The Cauchy-Riemann equations in anticomuting variables
The integrability of new two-component KdV equation.
The meaning of time and covariant superderivatives in supermechanics.
The quantum 3D superparticle.
Tunnel effect and symmetries for non-selfadjoint operators
We study low lying eigenvalues for non-selfadjoint semiclassical differential operators, where symmetries play an important role. In the case of the Kramers-Fokker-Planck operator, we show how the presence of certain supersymmetric and -symmetric structures leads to precise results concerning the reality and the size of the exponentially small eigenvalues in the semiclassical (here the low temperature) limit. This analysis also applies sometimes to chains of oscillators coupled to two heat baths,...
Two-dimensional supersymmetric quantum mechanics: two fixed centers of force.