BRAID GROUPS, ANYONS AND GAUGE INVARIANCE

1991 ◽  
Vol 05 (10) ◽  
pp. 1649-1664 ◽  
Author(s):  
Yong-Shi Wu
Keyword(s):  
Mechanical Properties ◽  
Braid Group ◽  
Group Analysis ◽  
Braid Groups ◽  
Quantum Mechanical ◽  
The Novel ◽  
And Topology ◽  
Bohm Effect ◽  
Aharonov Bohm ◽  
Nontrivial Topology

The structure of braid groups on topologically nontrivial surfaces is reviewed. The physical meaning of the braid relations and their implications on quantum mechanical properties of anyonic quasiparticles are discussed. These include not only the exotic statistics of anyons but also the Aharonov-Bohm effect for the anyons on a surface with holes. Several results on the novel properties of anyons or their states, which were previously derived by microscopic considerations, are reproduced by this seemingly kinematic and topology-dependent braid group analysis. It is suggested that in the thermodynamic limit, the global excitations in a system on a surface of nontrivial topology do not interfere with properties of local anyonic quasiparticles.

Observation of a gravitational Aharonov-Bohm effect

Science ◽  
2022 ◽  
Vol 375 (6577) ◽  
pp. 226-229 ◽  
Author(s):  
Chris Overstreet ◽  
Peter Asenbaum ◽  
Joseph Curti ◽  
Minjeong Kim ◽  
Mark A. Kasevich
Keyword(s):  
Wave Packets ◽  
Gravitational Interaction ◽  
Large Mass ◽  
Mechanical Effect ◽  
Quantum Mechanical ◽  
Electron Wave ◽  
Rubidium Atoms ◽  
Quantum Mechanical Effect ◽  
Bohm Effect ◽  
Aharonov Bohm

Gravitational interference The Aharonov-Bohm effect is a quantum mechanical effect in which a magnetic field affects the phase of an electron wave as it propagates along a wire. Atom interferometry exploits the wave characteristic of atoms to measure tiny differences in phase as they take different paths through the arms of an interferometer. Overstreet et al . split a cloud of cold rubidium atoms into two atomic wave packets about 25 centimeters apart and subjected one of the wave packets to gravitational interaction with a large mass (see the Perspective by Roura). The authors state that the observed phase shift is consistent with a gravitational Aharonov-Bohm effect. —ISO

NOVEL INTERFERENCE EFFECTS IN MULTIPLY CONNECTED NORMAL METAL RINGS

1994 ◽  
Vol 08 (05) ◽  
pp. 301-310 ◽  
Author(s):  
A.M. JAYANNAVAR ◽  
P. SINGHA DEO
Keyword(s):  
Quantum Interference ◽  
Normal Metal ◽  
Quantum Mechanical ◽  
Small Field ◽  
Interference Effects ◽  
Multiply Connected ◽  
Small Magnetic Field ◽  
Metal Rings ◽  
Bohm Effect ◽  
Aharonov Bohm

We have investigated the magnetoconductance of a normal metal loop connected to ideal wires in the presence of magnetic flux. The quantum mechanical potential, V, in the loop is much higher than that in the connecting wires (V=0). The electrons with energies less than the potential height on entering the loop propagate as evanescent modes. In such a situation, the contribution to the conductance arises from two non-classical effects, namely, Aharonov-Bohm effect and quantum tunneling. For this case we show that, on application of a small magnetic field, the conductance initially always decreases, or small field magnetoconductance is always negative. This is in contrast to the behavior in the absence of the barrier, wherein the small field magnetoconductance is either positive or negative depending on the Fermi energy and other geometric details. We also discuss the possibility of a better switch action based on quantum interference effects in such structures.

scholarly journals Aharonov–Bohm effect revisited

2015 ◽  
Vol 27 (02) ◽  
pp. 1530001 ◽  
Author(s):  
Gregory Eskin
Keyword(s):  
Quantum Mechanical ◽  
Scattering Problems ◽  
Seminal Paper ◽  
Inverse Boundary ◽  
Yang Mills ◽  
Different Types ◽  
Gravitational Analog ◽  
Bohm Effect ◽  
Inverse Boundary Value Problems ◽  
Aharonov Bohm

Aharonov–Bohm effect is a quantum mechanical phenomenon that attracted the attention of many physicists and mathematicians since the publication of the seminal paper of Aharonov and Bohm [1] in 1959.We consider different types of Aharonov–Bohm effects such as the magnetic AB effect, electric AB effect, combined electromagnetic AB effect, AB effect for the Schrödinger equations with Yang–Mills potentials, and the gravitational analog of AB effect.We shall describe different approaches to prove the AB effect based on the inverse scattering problems, the inverse boundary value problems in the presence of obstacles, spectral asymptotics, and the direct proofs of the AB effect.

