Weak supersymmetric su(N|1) quantum systems

Supersymmetric Biorthogonal Quantum Systems

We discuss supersymmetric biorthogonal systems, with emphasis given to the periodic solutions that occur at spectral singularities of PT symmetric models. For these periodic solutions, the dual functions are associated polynomials that obey inhomogeneous equations. We construct in detail some explicit examples for the supersymmetric pairs of potentials V± (z) = −U (z) 2 ±z d dz U (z) where U (z...

Covariant Hamiltonian evolution in supersymmetric quantum systems

We develop a general formalism for covariant Hamiltonian evolution of supersymmetric (field) theories by making use of the fact that these can be represented on the exterior bundle over their bosonic configuration space as generalized Dirac-Kähler systems of the form (d±d†) |ψ〉 = 0. By using suitable deformations of the supersymmetry generators we find covariant Hamiltonians for target spaces w...

Weak and strong typicality in quantum systems.

We study the properties of mixed states obtained from eigenstates of many-body lattice Hamiltonians after tracing out part of the lattice. Two scenarios emerge for generic systems: (i) The diagonal entropy becomes equivalent to the thermodynamic entropy when a few sites are traced out (weak typicality); and (ii) the von Neumann (entanglement) entropy becomes equivalent to the thermodynamic entr...

Quantum Systems in Weak Gravitational Fields

and supersymmetric quantum mechanics

Standard and non-standard associated Legendre equations and supersymmetric quantum mechanics Abstract. A simple supersymmetric approach recently used by Dutt, Gan-gopadhyaya, and Sukhatme (hep-th/9611087, Am. J. Phys., to appear) for spherical harmonics is generalized to Gegenbauer and Jacobi equations. The coordinate transformation procedure is well known to the authors writing on supersymmetr...