Nuclear physics. B, ISSN 0550-3213, 06/2012, Volume 859, Issue 2, pp. 261 - 268

Topological superconductors classified as type D admit zero-energy Majorana fermions inside vortex cores, and consequently the exchange statistics of vortices becomes non-Abelian, giving a promising...

Non-Abelian statistics | Topological superconductors and insulators | Quantum vortices | Physical Sciences | Physics, Particles & Fields | Physics | Science & Technology

Non-Abelian statistics | Topological superconductors and insulators | Quantum vortices | Physical Sciences | Physics, Particles & Fields | Physics | Science & Technology

Journal Article

J Phys Soc Jpn, ISSN 0031-9015, 4/2011, Volume 80, Issue 4, pp. 044603 - 044603-12

.... The associated low-energy excitations are calculated in connection with the possible existence of Majorana zero modes obeying non-Abelian statistics...

Bogoliubov-de gennes equation | Non-abelian statistics | Vortex | Zero energy state | Ginzburg-landau theory | Chiral p-wave superfluids | Physics, Multidisciplinary | Physical Sciences | Physics | Science & Technology | Physics - Superconductivity

Bogoliubov-de gennes equation | Non-abelian statistics | Vortex | Zero energy state | Ginzburg-landau theory | Chiral p-wave superfluids | Physics, Multidisciplinary | Physical Sciences | Physics | Science & Technology | Physics - Superconductivity

Journal Article

Nuclear physics. B, ISSN 0550-3213, 1999, Volume 556, Issue 3, pp. 530 - 544

We introduce the notion of ‘order-
k non-abelian exclusion statistics’. We derive the associated thermodynamic equations by employing the thermodynamic Bethe ansatz for specific non-diagonal scattering matrices...

Conformal field theory | Quantum Hall effect | Non-abelian statistics | international | Physical Sciences | Physics, Particles & Fields | Physics | Science & Technology

Conformal field theory | Quantum Hall effect | Non-abelian statistics | international | Physical Sciences | Physics, Particles & Fields | Physics | Science & Technology

Journal Article

Proceedings of the National Academy of Sciences - PNAS, ISSN 1091-6490, 11/2016, Volume 113, Issue 44, pp. 12386 - 12390

Some theories predict that the filling factor 5/2 fractional quantum Hall state can exhibit non-Abelian statistics, which makes it a candidate for fault-tolerant topological quantum computation...

Fractional quantum Hall effect | Edge-current tunneling | Quantum point contact | 5/2 fractional quantum Hall state | Non-Abelian statistics | Physical Sciences | edge-current tunneling | non-Abelian statistics | 2 fractional quantum Hall state | quantum point contact | fractional quantum Hall effect

Fractional quantum Hall effect | Edge-current tunneling | Quantum point contact | 5/2 fractional quantum Hall state | Non-Abelian statistics | Physical Sciences | edge-current tunneling | non-Abelian statistics | 2 fractional quantum Hall state | quantum point contact | fractional quantum Hall effect

Journal Article

Proceedings of the National Academy of Sciences - PNAS, ISSN 1091-6490, 05/2009, Volume 106, Issue 22, pp. 8853 - 8858

A standing problem in low-dimensional electron systems is the nature of the 5/2 fractional quantum Hall (FQH) state: Its elementary excitations are a focus for...

Quasiparticles | Electric potential | Magnetic flux | Temperature dependence | Magnetic fields | Electric current | Fast Fourier transformations | Interferometers | Electrons | Low temperature | Fractional quantum Hall effect | 5/2 fractional quantum Hall effect | Topological quantum computation | Non-Abelian statistics | Science & Technology - Other Topics | Multidisciplinary Sciences | Science & Technology | Electron mobility | Quantum Hall effect | Research | Observations | Oscillation | Measurement | Topology | Quantum theory | topological quantum computation | Physical Sciences | 2 fractional quantum Hall effect | non-Abelian statistics | fractional quantum Hall effect

Quasiparticles | Electric potential | Magnetic flux | Temperature dependence | Magnetic fields | Electric current | Fast Fourier transformations | Interferometers | Electrons | Low temperature | Fractional quantum Hall effect | 5/2 fractional quantum Hall effect | Topological quantum computation | Non-Abelian statistics | Science & Technology - Other Topics | Multidisciplinary Sciences | Science & Technology | Electron mobility | Quantum Hall effect | Research | Observations | Oscillation | Measurement | Topology | Quantum theory | topological quantum computation | Physical Sciences | 2 fractional quantum Hall effect | non-Abelian statistics | fractional quantum Hall effect

Journal Article

Nuclear physics. B, ISSN 0550-3213, 11/1996, Volume 479, Issue 3, pp. 529 - 553

...) non-Abelian statistics group SO(2n). In the four-quasihole case, this is supported by an explicit calculation of the corresponding conformal blocks in the c = 1/2...

