Two approaches to fractional statistics in the quantum Hall effect: idealizations and the curious case of the anyon

DOI10.1007/s10701-015-9899-0zbMath1327.81021OpenAlexW2062171876MaRDI QIDQ893788

Elay Shech

Publication date: 20 November 2015

Published in: Foundations of Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10701-015-9899-0

zbMATH Keywords

approximationreductionrepresentationquantum Hall effectexplanationAharonov-Bohm effectfractional statisticsanyonsemergence

Mathematics Subject Classification ID

General and philosophical questions in quantum theory (81P05) Many-body theory; quantum Hall effect (81V70) Physics (00A79)

Related Items

Emergence and mechanism in the fractional quantum Hall effect ⋮ The non-ideal theory of the Aharonov-Bohm effect ⋮ Non-locality in intrinsic topologically ordered systems ⋮ Emergence and topological order in classical and quantum systems ⋮ Similarity structure and diachronic emergence ⋮ Properties of size-dependent models having quasiperiodic boundary conditions ⋮ A new look at emergence. Or when \textit{after} is different ⋮ Idealizations, essential self-adjointness, and minimal model explanation in the Aharonov-Bohm effect ⋮ The infinite limit as an eliminable approximation for phase transitions ⋮ Philosophical issues concerning phase transitions and anyons: emergence, reduction, and explanatory fictions ⋮ Infinitesimal idealization, easy road nominalism, and fractional quantum statistics ⋮ The role of idealizations in the Aharonov-Bohm effect

Cites Work

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• Aharonov-Bohm effect and high-velocity estimates of solutions to the Schrödinger equation
• Supersymmetric structure of quantum Hall effects in graphene
• Impenetrability of Aharonov-Bohm solenoids: proof of norm resolvent convergence
• Holism and structuralism in \(U(1)\) gauge theory
• Critical phenomena and breaking drops: infinite idealizations in physics
• Which gauge matters?
• Less is different: emergence and reduction reconciled
• High-velocity estimates for the scattering operator and Aharonov-Bohm effect in three dimensions
• Taking thermodynamics too seriously
• Falling cats, parallel parking, and polarized light
• On geometric interpretation of the Aharonov-Bohm effect
• Mathematical justification of the Aharonov-Bohm Hamiltonian
• Electron holography.
• The quantum Hall effect
• On geometric interpretation of the Berry phase
• The quantum Hall effect. Poincaré seminar 2004. Papers of the workshop, Paris, France, November 13, 2004.
• Anyons and the quantum Hall effect -- a pedagogical review
• Theory of braids
• Quantization and superselection sectors III: Multiply connected spaces and indistinguishable particles
• Introduction to Topological Quantum Computation
• Non-Abelian anyons and topological quantum computation
• Significance of Electromagnetic Potentials in the Quantum Theory
• Remarks on the Possibility of Quantum Electrodynamics without Potentials
• The Aharonov–Bohm effect and Tonomura et al. experiments: Rigorous results
• Quantal phase factors accompanying adiabatic changes
• Anyons
• Understanding Electromagnetism
• Condition for Nonexistence of Aharonov-Bohm Effect
• Can elementary quantum mechanics explain the Aharonov–Bohm effect?
• Scattering and self-adjoint extensions of the Aharonov–Bohm Hamiltonian
• Further Discussion of the Role of Electromagnetic Potentials in the Quantum Theory
• Modeling and Control of Complex Physical Systems
• Configuration Spaces.
• Curie's Principle and spontaneous symmetry breaking
• The Braid Groups.
• The Connection Between Spin and Statistics
• The Refractive Index in Electron Optics and the Principles of Dynamics
• Interpreting Quantum Theories