Self-duality and the Supersymmetric KdV Hierarchy

We show how the supersymmetric KdV equation can be obtained from the self-duality condition on Yang-Mills fields in four dimension associated with the graded Lie algebra OSp(2/1). We also obtain the hierarchy of Susy KdV equations from such a condition. We formulate the Susy KdV hierarchy as a vanishing curvature condition associated with the U(1) group and show how an Abelian self-duality condition in four dimension can also lead to these equations.Comment: 10 page

A Nonstandard Supersymmetric KP Hierarchy

We show that the supersymmetric nonlinear Schr\"odinger equation can be written as a constrained super KP flow in a nonstandard representation of the Lax equation. We construct the conserved charges and show that this system reduces to the super mKdV equation with appropriate identifications. We construct various flows generated by the general nonstandard super Lax equation and show that they contain both the KP and mKP flows in the bosonic limits. This nonstandard supersymmetric KP hierarchy allows us to construct a new super KP equation which is nonlocal.Comment: 18 pages, plain TeX, UR-1367, ER-40685-81

Coherent Magnetotransport Through an Artificial Molecule

The conductance in an extended multiband Hubbard model describing linear arrays of up to ten quantum dots is calculated via a Lanczos technique. A pronounced suppression of certain resonant conductance peaks in an applied magnetic field due to a density-dependent spin-polarization transition is predicted to be a clear signature of a coherent ``molecular'' wavefunction in the array. A many-body enhancement of localization is predicted to give rise to a {\em giant magnetoconductance} effect in systems with magnetic scattering.Comment: 4 pages, REVTEX 3.0, 5 figures included as postscript file

Self-Duality and the KdV Hierarchy

We derive the entire KdV hierarchy as well as the recursion relations from the self-duality condition on gauge fields in four dimensions.Comment: 7 page

Exact Effective Action for (1+1 Dimensional) Fermions in an Abelian Background at Finite Temperature

In an effort to further understand the structure of effective actions for fermions in an external gauge background at finite temperature, we study the example of 1+1 dimensional fermions interacting with an arbitrary Abelian gauge field. We evaluate the effective action exactly at finite temperature. This effective action is non-analytic as is expected at finite temperature. However, contrary to the structure at zero temperature and contrary to naive expectations, the effective action at finite temperature has interactions to all (even) orders (which, however, do not lead to any quantum corrections). The covariant structure thus obtained may prove useful in studying 2+1 dimensional models in arbitrary backgrounds. We also comment briefly on the solubility of various 1+1 dimensional models at finite temperature.Comment: A few clarifying remarks added;21 page

Specific heat at constant volume in the thermodynamic model

A thermodynamic model for multifragmentation which is frequently used appears to give very different values for specific heat at constant volume depending upon whether canonical or grand canonical ensemble is used. The cause for this discrepancy is analysed.Comment: Revtex, 7 pages including 4 figure