منابع مشابه
Nonclassical Eigenvalue Asymptotics *
1 he leading asymptotics for the growth of the number of eigenvalues of the two-dimensional Dirichlet Laplacian in the regions {(x, y)l 1x1 " / yl < 11 and for 4 + lxlD I yj4 all of which are non-Weyl because of infinite phase space volumes are computed. Along the way, a general inequality on quantum partition functions coriputed in a kind of Born-Oppenheimer approximation is proved.
متن کاملNonclassical Eigenvalue Asymptotics for Operators of Schrödinger
which depends on the volume u)n of the unit sphere in R n and the beta function. Assuming /3 < 2 we see that integral (2) becomes divergent if V (x) vanishes to a sufficiently high order. The simplest such potential is V(x,y) = \x\\y\P o n R n + R m . The Weyl (volume counting) principle, when applied to the corresponding Schrödinger operator — A-hV(x), fails to predict discrete spectrum below ...
متن کاملThe Riemann Zeros and Eigenvalue Asymptotics
Comparison between formulae for the counting functions of the heights tn of the Riemann zeros and of semiclassical quantum eigenvalues En suggests that the tn are eigenvalues of an (unknown) hermitean operator H, obtained by quantizing a classical dynamical system with hamiltonian Hcl. Many features of Hcl are provided by the analogy; for example, the “Riemann dynamics” should be chaotic and ha...
متن کاملEigenvalue Asymptotics in a Twisted Waveguide
We consider a twisted quantum wave guide i.e. a domain of the form Ωθ := rθω × R where ω is a connected open and bounded subset of R2 and rθ = rθ(x3) is a rotation by the angle θ(x3) depending on the longitudinal variable x3. We are interested in the spectral analysis of the Dirichlet Laplacian H acting in Ωθ. We suppose that the derivative θ̇ of the rotation angle can be written as θ̇(x3) = β − ...
متن کاملAsymptotics of Some Nonlinear Eigenvalue Problems for a MEMS Capacitor: Part I: Fold Point Asymptotics
Several nonlinear eigenvalue problems modeling the steady-state deflection of an elastic membrane associated with a MEMS capacitor under a constant applied voltage are analyzed using formal asymptotic methods. The nonlinear eigenvalue problems under consideration represent various regular and singular perturbations of the basic membrane nonlinear eigenvalue problem ∆u = λ/(1 + u) in Ω with u = ...
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: Journal of Functional Analysis
سال: 1983
ISSN: 0022-1236
DOI: 10.1016/0022-1236(83)90047-2