The Aharonov-Bohm effect Part one: Theory

Peshkin, Michael A.

doi:10.1007/bfb0032077

Cited by 141 publications

(263 citation statements)

References 25 publications

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“…We believe that the above misconceptions (and the overlooking of the nonlocal terms) are the basic reason why "it appears that no exact theoretical treatment has been given" (for the electric Aharonov-Bohm effect), as correctly stated by Peshkin in his Appendix B of Ref. [3].…”

Section: Discussionmentioning

confidence: 97%

“…The reader is referred to Appendix B of Peshkin [3] that demonstrates the intricasies of the electric Aharonov-Bohm effect, to which we return with an important comment at the end of the paper (Section XI)).…”

Section: Motivationmentioning

confidence: 99%

“…For the "electric analog" of the van Kampen case, we note that, although this has never really been discussed in the literature, nevertheless, it has been essentially briefly mentioned in Appendix B of Peshkin [3] (where the case that "first the particle exits the cages, and only then we switch on the outside electric field" is made, together with the comment that the results must be "consistent with ordinary ideas about Causality"; Peshkin correctly states:…”

Section: The Van Kampen Thought-experiments -Causal Issues Hid-denmentioning

confidence: 99%

“…If we view the form (B.5) and (B.6) of ref. [3] as an ansatz, then it is understandable why a condition (Peshkin's eqn. (B.8), and later (B.9)) needs to be enforced on the electric field outside the cages (in order for the extra (annoying) terms (that show up from expansion of the squared minimal substitution) to vanish and for (B.5) to be a solution).…”

Section: The Van Kampen Thought-experiments -Causal Issues Hid-denmentioning

confidence: 99%

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Nonlocal phases of local quantum mechanical wavefunctions in static and time-dependent Aharonov–Bohm experiments

Moulopoulos¹

2010

J. Phys. A: Math. Theor.

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We show that the standard Dirac phase factor is not the only solution of the gauge transformation equations. The full form of a general gauge function (that connects systems that move in different sets of scalar and vector potentials), apart from Dirac phases also contains terms of classical fields that act nonlocally (in spacetime) on the local solutions of the time-dependent Schrödinger equation: the phases of wavefunctions in the Schrödinger picture are affected nonlocally by spatially and temporally remote magnetic and electric fields, in ways that are fully explored. These contributions go beyond the usual Aharonov-Bohm effects (magnetic or electric).

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Section: Discussionmentioning

confidence: 97%

Section: Motivationmentioning

confidence: 99%

Section: The Van Kampen Thought-experiments -Causal Issues Hid-denmentioning

confidence: 99%

Section: The Van Kampen Thought-experiments -Causal Issues Hid-denmentioning

confidence: 99%

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Nonlocal phases of local quantum mechanical wavefunctions in static and time-dependent Aharonov–Bohm experiments

Moulopoulos¹

2010

J. Phys. A: Math. Theor.

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“…This could be really confusing when some discrepant magnitudes of those potentials are essentially incomparable. The meaning of the A-B effect is that an impact of the potentials on charged particles exists even in the regions where the given fields (and thus also the forces acting on the particles) vanish -compare [21][22][23]. Since impacts of electromagnetic, electrostatic and gravitational forces are conceptually similar, the lesson learned from the A-B effect pertains to (and therefore it could be transferred onto) quasi-static gravitational fields.…”

Section: Galilei Was Wrong: Constitution Of Matter Of Mass Sources Ofmentioning

confidence: 99%

Galilei was Wrong: Angular Nonradial Effects of Radial Gravity Depend on Density of Matter

