Spectral shift function for the Stark operator in the large coupling constant limit
نویسندگان
چکیده
Let H be the Stark operator in R3 and let V = V (x) be a non-negative potential which decays at infinity as |x|−l for a sufficiently large l > 0. The spectral shift function for the pair of operators H + tV , H is studied in the asymptotic regime t →∞. The leading term of the asymptotics is obtained; the result is in agreement with the phase space volume considerations.
منابع مشابه
Spectral shift function of the Schrödinger operator in the large coupling constant limit
The function ξ(λ) = ξ(λ; H, H0) is called the spectral shift function for the pair H0, H. A detailed exposition of the spectral shift function theory can be found in the book [9]; see also the survey [3]. Let us consider the (selfadjoint) Laplace operator ∆ in L(R), d ≥ 1. Define the operator H0 = h(−∆), where the function h : [0, +∞) → R satisfies h ∈ C(R), h(0) = 0, h′(r) > 0 ∀r > 0, there ex...
متن کاملSpectral Shift Function of the Schrr Odinger Operator in the Large Coupling Constant Limit, Ii. Positive Perturbations
For the operator ?4 in L 2 (R d), d 1, a perturbation potential V (x) 0, and a coupling constant > 0, the spectral shift function (; ?4 + V; ?4) is considered. Assuming that V (x) decays as jxj ?l , l > d, for large x, we prove that the leading term of the asymp-totics of the spectral shift function as ! 1 has the form C d=l , where the coeecient C = C(d; l) is explicitly computed. The asymptot...
متن کاملSpectral Shift Function of the Schrödinger Operator in the Large Coupling Constant Limit, Ii. Positive Perturbations
For the operator −∆ in L2(Rd), d ≥ 1, a perturbation potential V (x) ≥ 0, and a coupling constant α > 0, the spectral shift function ξ(λ;−∆ + αV,−∆) is considered. Assuming that V (x) decays as |x|−l, l > d, for large x, we prove that the leading term of the asymptotics of the spectral shift function as α → ∞ has the form Cαd/l, where the coefficient C is explicitly computed. The asymptotics is...
متن کاملDilations, models, scattering and spectral problems of 1D discrete Hamiltonian systems
In this paper, the maximal dissipative extensions of a symmetric singular 1D discrete Hamiltonian operator with maximal deficiency indices (2,2) (in limit-circle cases at ±∞) and acting in the Hilbert space ℓ_{Ω}²(Z;C²) (Z:={0,±1,±2,...}) are considered. We consider two classes dissipative operators with separated boundary conditions both at -∞ and ∞. For each of these cases we establish a self...
متن کاملLarge Amplitude Vibration Analysis of Graphene Sheets as Resonant Mass Sensors Using Mixed Pseudo-Spectral and Integral Quadrature Methods
The present paper investigates the potential application of graphene sheets with attached nanoparticles as resonant sensors by introducing a nonlocal shear deformation plate model. To take into account an elastic connection between the nanoplate and the attached nanoparticle, the nanoparticle is considered as a mass-spring system. Then, a combination of pseudo-spectral and integral quadrature m...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
- Asymptotic Analysis
دوره 51 شماره
صفحات -
تاریخ انتشار 2007