4 research outputs found
PT-symmetric supersymmetry in a solvable short-range model
The simplest purely imaginary and piecewise constant -symmetric
potential located inside a larger box is studied. Unless its strength exceeds a
certain critical value, all the spectrum of its bound states remains real and
discrete. We interpret such a model as an initial element of the generalized
non-Hermitian Witten's hierarchy of solvable Hamiltonians and construct its
first supersymmetric (SUSY) partner in closed form.Comment: 3 figures, 1 tabl
PT-supersymmetric partner of a short-range square well
In a box of size , a spatially antisymmetric square-well potential of a
purely imaginary strength and size is interpreted as an
initial element of the SUSY hierarchy of solvable Hamiltonians, the energies of
which are all real for . The first partner potential is constructed
in closed form and discussed.Comment: 8 pages, no figure, presented at PHHQP3, Istanbul, June 20-22, 2005,
to be published in Czech. J. Phy
Renormalisation and fixed points in Hilbert Space
The energies of low-lying bound states of a microscopic quantum many-body
system of particles can be worked out in a reduced Hilbert space. We present
here and test a specific non-perturbative truncation procedure. We also show
that real exceptional points which may be present in the spectrum can be
identified as fixed points of coupling constants in the truncation procedure.Comment: 4 pages, 1 tabl