Jacobi operators with λ-scaled diagonals exhibit essentially singular limits as λ→0, with subsequential strong resolvent convergence to any self-adjoint extension of the limit, applied to show non-unique selection in higher-order squeezing operators.
Oscillatory behavior of large eigenvalues in quantum Rabi models
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abstract
We investigate the large $n$ asymptotics of the $n$-th eigenvalue for a class of unbounded self-adjoint operators defined by infinite Jacobi matrices with discrete spectrum. In the case of the quantum Rabi model we obtain the first three terms of the asymptotics which determine the parameters of the model. This paper is based on our previous paper [5] that it completes and improves.
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Essentially singular limits of Jacobi operators and applications to higher-order squeezing
Jacobi operators with λ-scaled diagonals exhibit essentially singular limits as λ→0, with subsequential strong resolvent convergence to any self-adjoint extension of the limit, applied to show non-unique selection in higher-order squeezing operators.