Paired states | Fractional quantum hall effect | Non-abelian statistics

Paired states | Fractional quantum hall effect | Non-abelian statistics

Journal Article

Science and technology of advanced materials, ISSN 1468-6996, 12/2014, Volume 15, Issue 6, pp. 064402 - 9

Non-Abelian statistics can be achieved by exchanging two vortices in topological superconductors with each grabbing a Majorana fermion (MF...

non-Abelian statistics | Majorana fermion | Bogoliubov-de Gennes equation | topological superconductor | quantum computation | Materials Science | Technology | Materials Science, Multidisciplinary | Science & Technology | Exchanging | Time dependence | Fermions | Vortices | Braiding | Topological superconductors | Electric potential | Mathematical analysis | Voltage | Fluid flow | Statistics | Gates

non-Abelian statistics | Majorana fermion | Bogoliubov-de Gennes equation | topological superconductor | quantum computation | Materials Science | Technology | Materials Science, Multidisciplinary | Science & Technology | Exchanging | Time dependence | Fermions | Vortices | Braiding | Topological superconductors | Electric potential | Mathematical analysis | Voltage | Fluid flow | Statistics | Gates

Journal Article

Physics letters. B, ISSN 0370-2693, 11/2003, Volume 575, Issue 1-2, pp. 126 - 130

...–Weyl zero mode on the string. Due to the zero mode, the axion strings obey non-Abelian statistics.

Fermionic zero mode | Axion | Majorana–Weyl fermion | Non-Abelian statistics | Majorana-Weyl fermion | Physical Sciences | Physics, Nuclear | Astronomy & Astrophysics | Physics, Particles & Fields | Physics | Science & Technology | Physics - High Energy Physics - Theory

Fermionic zero mode | Axion | Majorana–Weyl fermion | Non-Abelian statistics | Majorana-Weyl fermion | Physical Sciences | Physics, Nuclear | Astronomy & Astrophysics | Physics, Particles & Fields | Physics | Science & Technology | Physics - High Energy Physics - Theory

Journal Article

Journal of algebraic combinatorics, ISSN 0925-9899, 8/2016, Volume 44, Issue 1, pp. 59 - 79

In (Bull Belg Math Soc Simon Stevin 4:299–316, 1997), Shult introduced a class of parapolar spaces, the so-called near-polar spaces. We introduce here the...

Universal projective embedding | 51A50 | 51A45 | Mathematics | Extraspecial 2-group | Minimal polarized embedding | Convex and Discrete Geometry | Universal/ Polarized non-abelian representation | Combinatorial group theory | Order, Lattices, Ordered Algebraic Structures | Group Theory and Generalizations | 20F05 | Combinatorics | Computer Science, general | 05B25 | Near-polar space | Physical Sciences | Science & Technology

Universal projective embedding | 51A50 | 51A45 | Mathematics | Extraspecial 2-group | Minimal polarized embedding | Convex and Discrete Geometry | Universal/ Polarized non-abelian representation | Combinatorial group theory | Order, Lattices, Ordered Algebraic Structures | Group Theory and Generalizations | 20F05 | Combinatorics | Computer Science, general | 05B25 | Near-polar space | Physical Sciences | Science & Technology

Journal Article

Journal of the Physical Society of Japan, ISSN 0031-9015, 1996, Volume 65, Issue 6, pp. 1617 - 1621

We study fractional exclusion statistics for SU(2) symmetric quantum systems ofarbitrary spin S by generalizing the thermodynamic equations with squeezed strings proposed by Ha...

fractional exclusion statistics | non-abelian statistics | ZN parafermion | Physics, Multidisciplinary | Physical Sciences | Physics | Science & Technology

fractional exclusion statistics | non-abelian statistics | ZN parafermion | Physics, Multidisciplinary | Physical Sciences | Physics | Science & Technology

Journal Article

Nuclear physics. B, ISSN 0550-3213, 2008, Volume 789, Issue 3, pp. 552 - 590

We review the topological quantum computation scheme of Das Sarma et al. from the perspective of the conformal field theory for the two-dimensional critical...

Conformal field theory | Topological quantum computation | Non-Abelian statistics | Physical Sciences | Physics, Particles & Fields | Physics | Science & Technology

Conformal field theory | Topological quantum computation | Non-Abelian statistics | Physical Sciences | Physics, Particles & Fields | Physics | Science & Technology

Journal Article

Solid state communications, ISSN 0038-1098, 08/2017, Volume 262, Issue C, pp. 1 - 6

...: strong spin-orbit coupling, applied magnetic field, and confinement by one-dimensional structures which complicates demonstrating non-Abelian statistics through braiding...

