scholarly journals Inverse problems for Schrödinger equations with Yang–Mills potentials in domains with obstacles and the Aharonov–Bohm effect

2005 ◽  
Vol 12 ◽  
pp. 23-32 ◽  
Author(s):  
G Eskin
Keyword(s):  
Inverse Problems ◽  
Schrodinger Equations ◽  
Schrödinger Equations ◽  
Yang Mills ◽  
Bohm Effect ◽  
Aharonov Bohm

Moment map and gauge geometric aspects of the Schrödinger and Pauli equations

2016 ◽  
Vol 13 (04) ◽  
pp. 1630004 ◽  
Author(s):  
Mauro Spera
Keyword(s):  
Geometric Quantization ◽  
Moment Map ◽  
Schrodinger Equations ◽  
Schrödinger Equations ◽  
Pauli Equation ◽  
Information Theoretic ◽  
Pilot Wave ◽  
The Moment ◽  
Aharonov Bohm ◽  
The Relationship

In this paper we discuss various geometric aspects related to the Schrödinger and the Pauli equations. First we resume the Madelung–Bohm hydrodynamical approach to quantum mechanics and recall the Hamiltonian structure of the Schrödinger equation. The probability current provides an equivariant moment map for the group [Formula: see text] of volume-preserving diffeomorphisms of [Formula: see text] (rapidly approaching the identity at infinity) and leads to a current algebra of Rasetti–Regge type. The moment map picture is then extended, mutatis mutandis, to the Pauli equation and to generalized Schrödinger equations of the Pauli–Thomas type. A gauge theoretical reinterpretation of all equations is obtained via the introduction of suitable Maurer–Cartan gauge fields and it is then related to Weyl geometric and pilot wave ideas. A general framework accommodating Aharonov–Bohm and Aharonov–Casher effects is presented within the gauge approach. Furthermore, a kind of holomorphic geometric quantization can be performed and yields natural “coherent state” representations of [Formula: see text]. The relationship with the covariant phase space and density manifold approaches is then outlined. Comments on possible extensions to nonlinear Schrödinger equations, on Fisher-information theoretic aspects and on stochastic mechanics are finally made.

scholarly journals FERMIONIC ZERO MODES IN SELF-DUAL VORTEX BACKGROUND

2005 ◽  
Vol 20 (39) ◽  
pp. 3045-3053 ◽  
Author(s):  
YONGQIANG WANG ◽  
TIEYAN SI ◽  
YUXIAO LIU ◽  
YISHI DUAN
Keyword(s):  
Phase Shift ◽  
Zero Mode ◽  
Two Dimensions ◽  
Two Dimensional ◽  
Yang Mills ◽  
Zero Modes ◽  
Extra Space ◽  
Bohm Effect ◽  
Aharonov Bohm ◽  
Unified Description

We study fermionic zero modes in the background of self-dual vortex on a two-dimensional non-compact extra space in 5+1 dimensions. In the Abelian Higgs model, we present a unified description of the topological and non-topological self-dual vortex on the extra two dimensions. Based on it, we study the localization of bulk fermions on a brane with the inclusion of Yang–Mills and gravity backgrounds in six dimensions. Through two simple cases, it is shown that the vortex background contributes a phase shift to the fermionic zero mode, this phase is actually origin from the Aharonov–Bohm effect.

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.

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.

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