On the deformation of linear Hamiltonian systems

Schmid, Harald

doi:10.1016/j.jmaa.2021.125051

Cited by 2 publications

(12 citation statements)

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“…[ 29 ] showed that the derivation of a PDE for the eigenvalues of the CP equations was not luck, because similar PDEs can also be obtained for other differential operators provided that some technical conditions are satisfied. In the following, we briefly present the main result in [ 29 ] needed for the reminder of our work. By

and

we denote the spectral parameter and the

identity matrix, respectively.…”

Section: Linear Hamiltonian Systems and The Cp Equationsmentioning

confidence: 99%

“…Then, ref. [ 29 ] proved that if, in addition, ( 2 ) is in the limit point case at a and b and

for all

, the eigenvalues

satisfy the quasilinear PDE

…”

Section: Linear Hamiltonian Systems and The Cp Equationsmentioning

confidence: 99%

“…Ref. [ 29 ] showed that some of the conditions listed above admit an equivalent formulation that is easier to verify. While conditions

and

remain unchanged, conditions

and

can be cast into the following ones…”

Section: Linear Hamiltonian Systems and The Cp Equationsmentioning

confidence: 99%

“…Sixteen years later, ref. [ 29 ] proved a theorem stating under which general conditions the eigenvalues of a linear Hamiltonian system satisfied a first order quasilinear partial differential equation with respect to the relevant physical parameters. Inspired by this result, we examined an explicit computation of the deformation matrix and found that the PDE obtained in [ 14 ] for a Kerr black hole can indeed be derived from the general theory developed in [ 29 ].…”

Section: Introductionmentioning

confidence: 99%

“…[ 29 ] proved a theorem stating under which general conditions the eigenvalues of a linear Hamiltonian system satisfied a first order quasilinear partial differential equation with respect to the relevant physical parameters. Inspired by this result, we examined an explicit computation of the deformation matrix and found that the PDE obtained in [ 14 ] for a Kerr black hole can indeed be derived from the general theory developed in [ 29 ]. However, we did not only limit ourselves to this exercise.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

On the Eigenvalues of the Fermionic Angular Eigenfunctions in the Kerr Metric

Batic

Karim

Nowakowski

2022

Entropy

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In view of a result recently published in the context of the deformation theory of linear Hamiltonian systems, we reconsider the eigenvalue problem associated with the angular equation arising after the separation of the Dirac equation in the Kerr metric, and we show how a quasilinear first order PDE for the angular eigenvalues can be derived efficiently. We also prove that it is not possible to obtain an ordinary differential equation for the eigenvalues when the role of the independent variable is played by the particle energy or the black hole mass. Finally, we construct new perturbative expansions for the eigenvalues in the Kerr case and obtain an asymptotic formula for the eigenvalues in the case of a Kerr naked singularity.

show abstract

and

we denote the spectral parameter and the

identity matrix, respectively.…”

Section: Linear Hamiltonian Systems and The Cp Equationsmentioning

confidence: 99%

“…Then, ref. [ 29 ] proved that if, in addition, ( 2 ) is in the limit point case at a and b and

for all

, the eigenvalues

satisfy the quasilinear PDE

…”

Section: Linear Hamiltonian Systems and The Cp Equationsmentioning