Wave dislocation lines threading interferometers

2007 ◽  
Vol 463 (2083) ◽  
pp. 1697-1711 ◽  
Author(s):  
M.V Berry
Keyword(s):  
Wave Function ◽  
Large Class ◽  
Phase Difference ◽  
Flux Line ◽  
Phase Shifts ◽  
Closed Circuit ◽  
Threading Dislocations ◽  
Aharonov Bohm ◽  
The Waves

In interferometers where a wave is divided into two beams that propagate along separate branches before being recombined, the closed circuit formed by the two branches must be threaded by wave dislocation lines. For a large class of interferometers, it is shown that the (signed) dislocation number, defined in a suitable asymptotic sense, jumps by +1 as the phase difference between the beams increases by 2 π . The argument is based on the single-valuedness of the wave function in the branches and leaking between them. In some cases, the jumps occur when the phase difference is an odd multiple of π . The same result holds for the Aharonov–Bohm wave function, where the waves passing above and below a flux line experience different phase shifts; in this case, where the wave is not concentrated onto branches, the threading dislocations coincide with the flux line.

scholarly journals Calculation of the Aharonov-Bohm wave function

1996 ◽  
Vol 54 (2) ◽  
pp. 1128-1135 ◽  
Author(s):  
M. Alvarez
Keyword(s):  
Wave Function ◽  
Aharonov Bohm

Nucleon-antinucleon interaction in the new Tamm-Dancoff approximation

1960 ◽  
Vol 257 (1288) ◽  
pp. 59-73
Keyword(s):  
Integral Equation ◽  
Wave Function ◽  
Cross Sections ◽  
Nucleon Nucleon ◽  
Phase Shifts ◽  
Exchange Term ◽  
Total Cross Sections ◽  
Nucleon Wave Function ◽  
Usual Manner ◽  
Order Of Magnitude

The nucleon-antinucleon ( N-N ) problem is formulated in the new Tamm-Dancoff (NTD) approximation in the lowest order, and the integral equation for N-N̅ scattering derived, taking account of both the exchange and annihilation interactions. It is found convenient to represent the N-N̅ wave-function as a 4 x 4 matrix, rather than the usual 16 x 1 matrix for the nucleon-nucleon wave-function, and a complete correspondence is established between these two representations. The divergences associated with the annihilation interaction and their renormalization are discussed in detail in the following paper (Mitra & Saxena 1960; referred to as II). The integral equation with the exchange interaction alone, is then separated into eigenstates of T, J, L and S in the usual manner and the various phase shifts obtained. The results of II for the contribution of the annihilation term are then used to calculate the complete phase shifts from which the various cross-sections (scattering and charge exchange) are derived. The results indicate that while the exchange term alone gives too small values for the total cross-sections versus energy, inclusion of the annihilation interaction without renormalization effects makes the cross-sections nearly three times larger than those observed. On the other hand, inclusion of the finite effects of renormalization (which manifest themselves essentially as a suppression of the virtual meson propagator) brings down these cross-sections to the order of magnitude of the observed ones.

scholarly journals The Quaternionic Commutator Bracket and Its Implications

Symmetry ◽  
2018 ◽  
Vol 10 (10) ◽  
pp. 513 ◽  
Author(s):  
Arbab Arbab ◽  
Mudhahir Al Ajmi
Keyword(s):  
Wave Function ◽  
Electromagnetic Field ◽  
Angular Momentum ◽  
Charged Particle ◽  
Magnetic Fields ◽  
Interaction Energy ◽  
Internal Structure ◽  
Magnetic Moments ◽  
Electric And Magnetic Fields ◽  
Aharonov Bohm

A quaternionic commutator bracket for position and momentum shows that the quaternionic wave function, viz. ψ ˜ = ( i c ψ 0 , ψ → ) , represents a state of a particle with orbital angular momentum, L = 3 ℏ , resulting from the internal structure of the particle. This angular momentum can be attributed to spin of the particle. The vector ψ → , points in an opposite direction of L → . When a charged particle is placed in an electromagnetic field, the interaction energy reveals that the magnetic moments interact with the electric and magnetic fields giving rise to terms similar to Aharonov–Bohm and Aharonov–Casher effects.

scholarly journals Wave Function Collapse in Atomic Physics

1993 ◽  
Vol 46 (1) ◽  
pp. 77 ◽  
Author(s):  
DT Pegg
Keyword(s):  
Wave Function ◽  
Quantum Mechanics ◽  
Quantum Optics ◽  
Phase Difference ◽  
Atomic Physics ◽  
Single Photon ◽  
Single Atom ◽  
Considerable Time ◽  
Wave Function Collapse ◽  
Statistical Results

Wave function collapse has been a contentious concept in quantum mechanics for a considerable time. Here we show examples of how the concept can be used to advantage in predicting the statistical results of three experiments in atomic physics and quantum optics: photon antibunching, single-photon phase difference states and interrupted single-atom fluorescence. We examine the question of whether or not collapse is 'really' a physical process, and discuss the consequences of simply omitting it but including the observer as a part of the overall system governed by the laws of quantum mechanics. The resulting entangled world does not appear to be inconsistent with experience.

scholarly journals Nucleon-Nucleon Potentials and Computation of Scattering Phase Shifts

2015 ◽  
Vol 5 (02) ◽  
pp. 73
Author(s):  
Jhasaketan Bhoi ◽  
Ujjwal Laha
Keyword(s):  
Wave Function ◽  
Quantum Mechanics ◽  
Ground State ◽  
Function Method ◽  
Nucleon Nucleon ◽  
Phase Shifts ◽  
Starting Point ◽  
Phase Function Method ◽  
Scattering Phase ◽  
Scattering Phase Shifts

<p>By judicious exploitation of supersymmetry formalism of quantum mechanics higher partial wave nucleon-nucleon potentials are generated from its ground state interactions. The nuclear Hulthen potential and the corresponding ground state wave function with the parameters of Arnold and MacKellar are used as the starting point of our calculation. We compute the scattering phase shifts for our constructed potentials through Phase Function Method to examine the merit of our approach to the problem.</p>

scholarly journals Ultrafast electron diffraction of THz-excited nanostructures

2019 ◽  
Vol 205 ◽  
pp. 08004
Author(s):  
Kathrin J. Mohler ◽  
Peter Baum
Keyword(s):  
Electron Diffraction ◽  
Phase Shifts ◽  
Time Dependent ◽  
Electromagnetic Response ◽  
Ultrafast Electron Diffraction ◽  
Single Cycle ◽  
Electromagnetic Potentials ◽  
Aharonov Bohm

We study the electromagnetic response of nanostructures to single-cycle THz excitation by using ultrafast electron diffraction. Although the nanostructures themselves are static, there exist complex sub-THz-cycle Bragg spot dynamics that relate via time-dependent Aharonov-Bohm-like phase shifts to the nanoscale electromagnetic potentials.

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