7 research outputs found
Non-perturbative calculations for the effective potential of the symmetric and non-Hermitian field theoretic model
We investigate the effective potential of the symmetric
field theory, perturbatively as well as non-perturbatively. For the
perturbative calculations, we first use normal ordering to obtain the first
order effective potential from which the predicted vacuum condensate vanishes
exponentially as in agreement with previous calculations. For the
higher orders, we employed the invariance of the bare parameters under the
change of the mass scale to fix the transformed form totally equivalent to
the original theory. The form so obtained up to is new and shows that all
the 1PI amplitudes are perurbative for both and regions. For
the intermediate region, we modified the fractal self-similar resummation
method to have a unique resummation formula for all values. This unique
formula is necessary because the effective potential is the generating
functional for all the 1PI amplitudes which can be obtained via and thus we can obtain an analytic calculation for the 1PI
amplitudes. Again, the resummed from of the effective potential is new and
interpolates the effective potential between the perturbative regions.
Moreover, the resummed effective potential agrees in spirit of previous
calculation concerning bound states.Comment: 20 page
Generalized eigenfunctions and spectral theory for strongly local Dirichlet forms
We present an introduction to the framework of strongly local Dirichlet forms
and discuss connections between the existence of certain generalized
eigenfunctions and spectral properties within this framework. The range of
applications is illustrated by a list of examples
Mesoscopic Description of Heterojunctions
Starting from the microscopic current associated with the single-electron wave functions and using Wannier functions suitably generalized for nonperiodic heterostructures we construct mesoscopic (either discrete or continuous) conserved currents associated with states having components only in the considered band. This provides a rigorous basis to the approximate envelope function approaches. As an application we analyze general one-dimensional heterojunctions, mapping explicitly the microscopic asymptotic states onto mesoscopic (one-band envelope) ones. This proves that, apart from the effective masses and the band offsets, the connection rules are characterized in general by three parameters, the values of which are unconstrained, confirming the results of phenomenological analyses