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

Moulopoulos, Konstantinos

doi:10.1088/1751-8113/43/35/354019

Cited by 14 publications

(46 citation statements)

References 24 publications

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“…It has been point out that, because of the electromagnetic gauge invariance and Lorentz invariance, the magnetic and electric contributions cancel each other in the time-dependent case, therefore, there is no net AB phase shift [52,53,54,55,56]. Because of this, a tiny deviation from zero indicates new physics.…”

Section: Discussionmentioning

confidence: 99%

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Time-dependent Aharonov–Bohm effect on the noncommutative space

Wang

Yang

2016

Physics Letters B

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We study the time-dependent Aharonov-Bohm effect on the noncommutative space. Because there is no net Aharonov-Bohm phase shift in the time-dependent case on the commutative space, therefore, a tiny deviation from zero indicates new physics. Based on the Seiberg-Witten map we obtain the gauge invariant and Lorentz covariant Aharonov-Bohm phase shift in general case on noncommutative space. We find there are two kinds of contribution: momentum-dependent and momentum-independent corrections. For the momentum-dependent correction, there is a cancellation between the magnetic and electric phase shifts, just like the case on the commutative space. However, there is a non-trivial contribution in the momentumindependent correction. This is true for both the time-independent and time-dependent Aharonov-Bohm effects on the noncommutative space. However, for the time-dependent Aharonov-Bohm effect, there is no overwhelming background which exists in the time-independent Aharonov-Bohm effect on both commutative and noncommutative space. Therefore, the time-dependent Aharonov-Bohm can be sensitive to the spatial noncommutativity. The net correction is proportional to the product of the magnetic fluxes through the fundamental area represented by the noncommutative parameter θ, and through the surface enclosed by the trajectory of charged particle. More interestingly, there is an anti-collinear relation between the logarithms of the magnetic field B and the averaged flux Φ/N (N is the number of fringes shifted). This nontrivial relation can also provide a way to test the spatial noncommutativity. For BΦ/N ∼ 1, our estimation on the experimental sensitivity shows that it can reach the 10GeV scale. This sensitivity can be enhanced by using stronger magnetic field strength, larger magnetic flux, as well as higher experimental precision on the phase shift.

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Section: Discussionmentioning

confidence: 99%

“…In this paper, we study the noncommutative corrections on the time-dependent AB effect [52,53,54,55,56]. It was shown that because of the gauge and Lorentz symmetries, the time-dependent AB phase shift vanishes on the commutative space.…”

Section: Introductionmentioning

confidence: 99%

Time-dependent Aharonov–Bohm effect on the noncommutative space

Wang

Yang

2016

Physics Letters B

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“…and in all cases one can obtain the general form of the wavefunctions (with similar procedures of simultaneous diagonalizations with H as earlier). In all cases, it seems that the extra phases that show up at the end results have the general form of the non-local terms of refs [5,6] involving also time-integrals of scalar potentials, surface integrals of the magnetic field, and mixed temporal and spatial integrals of the electric field (this essentially being a generalization of the electric Aharonov-Bohm effect). All this needs, however, a more detailed and self-contained presentation which we leave for the future.…”

Section: Inclusion Of a Homogeneous Electric Fieldmentioning

confidence: 92%

“…Hence, the formal solution (meaning: before any imposition of boundary conditions) of the TDSE for the set of potentials ( 2 A , V 2 ) is the above Ψ 2. This formal connection between two systems (in which the same particle of charge -e moves in the above two different sets of potentials) may be seen as a mapping between the two problems, and this has been exploited recently [5,6] for advancing new solutions of t-dependent Aharonov-Bohm configurations, both of the magnetic and the electric type, an area that after [5,6] seems to be growing rapidly [7]. In a similar manner, if we look at the t-independent Schrodinger equation (TISE), we can see that a similar formal mapping is also valid for the stationary state solutions, i.e.…”

Section: Introductionmentioning

confidence: 99%

The “Forgotten” Pseudomomenta and Gauge Changes in Generalized Landau Level Problems: Spatially Nonuniform Magnetic and Temporally Varying Electric Fields