On braids and groups Gnk

2015 ◽  
Vol 24 (13) ◽  
pp. 1541009 ◽  
Author(s):  
Vassily Olegovich Manturov ◽  
Igor Mikhailovich Nikonov
Keyword(s):  
Dynamical Systems ◽  
Braid Group ◽  
Knot Theory ◽  
Free Groups ◽  
Braid Groups ◽  
The Other ◽  
Pure Braid Group ◽  
And Topology ◽  
Other Hand ◽  
Definition Of

In [Non-reidemeister knot theory and its applications in dynamical systems, geometry, and topology, preprint (2015), arXiv:1501.05208.] the first author gave the definition of [Formula: see text]-free braid groups [Formula: see text]. Here we establish connections between free braid groups, classical braid groups and free groups: we describe explicitly the homomorphism from (pure) braid group to [Formula: see text]-free braid groups for important cases [Formula: see text]. On the other hand, we construct a homomorphism from (a subgroup of) free braid groups to free groups. The relations established would allow one to construct new invariants of braids and to define new powerful and easily calculated complexities for classical braid groups.

Phenomena and devices at the quantum scale and the mesoscale

2017 ◽  
Author(s):  
Sandip Tiwari
Keyword(s):  
Coulomb Blockade ◽  
Secure Communication ◽  
Quantum Hall ◽  
Nanoscale Device ◽  
Self Energy ◽  
Stability Diagrams ◽  
Charge Stability ◽  
Bohm Effect ◽  
Aharonov Bohm ◽  
Non Locality

Unique nanoscale phenomena arise in quantum and mesoscale properties and there are additional intriguing twists from effects that are classical in origin. In this chapter, these are brought forth through an exploration of quantum computation with the important notions of superposition, entanglement, non-locality, cryptography and secure communication. The quantum mesoscale and implications of nonlocality of potential are discussed through Aharonov-Bohm effect, the quantum Hall effect in its various forms including spin, and these are unified through a topological discussion. Single electron effect as a classical phenomenon with Coulomb blockade including in multiple dot systems where charge stability diagrams may be drawn as phase diagram is discussed, and is also extended to explore the even-odd and Kondo consequences for quantum-dot transport. This brings up the self-energy discussion important to nanoscale device understanding.

scholarly journals Two-flux tunable Aharonov-Bohm effect in a photonic lattice

2021 ◽  
Vol 104 (2) ◽  
Author(s):  
V. Brosco ◽  
L. Pilozzi ◽  
C. Conti
Keyword(s):  
Bohm Effect ◽  
Aharonov Bohm

scholarly journals A Review on Tailoring Stiffness in Compliant Systems, via Removing Material: Cellular Materials and Topology Optimization

2021 ◽  
Vol 11 (8) ◽  
pp. 3538
Author(s):  
Mauricio Arredondo-Soto ◽  
Enrique Cuan-Urquizo ◽  
Alfonso Gómez-Espinosa
Keyword(s):  
Mechanical Properties ◽  
Topology Optimization ◽  
Evolutionary Process ◽  
Cellular Materials ◽  
Related Literature ◽  
And Topology ◽  
Fundamental Process ◽  
Compliant Systems ◽  
Basic Concepts

Cellular Materials and Topology Optimization use a structured distribution of material to achieve specific mechanical properties. The controlled distribution of material often leads to several advantages including the customization of the resulting mechanical properties; this can be achieved following these two approaches. In this work, a review of these two as approaches used with compliance purposes applied at flexure level is presented. The related literature is assessed with the aim of clarifying how they can be used in tailoring stiffness of flexure elements. Basic concepts needed to understand the fundamental process of each approach are presented. Further, tailoring stiffness is described as an evolutionary process used in compliance applications. Additionally, works that used these approaches to tailor stiffness of flexure elements are described and categorized. Finally, concluding remarks and recommendations to further extend the study of these two approaches in tailoring the stiffness of flexure elements are discussed.

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