Czajko

2014

ILCPA

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Although in mathematical sense the actual meaning of Galilei's experiments conducted at leaning tower of Pisa is that he failed to detect any measurable impact of composition of matter on gravitating bodies, the obvious failure is mistakenly interpreted as experimental confirmation of lack of the impact instead. Galilei did not really perform internal validity checks of his experiments, because he did not ensure that he actually measured what he was supposed to measure. However, a modern experiment devised to test the impact of large mass on gravitational phenomena has revealed presence of (formerly unanticipated) extraneous frequency decrease in rays coming from Taurus A, when they passed close to our Sun (i.e. near occultation). The experiment has effectively confirmed that density of matter of the mass source of locally dominant gravitational field (which was our Sun's field) affects gravitational interactions happening on equipotential surfaces surrounding gravity center of the field. Also very similar experiment involving radio waves, which too exhibited (formerly unexpected) frequency decrease when they traveled along practically equipotential surface of Earth, has reaffirmed that conclusion. Hence contrary to Galilei, effects of nonradial (i.e. tangential and/or binormal) components of radial gravitational force fields depend (inversely) on (equipotential exposure to) the, assumed as practically constant and uniformly distributed, density of matter of the mass source of the local field.

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Complex States of Simple Molecular Systems

Englman¹,

Yahalom²

2002

Advances in Chemical Physics

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A review is given of phase properties in molecular wave functions, composed of a number of (and, at least, two) electronic states that become degenerate at some nearby values of the nuclear configuration. Apart from discussing phases and interference in classical (non-quantal) systems, including light-waves, the review looks at the constructability of complex wave functions from observable quantities ("the phase problem"), at the controversy regarding quantum mechanical phase-operators, at the modes of observability of phase and at the role of phases in some non-demolition measurements. Advances in experimental and (especially) theoretical aspects of Aharonov-Bohm and topological (Berry) phases are described, including those involving two-electron and relativistic systems. Several works in the phase control and revivals of molecular wave-packets are cited as developments and applications of complex-function theory. Further topics that this review touches on are: coherent states, semiclassical approximations and the Maslov index. The interrelation between time and the complex state is noted in the contexts of time delays in scattering, of time-reversal invariance and of the existence of a molecular time-arrow.When the stationary Born-Oppenheimer description for nearly degenerate state is regarded as "embedded" in a broader dynamic formulation, namely through solution of the time dependent Schrödinger equation, the wave function becomes necessarily complex. The analytic behavior of this function in the complex time-plane can be exploited to gain information about the connection between phases and moduli of the componentamplitudes. One form of this connection are a pair of reciprocal (Kramers-Kronig type) relations in the complex time-domain. These show that certain phase changes in a component amplitude (such as, e.g., lead to a non-zero Berry-phase) require changes in the amplitude-moduli, too, and imply degeneracies of the electronic state.The subject of conical degeneracy, or intersection, of adjacent potential surface is extended to nonlinear nuclear-electronic coupling, which can then result in multiple conical degeneracies on a nuclear coordinate plane. We treat cases of double and fourfold intersections, the latter under trigonal symmetry, and employ an analytic-graphical phase tracing method to obtain the resulting Berry phases as the system circles around some or all of the degeneracy points. These phases can take up values that are all integral multiples of π, with integers that vary with the physical situation (or with the model postulated for it).A further type of invariance, with respect to gauge transformation, is also tied to the complex form of the wave function. For a many-component state this leads to a consideration of tensorial (Yang-Mills type) fields F for molecular systems. It is shown that it is the truncation of the Born-Oppenheimer electron-nuclear superposition that generates the molecular Yang-Mills fields.The equations of motion for the nuclear degrees of freedom are derived from a Lagr...

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The Aharonov-Bohm effect Part one: Theory

Cited by 141 publications

References 25 publications

Nonlocal phases of local quantum mechanical wavefunctions in static and time-dependent Aharonov–Bohm experiments

Nonlocal phases of local quantum mechanical wavefunctions in static and time-dependent Aharonov–Bohm experiments

Galilei was Wrong: Angular Nonradial Effects of Radial Gravity Depend on Density of Matter

Complex States of Simple Molecular Systems

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