Konstantinou¹,

Moulopoulos²

2017

Int J Theor Phys

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By perceiving gauge invariance as an analytical tool in order to get insight into the states of the "generalized Landau problem" (a charged quantum particle moving inside a magnetic, and possibly electric field), and motivated by an early article that correctly warns against a naive use of gauge transformation procedures in the usual Landau problem (i.e. with the magnetic field being static and uniform), we first show how to bypass the complications pointed out in that article by solving the problem in full generality through gauge transformation techniques in a more appropriate manner. Our solution provides in simple and closed analytical forms all Landau Level-wavefunctions without the need to specify a particular vector potential. This we do by proper handling of the so-called pseudomomentum K (or of a quantity that we term pseudoangular momentum L z ), a method that is crucially different from the old warning argument, but also from standard treatments in textbooks and in research literature (where the usual Landauwavefunctions are employed -labeled with canonical momenta quantum numbers). Most importantly, we go further by showing that a similar procedure can be followed in the more difficult case of spatially-nonuniform magnetic fields: in such case we define K and L z as plausible generalizations of the previous ordinary case, namely as appropriate line integrals of the inhomogeneous magnetic fieldour method providing closed analytical expressions for all stationary state wavefunctions in an easy manner and in a broad set of geometries and gauges. It can thus be viewed as complementary to the few existing works on inhomogeneous magnetic fields, that have so far mostly focused on determining the energy eigenvalues rather than the corresponding eigenkets (on which they have claimed that, even in the simplest cases, it is not possible to obtain in closed form the associated wavefunctions). The analytical forms derived here for these wavefunctions enable us to also provide explicit Berry's phase calculations and a quick study of their connection to probability currents and to some recent interesting issues in elementary Quantum Mechanics and Condensed Matter Physics. As an added feature, we also show how the possible presence of an additional electric field can be treated through a further generalization of pseudomomenta and their proper handling.

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“…In this case, the magnetic field and the electric field can be written as B(t) = ∇× A(t) and E(t) = −∂ t A(t), respectively. It has been shown that there is an exact cancellation between the magnetic and electric AB phase shifts, and therefore there is no net phase shift [31,32,33,34,35]. However, because the noncommutative corrections directly involve the local interactions between the charged particle and the electromagnetic field strength, therefore the cancellation may not happen exactly.…”

Section: Noncommutative Corrections On the Time-dependent Ab Effectmentioning

confidence: 99%

Probing the noncommutative effects of phase space in the time-dependent Aharonov–Bohm effect

Ma¹,

Wang²,

Yang³

2017

Annals of Physics

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We study the noncommutative corrections on the time-dependent Aharonov-Bohm effect when both the coordinate-coordinate and momentum-momentum noncommutativities are considered. This study is motivated by the recent observation that there is no net phase shift in the time-dependent AB effect on the ordinary space, and therefore tiny derivation from zero can indicate new physics. The vanishing of the timedependent AB phase shift on the ordinary space is preserved by the gauge and Lorentz symmetries. However, on the noncomutative phase space, while the ordinary gauge symmetry can be kept by the Seiberg-Witten map, but the Lorentz symmetry is broken. Therefore nontrivial noncommutative corrections are expected.We find there are three kinds of noncommutative corrections in general: 1) ξ-dependent correction which comes from the noncommutativity among momentum operators; 2) momentum-dependent correction which is rooted in the nonlocal interactions in the noncommutative extended model; 3) momentum-independent correction which emerges become of the gauge invariant condition on the nonlocal interactions in the noncommutative model. We proposed two dimensionless quantities, which are based on the distributions of the measured phase shift with respect to the external magnetic field and to the cross section enclosed by the particle trajectory, to extract the noncommutative parameters. We find that stronger (weaker) magnetic field strength can give better bounds on the coordinate-coordinate (momentum-momentum) noncommutative parameter, and large parameter space region can be explored by the time-dependent AB effect.

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

Cited by 14 publications

References 24 publications

Time-dependent Aharonov–Bohm effect on the noncommutative space

Time-dependent Aharonov–Bohm effect on the noncommutative space

The “Forgotten” Pseudomomenta and Gauge Changes in Generalized Landau Level Problems: Spatially Nonuniform Magnetic and Temporally Varying Electric Fields

Probing the noncommutative effects of phase space in the time-dependent Aharonov–Bohm effect

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