Winter (or delta-shell) Model at Small and Intermediate Volumes
- URL: http://arxiv.org/abs/2202.07616v1
- Date: Tue, 15 Feb 2022 18:01:42 GMT
- Title: Winter (or delta-shell) Model at Small and Intermediate Volumes
- Authors: U. G. Aglietti and A. Cubeddu
- Abstract summary: We consider a small resonating cavity weakly coupled to a large one, for small and intermediate volumes (lengths)
We find that each resonant state is represented, at finite volume, by a cluster of states, each one resonating in a specific coupling region, centered around a state resonating at very small couplings.
We construct a first resummation scheme having a clear physical picture, which is based on a function-series expansion, as well as a second scheme based on a recursion equation.
- Score: 0.0
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: We consider Winter (or delta-shell) model at finite volume, describing a
small resonating cavity weakly coupled to a large one, for small and
intermediate volumes (lengths). By defining N as the ratio of the length of the
large cavity over the small one, we study the symmetric case N=1, in which the
two cavities actually have the same length, as well as the cases N=2,3,4.
By increasing N in the above range, the transition from a simple quantum
oscillating system to a system having a resonance spectrum is investigated. We
find that each resonant state is represented, at finite volume, by a cluster of
states, each one resonating in a specific coupling region, centered around a
state resonating at very small couplings.
We derive high-energy expansions for the particle momenta in the above N
cases, which (approximately) resum their perturbative series to all orders in
the coupling among the cavities. These new expansions converge rather quickly
with the order, provide, surprisingly, a uniform approximation in the coupling
and also work, again surprisingly, at low energies.
We construct a first resummation scheme having a clear physical picture,
which is based on a function-series expansion, as well as a second scheme based
on a recursion equation. The two schemes coincide at leading order, while they
differ from next-to-leading order on. In particular, the recursive scheme
realizes an approximate resummation of the function-series expansion generated
within the first scheme.
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