of the former being gauge dependent and thus unobservable. Here we shall, with a general proof followed by a few examples, demonstrate that the AB effect can be fully accounted for by considering only the gauge-invariant B field, as long as it is included as part of the quantum action of the entire isolated system. The price for the gauge-invariant formulation is that we must give up locality---the AB phase for the particle will arise from the change in the action for the B field in the region inaccessible to the particle.
The AB (Aharonov-Bohm) effect is a pivotal quantum mechanical phenomenon that illustrates the fundamental role of the electromagnetic vector potential A in determining the phase of a charged particle's wave function, even in regions where the magnetic field B is zero.This effect demonstrates that quantum particles are influenced not only by the fields directly present but also by the potentials associated with those fields.In the AB effect, an electron beam is split into two paths, with one path encircling a solenoid and the other bypassing it.Despite the absence of a magnetic field in the regions traversed by the beams, the vector potential A associated with the magnetic flux through the solenoid induces a phase shift in the electron's wave function.This phase shift, quantified by qc , manifests as a change in the interference pattern observed in the detection screen.The phenomenon underscores the principle of gauge invariance in QED (quantum electrodynamics), where physical observables remain invariant under local gauge transformations of the vector and scalar potentials.This reinforces the notion that the vector potential A has a profound impact on quantum systems, beyond its classical role.This article outlines the AB effect, including its theoretical framework, experimental observations, and implications.The focus on the role of the vector potential in quantum mechanics provides a comprehensive understanding of this important phenomenon.