Supersymmetric quantum mechanics living on topologically nontrivial Riemann surfaces

Abstract

Supersymmetric quantum mechanics is constructed in a new non-Hermitian representation. Firstly, the map between the partner operators $H^{(\pm )}$ is chosen antilinear. Secondly, both these components of a super-Hamiltonian $\mathcal{H}$ are defined along certain topologically nontrivial complex curves $r^{(\pm )}(x)$ which spread over several Riemann sheets of the wave function. The non-uniqueness of our choice of the map $\mathcal{T}$ between "tobogganic" partner curves $r^{(+)}(x)$ and $r^{(-)}(x)$ is emphasized.

14pp

References in corpus (5)

• Spiked potentials and quantum toboggans
• Exact Isospectral Pairs of PT-Symmetric Hamiltonians
• Quantum toboggans with two branch points
• Identification of observables in quantum toboggans
• Quantum knots

Cited by in corpus (2)

• Topology-controlled spectra of imaginary cubic oscillators in the large-L approach
• Broken Hermiticity phase transition in Bose-Hubbard model