Asymptotics of resonances for 1D Stark operators

Korotyaev, Evgeny L.

doi:10.1007/s11005-017-1033-0

Cited by 20 publications

(9 citation statements)

References 30 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…Finally, it is worthy to mention that one-dimensional Stark operators have been studied mostly when defined on the whole real line, see for instance [2,11,12]. As it is well-known, Stark operators on the real line are characterized by the presence of resonances; see [13,14] for some recent developments on this subject.…”

Section: Introduction and Statement Of Resultsmentioning

confidence: 99%

One-dimensional Stark operators in the half-line

Toloza¹,

Uribe²

2021

Preprint

View full text Add to dashboard Cite

show abstract

Section: Introduction and Statement Of Resultsmentioning

confidence: 99%

One-dimensional Stark operators in the half-line

Toloza¹,

Uribe²

2021

Preprint

View full text Add to dashboard Cite

show abstract

“…Resonances for Schrödinger operator with a step-like potential were discussed by Christiansen [8]. Stark operator with compactly supported potentials was studied in [15,44,45]. Resonances were also considered for three and fourth order differential operator with compactly supported coefficients on the line, see [46,5].…”

Section: A Short Reviewmentioning

confidence: 99%

Inverse resonance scattering for Dirac operators on the half-line

Mokeev

2021

Anal.Math.Phys.

View full text Add to dashboard Cite

We consider Schrödinger equations with linearly energy-depending potentials which are compactly supported on the half-line. We first provide estimates of the number of eigenvalues and resonances for such complex-valued potentials under suitable regularity assumptions. Then, we consider a specific class of energy-dependent Schrödinger equations without eigenvalues, defined with Miura potentials and boundary conditions at the origin. We solve the inverse resonance problem in this case and describe sets of iso-resonance potentials and boundary condition parameters. Our strategy consists in exploiting a correspondance between Schrödinger and Dirac equations on the half-line. As a byproduct, we describe similar sets for Dirac operators and show that the scattering problem for Schrödinger equation or Dirac operator with an arbitrary boundary condition can be reduced to the scattering problem with the Dirichlet boundary condition. 1.1. The potential class P: Eigenvalues and resonances estimates. Let γ > 0 and define the class of potential perturbations P := {(p, q) ∈ W 1,1 (R + ) × L 1 (R + ) | max supp(|p| + |q|) = γ}.

show abstract

“…By comparison, one-dimensional Stark operators on the real line have attracted much more attention (for rather obvious reasons); see for instance [1,[5][6][7]11,15]. As it is well-known, Stark operators on the real line are characterized by the presence of resonances; see [8,9] for some recent developments on this subject.…”

Section: Introductionmentioning

confidence: 99%

The Dirichlet problem for perturbed Stark operators in the half-line

Toloza¹,

Uribe²

2022

Preprint

View full text Add to dashboard Cite

We consider the perturbed Stark operator H q ϕ = −ϕ ′′ + xϕ + q(x)ϕ, ϕ(0) = 0, in L 2 (R + ), where q is a real function that belongs tobe the spectrum and associated set of norming constants of H q . Let {a n } n=1 be the zeros of the Airy function of the first kind, and let ω r : N → R be defined by the rule ω r (n, uniformly on bounded subsets of A r . Along the way, we also show that λ n : A r → R and κ n : A r → R are real analytic maps.

show abstract

Asymptotics of resonances for 1D Stark operators

Abstract: Abstract. We consider the Stark operator perturbed by a compactly supported potentials on the real line. We determine forbidden domain for resonances, asymptotics of resonances at high energy and asymptotics of the resonance counting function for large radius.

Cited by 20 publications

References 30 publications

One-dimensional Stark operators in the half-line

One-dimensional Stark operators in the half-line

Inverse resonance scattering for Dirac operators on the half-line

The Dirichlet problem for perturbed Stark operators in the half-line

Contact Info

Product

Resources

About