Anyons in a magnetic field

Journal Article · Wed May 20 04:00:00 EDT 1992 · International Journal of Modern Physics B; (United States)

DOI:https://doi.org/10.1142/S0217979292000797· OSTI ID:7034401

Karlhede, A; Westerberg, E ^[1]

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1. Stockholm Univ. (Sweden). Dept. of Theoretical Physics

In this paper, the authors consider N anyons, with statistical parameter {nu}, in a homogeneous magnetic field and discuss exact and perturbative solutions. The authors show that the energy, E{nu}, obeys {minus}1/2N (N {minus} 1) {le} dE/d{nu} {le} 0 for any Bose or fermi state and that the extremal cases correspond to the states where the relative angular momenta of all pairs of particles are negative and non-negative, respectively. The anyonic continuations of these extremal states are given, their energy is linear in {nu}. The authors conjecture that the above bounds on dE/d{nu} hold for any {nu}. This implies that the energy of any many-anyon state decreases monotonically with the statistical parameter {nu} ({nu} taking any real value). For small enough {nu}, E = const. {minus} 1/2N (N {minus} 1){nu} and the wave function is known. Increasing {nu}, the wave function becomes singular at some Bose point. In the following intermediate region (which may be absent), E({nu}) decreases more slowly; the exact form of E({nu}) and the wave function are unknown. Increasing {nu} further, above some Bose point the energy becomes constant and the wave function is again known.

• OSTI ID: 7034401
• Journal Information: International Journal of Modern Physics B; (United States), Journal Name: International Journal of Modern Physics B; (United States) Vol. 6:10; ISSN 0217-9792; ISSN IJPBE
• Country of Publication: United States
• Language: English

Related Subjects

661100 -- Classical & Quantum Mechanics-- (1992-)
665411* -- Basic Superconductivity Studies-- (1992-)
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
75 CONDENSED MATTER PHYSICS
SUPERCONDUCTIVITY AND SUPERFLUIDITY
ANGULAR MOMENTUM
ANIONS
CHARGED PARTICLES
ENERGY
FUNCTIONS
IONS
MAGNETIC FIELDS
MECHANICS
PERTURBATION THEORY
SINGULARITY
SOLIDS
STATISTICAL MECHANICS
WAVE FUNCTIONS