TY - JOUR
T1 - Instability of Resonances Under Stark Perturbations
AU - Jensen, Arne
AU - Yajima, Kenji
PY - 2019/2/5
Y1 - 2019/2/5
N2 - Let Hε=-d2dx2+εx+V, ε≥ 0 , on L
2(R). Let V=∑k=1Nck|ψk⟩⟨ψk| be a rank N operator, where the ψ
k∈ L
2(R) are real, compactly supported, and even. Resonances are defined using analytic scattering theory. The main result is that if ζ
n, Imζn<0, are resonances of Hεn for a sequence ε
n↓ 0 as n→ ∞ and ζ
n→ ζ as n→ ∞, Imζ0<0, then ζ is not a resonance of H.
AB - Let Hε=-d2dx2+εx+V, ε≥ 0 , on L
2(R). Let V=∑k=1Nck|ψk⟩⟨ψk| be a rank N operator, where the ψ
k∈ L
2(R) are real, compactly supported, and even. Resonances are defined using analytic scattering theory. The main result is that if ζ
n, Imζn<0, are resonances of Hεn for a sequence ε
n↓ 0 as n→ ∞ and ζ
n→ ζ as n→ ∞, Imζ0<0, then ζ is not a resonance of H.
UR - http://www.scopus.com/inward/record.url?scp=85058419139&partnerID=8YFLogxK
U2 - 10.1007/s00023-018-0746-7
DO - 10.1007/s00023-018-0746-7
M3 - Journal article
SN - 1424-0637
VL - 20
SP - 675
EP - 687
JO - Annales Henri Poincare
JF - Annales Henri Poincare
IS - 2
ER -