Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
1993-03-04
Phys.Lett.B306:100-107,1993
Physics
High Energy Physics
High Energy Physics - Theory
13 pages (+1 figure, available upon request), CERN-TH 6810/93
Scientific paper
10.1016/0370-2693(93)91144-C
The Laughlin states for $N$ interacting electrons at the plateaus of the fractional Hall effect are studied in the thermodynamic limit of large $N$. It is shown that this limit leads to the semiclassical regime for these states, thereby relating their stability to their semiclassical nature. The equivalent problem of two-dimensional plasmas is solved analytically, to leading order for $N\to\infty$, by the saddle point approximation - a two-dimensional extension of the method used in random matrix models of quantum gravity and gauge theories. To leading order, the Laughlin states describe classical droplets of fluids with uniform density and sharp boundaries, as expected from the Laughlin ``plasma analogy''. In this limit, the dynamical $W_\infty$-symmetry of the quantum Hall states expresses the kinematics of the area-preserving deformations of incompressible liquid droplets.
Cappelli Andrea
Trugenberger Carlo A.
Zemba Guillermo R.
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