Universal structure of the edge states of the fractional quantum Hall states

We present an effective theory for the bulk fractional quantum Hall states on the Jain sequences on closed surfaces and show that it has a universal form whose structure does not change from fraction to fraction. The structure of this effective theory follows from the condition of global consistency of the flux attachment transformation on closed surfaces. We derive the theory of the edge states on a disk that follows naturally from this globally consistent theory on a torus. We find that, for a fully polarized two-dimensional electron gas, the edge states for all the Jain filling fractions $\nu=p/(2np+1)$ have only one propagating edge field that carries both energy and charge, and two non-propagating edge fields of topological origin that are responsible for the statistics of the excitations. Explicit results are derived for the electron and quasiparticle operators and for their propagators at the edge. We show that these operators create states with the correct charge and statistics. It is found that the tunneling density of states for all the Jain states scales with frequency as $|\omega|^{(1-\nu)/\nu}$.Comment: 10 page

Research of relative motion of a material corpuscle on a surface of the horizontal cylinder which is twirled about an axis of yaw

Аналітично розглянуто відносний рух частинки по внутрішній поверхні циліндра із горизонтальною віссю, який обертається навколо вертикальної осі. Складено систему диференціальних рівнянь руху частинки, яку розв’язано чисельними методами. Знайдено кінематичні характеристики, з’ясовано закономірності відносного руху частинки по поверхні циліндра. The corpuscle relative motion on an interior surface of the cylinder from a horizontal axis which is twirled about an axis of yaw is observed. It is made system of the differential equations of driving of a corpuscle which it is solved by numerical methods. Motion characteristics are discovered, regularity of relative motion of a corpuscle on a cylinder surface is become clear