D. Magnetic textures | D. Non-Abelian statistics | A. Two-dimensional electron gas | A. Superconductors | D. Majorana bound states | A. Magnetic tunnel junctions | Physics, Condensed Matter | Physical Sciences | Physics | Science & Technology | Atoms | Control systems | Spin coupling | Magnetization | Magnetic fields | Epitaxy | Physics - Mesoscale and Nanoscale Physics

D. Magnetic textures | D. Non-Abelian statistics | A. Two-dimensional electron gas | A. Superconductors | D. Majorana bound states | A. Magnetic tunnel junctions | Physics, Condensed Matter | Physical Sciences | Physics | Science & Technology | Atoms | Control systems | Spin coupling | Magnetization | Magnetic fields | Epitaxy | Physics - Mesoscale and Nanoscale Physics

Journal Article

Journal of statistical mechanics, ISSN 1742-5468, 05/2018, Volume 2018, Issue 5, p. 53101

Matrix product state techniques provide a very efficient way to numerically evaluate certain classes of quantum Hall wave functions that can be written as...

conformal field theory | fractional QHE | fractional statistics | tensor network simulations | Mechanics | Physical Sciences | Technology | Physics | Physics, Mathematical | Science & Technology | Physics - Strongly Correlated Electrons | quasi-particles | non-abelian statistics | quantum hall states | Annan fysik | tensor | conductance | many-body systems | Other Physics Topics | field | network simulations | renormalization | one-component plasma | fractional quantization | theory | excitations

conformal field theory | fractional QHE | fractional statistics | tensor network simulations | Mechanics | Physical Sciences | Technology | Physics | Physics, Mathematical | Science & Technology | Physics - Strongly Correlated Electrons | quasi-particles | non-abelian statistics | quantum hall states | Annan fysik | tensor | conductance | many-body systems | Other Physics Topics | field | network simulations | renormalization | one-component plasma | fractional quantization | theory | excitations

Journal Article

14.
Full Text
Rational Points and Arithmetic of Fundamental Groups

: Evidence for the Section Conjecture

2012, 2013, Lecture Notes in Mathematics, ISBN 9783642306730, Volume 2054, 256

The section conjecture in anabelian geometry, announced by Grothendieck in 1983, is concerned with a description of the set of rational points of a hyperbolic...

Rational points (Geometry) | Algebraic Geometry | Mathematics | Number Theory | Mathematics and Statistics | Fundamental groups (Mathematics)

Rational points (Geometry) | Algebraic Geometry | Mathematics | Number Theory | Mathematics and Statistics | Fundamental groups (Mathematics)

eBook

Stochastic processes and their applications, ISSN 0304-4149, 07/2017, Volume 127, Issue 7, pp. 2339 - 2345

A scenery f on a finite group G is a function from G to {0,1}. A random walk v(t) on G is said to be able to distinguish two sceneries if the distributions of...

Random walks | Sceneries | Finite non-abelian groups | Statistics & Probability | Physical Sciences | Mathematics | Science & Technology

Random walks | Sceneries | Finite non-abelian groups | Statistics & Probability | Physical Sciences | Mathematics | Science & Technology

Journal Article

Journal of algebraic combinatorics, ISSN 0925-9899, 2/2011, Volume 33, Issue 1, pp. 127 - 140

We prove that the near hexagon
$Q(5,2)\times\mathbb{L}_{3}$
has a non-abelian representation in the extra-special 2-group
$2^{1+12}_{+}$
and that the near...

Near hexagon | Non-abelian representation | Convex and Discrete Geometry | Extra-special 2-group | Mathematics | Group Theory and Generalizations | Order, Lattices, Ordered Algebraic Structures | Computer Science, general | Combinatorics | Physical Sciences | Science & Technology | Sciences education

Near hexagon | Non-abelian representation | Convex and Discrete Geometry | Extra-special 2-group | Mathematics | Group Theory and Generalizations | Order, Lattices, Ordered Algebraic Structures | Computer Science, general | Combinatorics | Physical Sciences | Science & Technology | Sciences education

Journal Article

Nuclear physics. B, ISSN 0550-3213, 2003, Volume 651, Issue 3, pp. 331 - 360

...–Read one, to describe another universality class relevant for this plateau. The ground state is still given by the Pfaffian and is completely polarized, however, the elementary quasiholes are charge 1/2 anyons with Abelian statistics
θ=
π...

Conformal field theory | Quantum Hall effect | Non-Abelian statistics | Quantum hall effect

Conformal field theory | Quantum Hall effect | Non-Abelian statistics | Quantum hall effect

Journal Article