Strong Coupling Asymptotics for a Singular Schrödinger Operator with an Interaction Supported by an Open Arc
نویسندگان
چکیده
منابع مشابه
Strong coupling asymptotics for a singular Schrödinger operator with an interaction supported by an open arc
We consider a singular Schrödinger operator in L(R) written formally as −∆ − βδ(x − γ) where γ is a C smooth open arc in R of length L with regular ends. It is shown that the jth negative eigenvalue of this operator behaves in the strong-coupling limit, β → +∞, asymptotically as Ej(β) = − β 4 + μj +O ( log β β ) , where μj is the jth Dirichlet eigenvalue of the operator − d 2 ds2 − κ(s) 2 4 on ...
متن کاملStrong coupling asymptotics for Schrödinger operators with an interaction supported by an open arc in three dimensions
We consider Schrödinger operators with a strongly attractive singular interaction supported by a finite curve Γ of lenghth L in R. We show that if Γ is C-smooth and has regular endpoints, the j-th eigenvalue of such an operator has the asymptotic expansion λj(Hα,Γ) = ξα+λj(S)+O(e) as the coupling parameter α → ∞, where ξα = −4 e2(−2πα+ψ(1)) and λj(S) is the j-th eigenvalue of the Schrödinger op...
متن کاملPersistent currents for 2 D Schrödinger operator with a strong δ - interaction on a loop
One of the most often studied features of mesoscopic systems are the persistent currents in rings threaded by a magnetic flux – let us mention, e.g., [CGR, CWB] and scores of other theoretical and experimental papers where they were discussed. For a charged particle (an electron) confined to a loop Γ the effect is manifested by the dependence of the corresponding eigenvalues λn on the flux φ th...
متن کاملar X iv : m at h - ph / 0 30 30 33 v 1 1 3 M ar 2 00 3 Strong - coupling asymptotic expansion for Schrödinger operators with a singular
We investigate a class of generalized Schrödinger operators in L 2 (R 3) with a singular interaction supported by a smooth curve Γ. We find a strong-coupling asymptotic expansion of the discrete spectrum in case when Γ is a loop or an infinite bent curve which is asymptotically straight. It is given in terms of an auxiliary one-dimensional Schrödinger operator with a potential determined by the...
متن کاملAsymptotics of Eigenvalues of the Schrr Odinger Operator with a Strong -interaction on a Loop
In this paper we investigate the operator H = ??(??) in L 2 (R 2), where > 0 and ? is a closed C 4 Jordan curve in R 2. We obtain the asymptotic form of each eigenvalue of H as tends to innnity. We also get the asymptotic form of the number of negative eigenvalues of H in the strong coupling asymptotic regime.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Communications in Partial Differential Equations
سال: 2014
ISSN: 0360-5302,1532-4133
DOI: 10.1080/03605302.2013.851213