arXiv subjects
Publications and source records attributed to Zhong-Shui Ma.
The quantum-mechanical problem of a many-particle system with a single impurity in one-dimension, interacting by a delta-function, is solved. The wave-function for a bosonic system and the related secular equation for the spectrum are obtained. The energy per length is calculated in the thermodynamic limit.
A simplest model of the persistent current in presence of many-body interaction in a mesoscopic ring is presented. The Bethe ansatz approach is used to find exact solutions. Both cases in the absence of impurity and in the presence of impurity are solved and compared. It is indicated that both impurity and hard-core interaction do not affect the result of persistent current explicitly if there is a large number of electrons in the ring.
The conductance sum rule for the hierarchical edge channel currents of a Fractional Quantum Hall Effect state is derived analytically within the Haldane-Halperin hierarchy scheme. We provide also an intuitive interpretation for the hierarchical drift velocities of the edge excitations.
We build the constraint that all electrons are in the lowest Landau level into the Chern-Simons field theory approach for the fractional quantum Hall system. We show that the constraint can be transmitted from one hierarchical state to the next. As a result, we derive in generic the equations of the fractionally charged vortices ( quasi-particles ) for arbitrary hierarchy filling. For a finite system, we show that the action for each hierarchical state can be divided into two parts: the surface part provides the action for the edge excitations while the remaining bulk part is exactly the action for the next hierarchical states. In particular, we not only show that the surface action for the edge excitations would be decoupled from the bulk at each hierarchy filling, but also derive the explicit expressions analytically for the drift velocities of the hierarchical edge excitations.
By applying the Dirac quantization method, we build the constraint that all electrons are in the lowest Landau level into the Chern-Simons field theory approach for the fractional quantum Hall system and show that the constraint can be transmuted from hierarchy to hierarchy. For a finite system, we derive that the action for each hierarchy can be split into two parts: a surface part provides the action for the edge excitations while the remaining part is precisely the bulk action for the next hierarchy. And the action for the edge could be decoupled from the bulk only at the hierarchy filling.