Topics in Statistic Mechanics
Topics in Statistic Mechanics
Topics in Statistic Mechanics
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Adv. Sta. Phy. Homework 7 Anyons Li,Zimeng PB06203182<br />
Anyons<br />
Edited by Li, Zimeng<br />
Contents:<br />
1. Fractional <strong>Statistic</strong>s<br />
2. Kitaev model<br />
3. Wen model<br />
1. Fractional <strong>Statistic</strong>s<br />
Particles <strong>in</strong> 3D are either bosons and fermions. In 2D, however, particles can obey<br />
fractional statistics(anyons).<br />
We use of the wavefunction to identify the phase change and the statistics of<br />
identical particles.If the Hamiltonian doesn't conta<strong>in</strong> long range <strong>in</strong>teractions, but only<br />
two nearest neighbours, we have the two particle configuration doubly connected and a<br />
double <strong>in</strong>terchange must give back the orig<strong>in</strong>al wavefunction <strong>in</strong> 3D or higher<br />
dimensions, lead<strong>in</strong>g to even (bosons) or odd (fermions) wavefunction.<br />
This effect makes accumulates 0 (bosons) and (fermions) only, say<strong>in</strong>g ,<br />
is 0 for bosons and 1 for fermions.While <strong>in</strong> 2D, the configuration space is <strong>in</strong>f<strong>in</strong>tely<br />
connected and is arbitrary(anyons).Anyons are particles which satisfy fractional<br />
statistics.The case which is corresponds to Quasiparticles half way between bosons<br />
and fermions, namely semions.<br />
2. Kitaev model<br />
See Ref.3 and 4<br />
3. Wen model<br />
See Ref.3 and 4<br />
Reference<br />
1.Zee A. Quantum field theory <strong>in</strong> a nutshell (Pr<strong>in</strong>ceton, 2003)(T)(ISBN 0691010196)<br />
(534s)<br />
2.Karlhede, Kivelson, Sondhi. The quantum Hall effect (Jerusalem 2002 w<strong>in</strong>ter school)(T)<br />
(109s)
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