• Corpus ID: 119420717

Classical and Quantum Mechanics of Anyons

@article{Date2003ClassicalAQ,
  title={Classical and Quantum Mechanics of Anyons},
  author={Ghanashyam Date and M. V. N. Murthy and Radhika Vathsan},
  journal={arXiv: Condensed Matter},
  year={2003}
}
We review aspects of classical and quantum mechanics of many anyons confined in an oscillator potential. The quantum mechanics of many anyons is complicated due to the occurrence of multivalued wavefunctions. Nevertheless there exists, for arbitrary number of anyons, a subset of exact solutions which may be interpreted as the breathing modes or equivalently collective modes of the full system. Choosing the three-anyon system as an example, we also discuss the anatomy of the so called “missing… 
Exchange and exclusion in the non-abelian anyon gas
We review and develop the many-body spectral theory of ideal anyons, i.e. identical quantum particles in the plane whose exchange rules are governed by unitary representations of the braid group on
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We study the spectrum of multiple non-Abelian anyons in a harmonic trap. The system is described by Chern-Simons theory, coupled to either bosonic or fermionic non-relativistic matter, and has an
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A simple quantum generalisation of the Liouville-Arnold criterion of classical integrability is proposed: A system is quantum-integrable if it has an abelian Lie group of Wigner symmetries of
Fermionic behavior of ideal anyons
TLDR
Upper and lower bounds on the ground-state energy of the ideal two-dimensional anyon gas are proved and the lower bounds extend to Lieb–Thirring inequalities for all anyons except bosons.
Many-anyon trial states
The problem of bounding the (Abelian) many-anyon ground-state energy from above, with a dependence on the statistics parameter which matches that of currently available lower bounds, is reduced to ...
Slobodna ekspanzija anyona
Anyoni su cestice cija se svojstva kontinuirano interpoliraju između bozona i fermiona, a cije je postojanje teorijski dozvoljeno u dvodimenzional

References

SHOWING 1-9 OF 9 REFERENCES
Fractional statistics and anyon superconductivity
The occurrence of fractional statistics has been discovered in more and more quantum field theory models, including some of the most geometrical and canonical ones. In a remarkable case, the
Chaos in classical and quantum mechanics
Contents: Introduction.- The Mechanics of Lagrange.- The Mechanics of Hamilton and Jacobi.- Integrable Systems.- The Three-Body Problem: Moon-Earth-Sun.- Three Methods of Section.- Periodic Orbits.-
Anyons: Quantum Mechanics of Particles with Fractional Statistics
to Fractional Statistics in Two Dimensions.- Fractional Statistics in the Chern-Simons Gauge.- Fractional Statistics in the Anyon Gauge.- Non-relativistic Chern-Simons Field Theory.- Anyons in a
Congruences and canonical forms for a positive matrix: Application to the Schweinler–Wigner extremum principle
It is shown that a N×N real symmetric [complex Hermitian] positive definite matrix V is congruent to a diagonal matrix modulo a pseudo-orthogonal [pseudo-unitary] matrix in SO(m,n)[SU(m,n)], for any
Fractional statistics and quantum theory
Fractional statistics in two dimensions quantum mechanics of anyons statistical mechanics of anyon gas fractional exclusion statistics introduction to Chern-Simons term anyon as soliton in field
Foundations of mechanics
Introduction Foreward by Tudor Ratiu and Richard Cushman Preliminaries Differential Theory Calculus on Manifolds Analytical Dynamics Hamiltonian and Lagrangian Systems Hamiltonian Systems with
Mathematical Methods of Classical Mechanics
Part 1 Newtonian mechanics: experimental facts investigation of the equations of motion. Part 2 Lagrangian mechanics: variational principles Lagrangian mechanics on manifolds oscillations rigid